Sample records for renormalization yields finitely

  1. Aspects of renormalization in finite-density field theory

    Energy Technology Data Exchange (ETDEWEB)

    Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia


    We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

  2. Massive renormalization scheme and perturbation theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Blaizot, Jean-Paul, E-mail: [Institut de Physique Théorique, CNRS/URA2306, CEA-Saclay, 91191 Gif-sur-Yvette (France); Wschebor, Nicolás [Instituto de Fìsica, Faculdad de Ingeniería, Universidade de la República, 11000 Montevideo (Uruguay)


    We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.

  3. Pokrovsky-Talapov model at finite temperature: a renormalization-group analysis

    NARCIS (Netherlands)

    Lazarides, A.; Tieleman, O.; de Morais Smith, C.


    We calculate the finite-temperature shift of the critical wave vector Qc of the Pokrovsky-Talapov model using a renormalization-group analysis. Separating the Hamiltonian into a part that is renormalized and one that is not, we obtain the flow equations for the stiffness and an arbitrary potential.

  4. The Schwinger α-PARAMETRIC Representation of the Finite-Temperature Field Theory:. Renormalization II (United States)

    Benhamou, Mabrouk; Kassou-Ou-Ali, Ahmed

    We extend to finite-temperature field theories, involving charged scalar or nonvanishing spin particles, the α parametrization of field theories at zero temperature. This completes a previous work concerning the scalar theory. As there, a function θ, which contains all temperature dependence, appears in the α integrand. The function θ is an extension of the usual theta function. The implications of the α parametrization for the renormalization problem are discussed.

  5. Functional renormalization group approach for inhomogeneous one-dimensional Fermi systems with finite-ranged interactions (United States)

    Weidinger, Lukas; Bauer, Florian; von Delft, Jan


    We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third-order truncated form of fRG, the dependence of the two-particle vertex is described by O (N4) independent variables, where N is the dimension of the single-particle system. In a previous paper [Bauer et al., Phys. Rev. B 89, 045128 (2014), 10.1103/PhysRevB.89.045128], the so-called coupled-ladder approximation (CLA) was introduced and shown to admit a consistent treatment for models with a purely onsite interaction, reducing the vertex to O (N2) independent variables. In this work, we introduce an extended version of this scheme, called the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual channels, measured by a feedback length L , using O (N2L2) independent variables for the vertex. We apply the eCLA in a static approximation and at zero temperature to three types of one-dimensional model systems, focusing on obtaining the linear response conductance. First, we study a model of a quantum point contact (QPC) with a parabolic barrier top and on-site interactions. In our setup, where the characteristic length lx of the QPC ranges between approximately 4-10 sites, eCLA achieves convergence once L becomes comparable to lx. It also turns out that the additional feedback stabilizes the fRG flow. This enables us, second, to study the geometric crossover between a QPC and a quantum dot, again for a one-dimensional model with on-site interactions. Third, the enlarged feedback also enables the treatment of a finite-ranged interaction extending over up to L sites. Using a simple estimate for the form of such a finite-ranged interaction in a QPC with a parabolic barrier top, we study its effects on the conductance and the density. We find that for low densities and sufficiently large interaction ranges the conductance

  6. Variational solution of the Gross-Neveu model; 2, finite-N and renormalization

    CERN Document Server

    Arvanitis, C; Iacomi, M; Kneur, J L; Neveu, A


    We show how to perform systematically improvable variational calculations in the O(2N) Gross-Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the renormalization group. The final point is a general framework for the calculation of non-perturbative quantities like condensates, masses, etc..., in an asymptotically free field theory. For the Gross-Neveu model, the numerical results obtained from a "two-loop" variational calculation are in very good agreement with exact quantities down to low values of N.

  7. Schwinger α-PARAMETRIC Representation of Finite Temperature Field Theories:. Renormalization (United States)

    Benhamou, M.; Kassou-Ou-Ali, A.

    We present the extension of the zero temperature Schwinger α-representation to the finite temperature scalar field theories. We give, in a compact form, the α-integrand of Feynman amplitudes of these theories. Using this representation, we analyze short-range divergences, and recover in a simple way the known result that the counterterms are temperature-independent.

  8. Renormalization of fermion mixing

    Energy Technology Data Exchange (ETDEWEB)

    Schiopu, R.


    Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by

  9. Optimized renormalization group flows (United States)

    Litim, Daniel F.


    We study the optimization of exact renormalization group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimized by appropriate choices of the regularization. We consider specific optimized regulators for bosonic and fermionic fields and compare the optimized ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and nonvanishing temperature. We find that optimized flows at finite temperature factorize. This corresponds to the disentangling of thermal and quantum fluctuations. A similar factorization is found at second order in the derivative expansion. The corresponding optimized flow for a ``proper-time renormalization group'' is also provided to leading order in the derivative expansion.

  10. Slope Safety Factor Calculations With Non-Linear Yield Criterion Using Finite Elements

    DEFF Research Database (Denmark)

    Clausen, Johan; Damkilde, Lars


    The factor of safety for a slope is calculated with the finite element method using a non-linear yield criterion of the Hoek-Brown type. The parameters of the Hoek-Brown criterion are found from triaxial test data. Parameters of the linear Mohr-Coulomb criterion are calibrated to the same triaxial...

  11. Renormalization group procedure for potential -g/r2 (United States)

    Dawid, S. M.; Gonsior, R.; Kwapisz, J.; Serafin, K.; Tobolski, M.; Głazek, S. D.


    Schrödinger equation with potential - g /r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

  12. Robust and efficient handling of yield surface discontinuities in elasto-plastic finite element calculations

    DEFF Research Database (Denmark)

    Clausen, Johan Christian; Damkilde, Lars; Andersen, Lars Vabbersgaard


    Purpose – The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element calcu....... Examples of “hard” problems are highly frictional soils and/or three-dimensional geometries. Originality/value – The proposed method makes finite element calculations using yield criteria with corners and apices, e.g. Mohr-Coulomb and Hoek-Brown, much more robust and stable.......Purpose – The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element...... documented in the literature all present “easy” calculation examples, e.g. low friction angles and few elements. The amendments presented in this paper result in robust elasto-plastic computations, making the solution of “hard” problems possible without introducing approximations in the yield surfaces...

  13. Exact multilocal renormalization group and applications to disordered problems (United States)

    Chauve, Pascal; Le Doussal, Pierre


    We develop a method, the exact multilocal renormalization group (EMRG) which applies to a broad set of theories. It is based on the systematic multilocal expansion of the Polchinski-Wilson exact renormalization group (ERG) equation together with a scheme to compute correlation functions. Integrating out explicitly the nonlocal interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation for a function, its local part. This is done perturbatively around fixed points, but exactly to any given order in the local part. It is thus controlled, at variance with projection methods, e.g., derivative expansions or local potential approximations. Our EMRG method is well-suited to problems such as the pinning of disordered elastic systems, previously described via functional renormalization group (FRG) approach based on a hard cutoff scheme. Since it involves arbitrary cutoff functions, we explicitly verify universality to O(ɛ=4-D), both of the T=0 FRG equation and of correlations. Extension to finite temperature T yields the finite size (L) susceptibility fluctuations characterizing mesoscopic behavior (Δχ)2¯~Lθ/T, where θ is the energy exponent. Finally, we obtain the universal scaling function to O(ɛ1/3) which describes the ground state of a domain wall in a random field confined by a field gradient, compare with exact results and variational method. Explicit two loop exact RG equations are derived and the application to the FRG problem is sketched.

  14. The Exact Renormalization Group -- renormalization theory revisited --


    Sonoda, Hidenori


    We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED in the four dimensional euclidean space.

  15. Finite stopping times for freely oscillating drop of a yield stress fluid

    CERN Document Server

    Cheng, Wanli


    The paper addresses the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. A variation inequality formulation is deduced for the problem of yield stress fluid dynamics with a free surface. Free surface is assumed to evolve with a normal velocity the flow. We also consider capillary forces acting along the free surface. Based on the variational inequality formulation an energy equality is obtained, where kinetic and free energy rate of change is in a balance with the internal energy viscoplastic dissipation and the work of external forces. Further, the paper considers free small-amplitude oscillations of a droplet of Herschel-Bulkley fluid under the action of surface tension forces. Under certain assumptions it is shown that the finite stopping time $T_f$ of oscillations exists once the yield stress parameter is positive and the flow index $\\alpha$ satisfies ($\\alpha\\ge1$). Results of several numerical experiments illustrate the analysis, reveal th...

  16. Renormalization scheme dependence with renormalization group summation (United States)

    McKeon, D. G. C.


    We consider all perturbative radiative corrections to the total e+e- annihilation cross section Re+e- showing how the renormalization group (RG) equation associated with the radiatively induced mass scale μ can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log, next-to-leading-log, etc., contributions to Re+e- using in turn the one-loop, two-loop, etc., contributions to the RG function β . A second summation shows how all logarithmic corrections to Re+e- can be expressed entirely in terms of the log-independent contributions when one employs the full β -function. Next, using Stevenson's characterization of any choice of renormalization scheme by the use of the contributions to the β -function arising beyond two-loop order, we examine the RG scheme dependence in Re+e- when using the second way of summing logarithms. The renormalization scheme invariants that arise are then related to the renormalization scheme invariants found by Stevenson. We next consider two choices of the renormalization scheme, one which can be used to express Re+e- solely in terms of two powers of a running coupling, and the second which can be used to express Re+e- as an infinite series in the two-loop running coupling (i.e., a Lambert W -function). In both cases, Re+e- is expressed solely in terms of renormalization scheme invariant parameters that are to be computed by a perturbative evaluation of Re+e-. We then establish how in general the coupling constant arising in one renormalization scheme can be expressed as a power series of the coupling arising in any other scheme. We then establish how, by using a different renormalization mass scale at each order of perturbation theory, all renormalization scheme dependence can be absorbed into these mass scales when one uses the second way of summing logarithmic corrections to Re+e-. We then employ the approach to renormalization scheme dependency that we have applied to Re+e- to a RG summed

  17. Two-loop renormalization in the standard model, part II. Renormalization procedures and computational techniques

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)


    In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, are discussed in part III where numerical results, e.g. for the complex poles of the unstable gauge bosons, are shown. An attempt is made to define the running of the electromagnetic coupling constant at the two-loop level. (orig.)

  18. The analytic renormalization group

    Directory of Open Access Journals (Sweden)

    Frank Ferrari


    Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

  19. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)


    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  20. Finite

    National Research Council Canada - National Science Library

    W.R. Azzam


    .... This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts...

  1. Non-perturbative renormalization of the lattice heavy quark classical velocity

    Energy Technology Data Exchange (ETDEWEB)

    Mandula, J.E. [Department of Energy, Washington, DC (United States). Div. of High Energy Physics; Ogilvie, M.C. [Washington Univ., St. Louis, MO (United States). Dept. of Physics


    We discuss the renormalization of the lattice formulation of the heavy quark effective theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration. (orig.).

  2. Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity (United States)

    Mandula, Jeffrey E.; Ogilvie, Michael C.


    We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.

  3. Renormalization in the gauge theories with spontaneously broken supersymmetry

    CERN Document Server

    Kazakov, D I; Velizhanin, V N; Kondrashuk, I N


    A review of recent results on renormalizations in gauge theories with spontaneously broken supersymmetry is given. It is shown that the renormalizations in a broken theory are completely defined by those in a rigid theory and may be obtained with the help of expansion over the Grassmannian variables. New exact as well as suitable approximate analytic solutions of the renormalization group equations are obtained in some particular models: the Minimal Supersymmetric Standard Model, supersymmetric Grand Unified Theories, softly broken finite theories, and N=2 supersymmetric Seiberg-Witten theory

  4. Contractor renormalization group and the Haldane conjecture

    Energy Technology Data Exchange (ETDEWEB)

    Weinstein, Marvin


    The contractor renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper [Phys. Rev. D 61, 034505 (2000)] I showed that the CORE method could be used to map a theory of free quarks and quarks interacting with gluons into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple CORE computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first-principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF.

  5. Renormalization and effective actions for general relativity

    Energy Technology Data Exchange (ETDEWEB)

    Neugebohrn, F.


    Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)

  6. Cook-Levin Theorem Algorithmic-Reducibility/Completeness = Wilson Renormalization-(Semi)-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') REPLACING CRUTCHES!!!: Models: Turing-machine, finite-state-models, finite-automata (United States)

    Young, Frederic; Siegel, Edward

    Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!

  7. Renormalization and plasma physics

    Energy Technology Data Exchange (ETDEWEB)

    Krommes, J.A.


    A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.

  8. A Finite Element Procedure for Interference - Fit and Cold - Working Problems with Limited Yielding (United States)


    Australian Nuclear Science and Technology Organisation Australian Airlines, Library Qantas Airways Limited Ansett Airlines of Australia, Library...AERONAUTICAL RESEARCH LABORATORIES Structures Report 425 A FINITE ELEMENT PROCEDURE FOR INTERFERENCE - FIT AND COLD - WORKING PROBLEMS WITH LIMITED ...changing loading. An 18 degree sector angle was dictated by a shape limitation for the innermost pin element whilst the division into generally four

  9. Renormalization of the Lattice Heavy Quark Classical Velocity (United States)

    Mandula, Jeffrey E.; Ogilvie, Michael C.


    In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the "classical velocity" v becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time — Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using two ensembles of lattices, one at β = 5.7 and the other at β = 6.1 The estimates agree, and indicate that for small classical velocities, ν→ is reduced by about 25-30%.

  10. Why one needs a functional renormalization group to survive in a ...

    Indian Academy of Sciences (India)

    In this paper, we discuss why functional renormalization is an essential tool to treat strongly disordered systems. More specifically, we treat elastic manifolds in a disordered environment. These are governed by a disorder distribution, which after a finite renormalization becomes non-analytic, thus overcoming the predictions ...

  11. Compressive Spectral Renormalization Method

    CERN Document Server

    Bayindir, Cihan


    In this paper a novel numerical scheme for finding the sparse self-localized states of a nonlinear system of equations with missing spectral data is introduced. As in the Petviashivili's and the spectral renormalization method, the governing equation is transformed into Fourier domain, but the iterations are performed for far fewer number of spectral components (M) than classical versions of the these methods with higher number of spectral components (N). After the converge criteria is achieved for M components, N component signal is reconstructed from M components by using the l1 minimization technique of the compressive sampling. This method can be named as compressive spectral renormalization (CSRM) method. The main advantage of the CSRM is that, it is capable of finding the sparse self-localized states of the evolution equation(s) with many spectral data missing.

  12. Holographic renormalization of 3D minimal massive gravity

    Energy Technology Data Exchange (ETDEWEB)

    Alishahiha, Mohsen [School of Physics, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Qaemmaqami, Mohammad M.; Naseh, Ali [School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Department of Physics, Isfahan University of Technology,P.O.Box 84156-83111, Isfahan (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)


    We study holographic renormalization of 3D minimal massive gravity using the Chern-Simons-like formulation of the model. We explicitly present Gibbons- Hawking term as well as all counterterms needed to make the action finite in terms of dreibein and spin-connection. This can be used to find correlation functions of stress tensor of holographic dual field theory.

  13. Technical fine-tuning problem in renormalized perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E.


    The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

  14. Renormalization for free harmonic oscillators


    Sonoda, H.


    We introduce a model of free harmonic oscillators that requires renormalization. The model is similar to but simpler than the soluble Lee model. We introduce two concrete examples: the first, resembling the three dimensional $\\phi^4$ theory, needs only mass renormalization, and the second, resembling the four dimensional $\\phi^4$ theory and the Lee model, needs additional renormalization of a coupling and a wave function.

  15. Can finite element models of ballooning procedures yield mechanical response of the cardiovascular site to overexpansion? (United States)

    Bosi, Giorgia M; Biffi, Benedetta; Biglino, Giovanni; Lintas, Valentina; Jones, Rod; Tzamtzis, Spyros; Burriesci, Gaetano; Migliavacca, Francesco; Khambadkone, Sachin; Taylor, Andrew M; Schievano, Silvia


    Patient-specific numerical models could aid the decision-making process for percutaneous valve selection; in order to be fully informative, they should include patient-specific data of both anatomy and mechanics of the implantation site. This information can be derived from routine clinical imaging during the cardiac cycle, but data on the implantation site mechanical response to device expansion are not routinely available. We aim to derive the implantation site response to overexpansion by monitoring pressure/dimensional changes during balloon sizing procedures and by applying a reverse engineering approach using a validated computational balloon model. This study presents the proof of concept for such computational framework tested in-vitro. A finite element (FE) model of a PTS-X405 sizing balloon (NuMed, Inc., USA) was created and validated against bench tests carried out on an ad hoc experimental apparatus: first on the balloon alone to replicate free expansion; second on the inflation of the balloon in a rapid prototyped cylinder with material deemed suitable for replicating pulmonary arteries in order to validate balloon/implantation site interaction algorithm. Finally, the balloon was inflated inside a compliant rapid prototyped patient-specific right ventricular outflow tract to test the validity of the approach. The corresponding FE simulation was set up to iteratively infer the mechanical response of the anatomical model. The test in this simplified condition confirmed the feasibility of the proposed approach and the potential for this methodology to provide patient-specific information on mechanical response of the implantation site when overexpanded, ultimately for more realistic computational simulations in patient-specific settings. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

  16. Estimation of the effective yield properties of human trabecular bone using nonlinear micro-finite element analyses. (United States)

    Wili, Patrik; Maquer, Ghislain; Panyasantisuk, Jarunan; Zysset, Philippe K


    Micro-finite element ([Formula: see text]FE) analyses are often used to determine the apparent mechanical properties of trabecular bone volumes. Yet, these apparent properties depend strongly on the applied boundary conditions (BCs) for the limited size of volumes that can be obtained from human bones. To attenuate the influence of the BCs, we computed the yield properties of samples loaded via a surrounding layer of trabecular bone ("embedded configuration"). Thirteen cubic volumes (10.6 mm side length) were collected from [Formula: see text]CT reconstructions of human vertebrae and femora and converted into [Formula: see text]FE models. An isotropic elasto-plastic material model was chosen for bone tissue, and nonlinear [Formula: see text]FE analyses of six uniaxial, shear, and multi-axial load cases were simulated to determine the yield properties of a subregion (5.3 mm side length) of each volume. Three BCs were tested. Kinematic uniform BCs (KUBCs: each boundary node is constrained with uniform displacements) and periodicity-compatible mixed uniform BCs (PMUBCs: each boundary node is constrained with a uniform combination of displacements and tractions mimicking the periodic BCs for an orthotropic material) were directly applied to the subregions, while the embedded configuration was achieved by applying PMUBCs on the larger volumes instead. Yield stresses and strains, and element damage at yield were finally compared across BCs. Our findings indicate that yield strains do not depend on the BCs. However, KUBCs significantly overestimate yield stresses obtained in the embedded configuration (+43.1 ± 27.9%). PMUBCs underestimate (-10.0 ± 11.2%), but not significantly, yield stresses in the embedded situation. Similarly, KUBCs lead to higher damage levels than PMUBCs (+51.0 ± 16.9%) and embedded configurations (+48.4 ± 15.0%). PMUBCs are better suited for reproducing the loading conditions in subregions of the trabecular bone and deliver a fair estimation

  17. Wavelets and renormalization

    CERN Document Server

    Battle, G A


    WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the F 4 3 quantum field theory is presented. It is due to Battle and

  18. Renormalization Group Functional Equations

    CERN Document Server

    Curtright, Thomas L


    Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.

  19. Infrared troubles of differential renormalization (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.

    The possibility of generalizing differential renormalization of D.Z. Freedman, K. Jonnson and J.I. Latorre in an invariant fashion to theories with infrared divergencies is investigated. It is concluded that the calculations on infrared differential renormalization lead to incorrect results.

  20. Functional renormalization group methods in quantum chromodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Braun, J.


    We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

  1. Anomalies and entanglement renormalization (United States)

    Bridgeman, Jacob C.; Williamson, Dominic J.


    We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.

  2. The Analytic Renormalization Group

    CERN Document Server

    Ferrari, Frank


    Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients $G_{k}$, $k\\in\\mathbb Z$, associated with the Matsubara frequencies $\

  3. Holographic renormalization in teleparallel gravity

    Energy Technology Data Exchange (ETDEWEB)

    Krssak, Martin [Universidade Estadual Paulista, Instituto de Fisica Teorica, Sao Paulo, SP (Brazil)


    We consider the problem of IR divergences of the action in the covariant formulation of teleparallel gravity in asymptotically Minkowski spacetimes. We show that divergences are caused by inertial effects and can be removed by adding an appropriate surface term, leading to the renormalized action. This process can be viewed as a teleparallel analog of holographic renormalization. Moreover, we explore the variational problem in teleparallel gravity and explain how the variation with respect to the spin connection should be performed. (orig.)

  4. Differential renormalization of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)


    The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab

  5. The renormalization scale-setting problem in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)


    A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending

  6. Thermal Renormalization Group-Equations and the Phase-Transition of Scalar O(N)-Theories


    Bergerhoff, Bastian; Reingruber, Juergen


    We discuss the formulation of "thermal renormalization group-equations" and their application to the finite temperature phase-transition of scalar O(N)-theories. Thermal renormalization group-equations allow for a computation of both the universal and the non-universal aspects of the critical behavior directly in terms of the zero-temperature physical couplings. They provide a nonperturbative method for a computation of quantities like real-time correlation functions in a thermal environment,...

  7. New applications of renormalization group methods in nuclear physics. (United States)

    Furnstahl, R J; Hebeler, K


    We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

  8. Exact renormalization group study of fermionic theories (United States)

    Comellas, Jordi; Kubyshin, Yuri; Moreno, Enrique


    The exact renormalization group approach (ERG) is developed for the case of pure fermionic theories by deriving a Grassmann version of the ERG equation and applying it to the study of fixed point solutions and critical exponents of the two-dimensional chiral Gross-Neveu model. An approximation based on the derivative expansion and a further truncation in the number of fields is used. Two solutions are obtained analytically in the limit N → ∞, with N being the number of fermionic species. For finite N some fixed point solutions, with their anomalous dimensions and critical exponents, are computed numerically. The issue of separation of physical results from the numerous spurious ones is discussed. We argue that one of the solutions we find can be identified with that of Dashen and Frishman, whereas the others seem to be new ones.

  9. Fermionic functional integrals and the renormalization group

    CERN Document Server

    Feldman, Joel; Trubowitz, Eugene


    This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...

  10. Entanglement renormalization for disordered systems (United States)

    Goldsborough, Andrew M.; Evenbly, Glen


    We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007), 10.1103/PhysRevLett.99.220405]. This method makes use of the strong disorder renormalization group to determine the order in which lattice sites are coarse-grained, which sets the overall structure of the corresponding tensor network ansatz, before optimization using variational energy minimization. Benchmark results from the disordered X X Z model demonstrates that this approach accurately captures ground-state entanglement in disordered systems, even at long distances. This approach leads to a new class of efficiently contractible tensor network ansatz for one-dimensional systems, which may be understood as a generalization of the multiscale entanglement renormalization ansatz for disordered systems.

  11. Dimensional renormalization: Ladders and rainbows

    Energy Technology Data Exchange (ETDEWEB)

    Delbourgo, R. [Physics Department, University of Tasmania, GPO Box 252C, Hobart, (Australia) 7001; Kalloniatis, A.C. [Institut fur Theoretische Physik, University of Erlangen-Nuremberg, Staudtstrasse 7, Erlangen, D-91058 (Germany); Thompson, G. [International Centre for Theoretical Physics, Grignano-Miramare, Trieste, 34100 (Italy)


    Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive the factors and renormalized Green{close_quote}s functions to {ital all} orders in perturbation theory for rainbow graphs and vertex (or scattering) diagrams at zero momentum transfer, in the context of dimensional regularization, and we prove that the correct anomalous dimensions for those processes emerge in the limit {ital D}{r_arrow}4. {copyright} {ital 1996 The American Physical Society.}

  12. Corner Transfer Matrix Renormalization Group Method


    Nishino, T.; Okunishi, K.


    We propose a new fast numerical renormalization group method,the corner transfer matrix renormalization group (CTMRG) method, which is based on a unified scheme of Baxter's corner transfer matrix method and White's density matrix renormalization groupmethod. The key point is that a product of four corner transfer matrices gives the densitymatrix. We formulate the CTMRG method as a renormalization of 2D classical models.

  13. Controlling sign problems in spin models using tensor renormalization (United States)

    Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan


    We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

  14. Fixed point of the parabolic renormalization operator

    CERN Document Server

    Lanford III, Oscar E


    This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...

  15. Finite element modeling of aponeurotomy: altered intramuscular myofascial force transmission yields complex sarcomere length distributions determining acute effects

    NARCIS (Netherlands)

    Yucesoy, C.A.; Koopman, B.H.; Grootenboer, H.J.; Huijing, P.A.J.B.M.


    Finite element modeling of aponeurotomized rat extensor digitorium longus muscle was performed to investigate the acute effects of proximal aponeurotomy. The specific goal was to assess the changes in lengths of sarcomeres within aponeurotomized muscle and to explain how the intervention leads to

  16. Matrix product density operators: Renormalization fixed points and boundary theories

    Energy Technology Data Exchange (ETDEWEB)

    Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)


    We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).

  17. On truncations of the exact renormalization group

    CERN Document Server

    Morris, T R


    We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.

  18. Renormalization and effective field theory

    CERN Document Server

    Costello, Kevin


    This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantum field theory can learn the powerful methodology of mathematical structure, while mathematicians can position themselves to use the magical ideas of quantum field theory in "mathematics" itself. The retelling of the tale mathematically by Kevin Costello is a beautiful tour de force. --Dennis Sullivan This book is quite a remarkable contribution. It should make perturbative quantum field theory accessible to mathematicians. There is a lot of insight in the way the author uses the renormalization group and effective field theory to analyze perturbative renormalization; this may serve as a springboard to a wider use of those topics, hopefully to an eventual nonperturbative understanding. --Edward Witten Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorio...

  19. Non-equilibrium phase transitions in the two-temperature Ising model with Kawasaki dynamics. Phase diagram from position space renormalization group transformation (United States)

    Renklioglu, B.; Yalabik, M. C.


    Phase transitions of the two-finite temperature Ising model on a square lattice are investigated by using a position space renormalization group (PSRG) transformation. Different finite temperatures, T x and T y , and also different time-scale constants, α x and α y for spin exchanges in the x and y directions define the dynamics of the non-equilibrium system. The critical surface of the system is determined by RG flows as a function of these exchange parameters. The Onsager critical point (when the two temperatures are equal) and the critical temperature for the limit when the other temperature is infinite, previously studied by the Monte Carlo method, are obtained. In addition, two steady-state fixed points which correspond to the non-equilibrium phase transition are presented. These fixed points yield the different universality class properties of the non-equilibrium phase transitions.

  20. One-loop renormalization of Resonance Chiral Theory: scalar and pseudoscalar resonances

    Energy Technology Data Exchange (ETDEWEB)

    Rosell, Ignasi [Departament de FIsica Teorica, IFIC, CSIC - Universitat de Valencia, Edifici d' Instituts de Paterna, Apt. Correus 22085, E-46071 Valencia (Spain); Ruiz-FemenIa, Pedro [Theory Division, Max-Planck-Institut fuer Physik, Foehringer Ring 6, D-80805 Munich (Germany); Portoles, Jorge [Departament de FIsica Teorica, IFIC, CSIC - Universitat de Valencia, Edifici d' Instituts de Paterna, Apt. Correus 22085, E-46071 Valencia (Spain)


    We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its {beta}-function at one-loop with the use of the background field method. Thus we also provide the full set of operators that renormalize the theory at one loop and render it finite.

  1. Introduction to the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Kopietz, Peter; Bartosch, Lorenz; Schuetz, Florian [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik


    This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. (orig.)

  2. Physical renormalization schemes and asymptotic safety in quantum gravity (United States)

    Falls, Kevin


    The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.

  3. Renormalization constants of the lattice energy momentum tensor using the gradient flow

    CERN Document Server

    Capponi, Francesco; Patella, Agostino; Rago, Antonio


    We employ a new strategy for a non perturbative determination of the renormalized energy momentum tensor. The strategy is based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow. The new set of identities exhibits many interesting qualities, arising from the UV finiteness of flowed composite operators. In this paper we show how this method can be used to non perturbatively renormalize the energy momentum tensor for a SU(3) Yang-Mills theory, and report our numerical results.

  4. Transfer group for renormalized multiple zeta values


    Ebrahimi-Fard, Kurusch; Manchon, Dominique; Singer, Johannes; Zhao, Jianqiang


    We describe in this work all solutions to the problem of renormalizing multiple zeta values at arguments of any sign in a quasi-shuffle compatible way. As a corollary we clarify the relation between different renormalizations at non-positive values appearing in the recent literature.

  5. Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)


    In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).

  6. Holographic trace anomaly at finite temperature (United States)

    Lee, Bum-Hoon; Nam, Siyoung; Park, Chanyong


    Using the holographic renormalization, we investigate the finite temperature and size effect to the energy-momentum tensor of the dual field theory and its renormalization group (RG) flow. Following the anti-de Sitter/conformal field theory correspondence, the dual field theory of the AdS space is well known to be a conformal field theory that has no nontrivial RG flow. Holographically, that theory can be lifted to a finite temperature version by considering a AdS black hole solution. Because the black hole horizon associated with temperature is dimensionful, it breaks the boundary conformal symmetry and leads to a nontrivial RG flow. In this work, we investigate the finite temperature and size correction to a strongly interacting conformal field theory along the Wisonian renormalization group flow.

  7. Canonical demon Monte Carlo renormalization group

    CERN Document Server

    Hasenbusch, M; Wieczerkowski, C


    We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. In contrast to the Microcanonical Renormalization Group invented by Creutz et al. our method does not suffer from systematical errors stemming from a simultaneous use of two different ensembles. We present numerical results for the O(3) nonlinear \\sigma-model.

  8. On truncations of the exact renormalization group (United States)

    Morris, Tim R.


    We investigate the Exact Renormalization Group (ERG) description of ( Z2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. The approximation is seen to be a good one, both qualitatively and quantitatively. We then consider the further approximation of truncating the lagrangian to polynomial in the field dependence. Concentrating on the non-perturbative three dimensional Wilson fixed point, we show that the sequence of truncations n = 2,3,…, obtained by expanding about the field ϕ = 0 and discarding all powers ϕ2 n+2 and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. Within the sequence of truncations, no completely reliable method exists to reject the many spurious solutions that are also generated. These properties are explained in terms of the analytic behaviour of the untruncated solutions - which we describe in some detail.

  9. Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz

    CERN Document Server

    Chua, Victor; Tiwari, Apoorv; Ryu, Shinsei


    The Multiscale Entanglement Renormalization Ansatz (MERA) is a tensor network based variational ansatz that is capable of capturing many of the key physical properties of strongly correlated ground states such as criticality and topological order. MERA also shares many deep relationships with the AdS/CFT (gauge-gravity) correspondence by realizing a UV complete holographic duality within the tensor networks framework. Motivated by this, we have re-purposed the MERA tensor network as an analysis tool to study the real-time evolution of the 1D transverse Ising model in its low energy excited state sector. We performed this analysis by allowing the ancilla qubits of the MERA tensor network to acquire quantum fluctuations, which yields a unitary transform between the physical (boundary) and ancilla qubit (bulk) Hilbert spaces. This then defines a reversible quantum circuit which is used as a `holographic transform' to study excited states and their real-time dynamics from the point of the bulk ancillae. In the ga...

  10. Complex-mass shell renormalization of the higher-derivative electrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Turcati, Rodrigo [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Universidade Federal do Espirito Santo, Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Laboratorio de Fisica Experimental (LAFEX), Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil); Neves, Mario Junior [Universidade Federal Rural do Rio de Janeiro, Departamento de Fisica, Rio de Janeiro (Brazil)


    We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron-positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed. (orig.)

  11. Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence (United States)

    Rubinstein, Robert


    Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

  12. Renormalization Analysis of a Composite Ultrasonic Transducer with a Fractal Architecture (United States)

    Algehyne, Ebrahem A.; Mulholland, Anthony J.

    To ensure the safe operation of many safety critical structures such as nuclear plants, aircraft and oil pipelines, non-destructive imaging is employed using piezoelectric ultrasonic transducers. These sensors typically operate at a single frequency due to the restrictions imposed on their resonant behavior by the use of a single length scale in the design. To allow these transducers to transmit and receive more complex signals it would seem logical to use a range of length scales in the design so that a wide range of resonating frequencies will result. In this paper, we derive a mathematical model to predict the dynamics of an ultrasound transducer that achieves this range of length scales by adopting a fractal architecture. In fact, the device is modeled as a graph where the nodes represent segments of the piezoelectric and polymer materials. The electrical and mechanical fields that are contained within this graph are then expressed in terms of a finite element basis. The structure of the resulting discretized equations yields to a renormalization methodology which is used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities. A comparison with a standard design shows some benefits of these fractal designs.

  13. Euclidean Epstein-Glaser renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Keller, Kai J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik


    In the framework of perturbative Algebraic Quantum Field Theory (pAQFT) I give a general construction of so-called 'Euclidean time-ordered products', i.e. algebraic versions of the Schwinger functions, for scalar quantum eld theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space (MQFT). An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction-) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-{delta}+m{sup 2}) of EQFT have a unique singularity structure, i.e. they are unique up to a smooth part. Second, one needs to (re-)introduce a (rather natural) 'Euclidean causality' condition for the recursion of Epstein and Glaser to be applicable. (orig.)

  14. Renormalization of minimally doubled fermions (United States)

    Capitani, Stefano; Creutz, Michael; Weber, Johannes; Wittig, Hartmut


    We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Boriçi-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Boriçi-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.

  15. Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group


    Jurgenson, E. D.; Navratil, P.; Furnstahl, R. J.


    The first practical method to evolve many-body nuclear forces to softened form using the Similarity Renormalization Group (SRG) in a harmonic oscillator basis is demonstrated. When applied to He4 calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force.

  16. Stope Stability Assessment and Effect of Horizontal to Vertical Stress Ratio on the Yielding and Relaxation Zones Around Underground Open Stopes Using Empirical and Finite Element Methods (United States)

    Sepehri, Mohammadali; Apel, Derek; Liu, Wei


    Predicting the stability of open stopes can be a challenging task for underground mine engineers. For decades, the stability graph method has been used as the first step of open stope design around the world. However, there are some shortcomings with this method. For instance, the stability graph method does not account for the relaxation zones around the stopes. Another limitation of the stability graph is that this method cannot to be used to evaluate the stability of the stopes with high walls made of backfill materials. However, there are several analytical and numerical methods that can be used to overcome these limitations. In this study, both empirical and numerical methods have been used to assess the stability of an open stope located between mine levels N9225 and N9250 at Diavik diamond underground mine. It was shown that the numerical methods can be used as complementary methods along with other analytical and empirical methods to assess the stability of open stopes. A three dimensional elastoplastic finite element model was constructed using Abaqus software. In this paper a sensitivity analysis was performed to investigate the impact of the stress ratio "k" on the extent of the yielding and relaxation zones around the hangingwall and footwall of the understudy stope.

  17. A functional renormalization group approach to non-equilibrium properties of mesoscopic interacting quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Pruschke, Th., E-mail: pruschke@theorie.physik.uni-goettingen.d [Insitute for Theoretical Physics, University of Goettingen, Friedrich-Hund-Platz 1, 37077 Goetingen (Germany); Dirks, A.; Gezzi, R. [Insitute for Theoretical Physics, University of Goettingen, Friedrich-Hund-Platz 1, 37077 Goetingen (Germany)


    We present an extension of the concepts of the functional renormalization group approach to quantum many-body problems in non-equilibrium situations. The approach is completely general and allows calculations for both stationary and time-dependent situations. As a specific example we study the stationary state transport through a quantum dot with local Coulomb correlations. We discuss the influence of finite bias voltage and temperature on the current and conductance.

  18. Volume renormalization and the Higgs (United States)

    Dai, De-Chang; Stojkovic, Dejan


    Traditionally, Quantum Field Theory (QFT) treats particle excitations as point-like objects, which is the source of ubiquitous divergences. We demonstrate that a minimal modification of QFT with finite-volume particles may cure QFT of divergences and illuminate the physics behind the mathematical construct of our theories. The method allows for a non-perturbative treatment of the free field and self-interacting theories (though extensions to all interacting field theories might be possible). In particular, non-perturbatively defined mass is finite. When applied to the standard model Higgs mechanism, the method implies that a finite range of parameters allows for creation of a well-defined Higgs particle, whose Compton wavelength is larger than its physical size, in the broken symmetry phase (as small oscillations around the vacuum). This has profound consequences for Higgs production at the LHC. The parameter range in which the Higgs excitation with the mass of 125 GeV behaves as a proper particle is very restricted.

  19. Renormalizations in softly broken SUSY gauge theories (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.


    The supergraph technique for calculations in supersymmetric gauge theories where supersymmetry is broken in a "soft" way (without introducing quadratic divergencies) is reviewed. By introducing an external spurion field the set of Feynman rules is formulated and explicit connections between the UV counterterms of a softly broken and rigid SUSY theories are found. It is shown that the renormalization constants of softly broken SUSY gauge theory also become external superfields depending on the spurion field. Their explicit form repeats that of the constants of a rigid theory with the redefinition of the couplings. The method allows us to reproduce all known results on the renormalization of soft couplings and masses in a softly broken theory. As an example the renormalization group functions for soft couplings and masses in the Minimal Supersymmetric Standard Model up to the three-loop level are calculated.

  20. Renormalizations in softly broken SUSY gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Avdeev, L.V.; Kazakov, D.I.; Kondrashuk, I.N. [Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Theoretical Physics


    The supergraph technique for calculations in supersymmetric gauge theories where supersymmetry is broken in a ``soft`` way (without introducing quadratic divergencies) is reviewed. By introducing an external spurion field the set of Feynman rules is formulated and explicit connections between the UV counterterms of a softly broken and rigid SUSY theories are found. It is shown that the renormalization constants of softly broken SUSY gauge theory also become external superfields depending on the spurion field. Their explicit form repeats that of the constants of a rigid theory with the redefinition of the couplings. The method allows us to reproduce all known results on the renormalization of soft couplings and masses in a softly broken theory. As an example the renormalization group functions for soft couplings and masses in the minimal supersymmetric standard model up to the three-loop level are calculated. (orig.). 16 refs.

  1. Three Topics in Renormalization and Improvement

    CERN Document Server

    Vladikas, A


    This is an expanded version of lecture notes, delivered at the XCIII Les Houches Summer School (August 2009). Our aim is to present three very specific topics: (i) The consequences of the loss of chiral symmetry in the Wilson lattice regularization of the fermionic action and its recovery in the continuum limit. The treatment of these arguments involves lattice Ward identities. (ii) The definition and properties of mass independent renormalization schemes, which are suitable for a non-perturbative computation of various operator renormalization constants. (iii) The modification of the Wilson fermion action, by the introduction of a chirally twisted mass term (known as twisted mass QCD - tmQCD), which results to improved (re)normalization and scaling properties for physical quantities of interest.

  2. Renormalized vacuum polarization of rotating black holes

    CERN Document Server

    Ferreira, Hugo R C


    Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2+1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization (and, more importantly, the renormalized stress-energy tensor), for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.

  3. Similarity renormalization group evolution of N N interactions within a subtractive renormalization scheme

    Directory of Open Access Journals (Sweden)

    Durães F.O.


    Full Text Available We apply the similarity renormalization group (SRG approach to evolve a nucleon-nucleon (N N interaction in leading-order (LO chiral effective field theory (ChEFT, renormalized within the framework of the subtracted kernel method (SKM. We derive a fixed-point interaction and show the renormalization group (RG invariance in the SKM approach. We also compare the evolution of N N potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS equation and the evolution with the similarity cutoff through the SRG transformation.

  4. Renormalization-group flows and fixed points in Yukawa theories

    DEFF Research Database (Denmark)

    Mølgaard, Esben; Shrock, R.


    We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar co....... In the regime of weak couplings where the perturbative calculations are most reliable, we find that the theories have no nontrivial fixed points, and the flow is toward a free theory in the infrared.......We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar...... coupling lambda by comparing the properties of flows obtained with the beta functions of these couplings calculated to different orders in the loop expansion. The results provide a determination of the region in y and lambda where calculations up to two loops can yield reasonably reliable results...

  5. A note on convex renorming and fragmentability

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    A note on convex renorming and fragmentability. A K MIRMOSTAFAEE. Department of Mathematics, Damghan University of Sciences, P.O. 36715/364,. Damghan, Iran. E-mail: ... general, the domain of sn+1 consists of partial plays of the type. (A1,... ,Ai,Bi,Ai+1,... ,An+1), where, for every i ≤ n, (A1 ...

  6. Renormalized Perturbation Theory A Missing Chapter

    CERN Document Server

    Stora, Raymond


    Renormalized perturbation theory à la BPHZ can be founded on causality as analyzed by H. Epstein and V. Glaser in the seventies. Here, we list and discuss a number of additional constraints of algebraic character some of which have to be considered as parts of the core of the BPHZ framework.

  7. Time-dependent spectral renormalization method (United States)

    Cole, Justin T.; Musslimani, Ziad H.


    The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

  8. Renormalization of Magnetic Excitations in Praseodymium

    DEFF Research Database (Denmark)

    Lindgård, Per-Anker


    The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev...

  9. Controlling sign problems in spin models using tensor renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Denbleyker, Alan [Iowa U.; Liu, Yuzhi [Colorado U.; Meurice, Y. [Iowa U.; Qin, M. P. [Beijing, Inst. Phys.; Xiang, T. [Beijing, Inst. Phys.; Xie, Z. Y. [Beijing, Inst. Phys.; Yu, J. F. [Beijing, Inst. Phys.; Zou, Haiyuan [Iowa U.


    We consider the sign problem for classical spin models at complex $\\beta =1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

  10. Spectral functions and transport coefficients from the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Tripolt, Ralf-Arno


    In this thesis we present a new method to obtain real-time quantities like spectral functions and transport coefficients at finite temperature and density using the Functional Renormalization Group approach. Our non-perturbative method is thermodynamically consistent, symmetry preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations. We demonstrate the applicability of this method by calculating mesonic spectral functions as well as the shear viscosity for the quark-meson model. In particular, results are presented for the pion and sigma spectral function at finite temperature and chemical potential, with a focus on the regime near the critical endpoint in the phase diagram of the quark-meson model. Moreover, the different time-like and space-like processes, which give rise to a complex structure of the spectral functions, are discussed. Finally, based on the momentum dependence of the spectral functions, we calculate the shear viscosity and the shear viscosity to entropy density ratio using the corresponding Green-Kubo formula.

  11. Noise spectrum of quantum transport through double quantum dots: Renormalization and non-Markovian effects

    Directory of Open Access Journals (Sweden)

    Pengqin Shi


    Full Text Available Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.

  12. Emergent Space-Time via a Geometric Renormalization Method

    CERN Document Server

    Rastgoo, Saeed


    We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the...

  13. Accurate renormalization group analyses in neutrino sector

    Energy Technology Data Exchange (ETDEWEB)

    Haba, Naoyuki [Graduate School of Science and Engineering, Shimane University, Matsue 690-8504 (Japan); Kaneta, Kunio [Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba 277-8568 (Japan); Takahashi, Ryo [Graduate School of Science and Engineering, Shimane University, Matsue 690-8504 (Japan); Yamaguchi, Yuya [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan)


    We investigate accurate renormalization group analyses in neutrino sector between ν-oscillation and seesaw energy scales. We consider decoupling effects of top quark and Higgs boson on the renormalization group equations of light neutrino mass matrix. Since the decoupling effects are given in the standard model scale and independent of high energy physics, our method can basically apply to any models beyond the standard model. We find that the decoupling effects of Higgs boson are negligible, while those of top quark are not. Particularly, the decoupling effects of top quark affect neutrino mass eigenvalues, which are important for analyzing predictions such as mass squared differences and neutrinoless double beta decay in an underlying theory existing at high energy scale.

  14. Renormalization of gauge theories without cohomology

    Energy Technology Data Exchange (ETDEWEB)

    Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa (Italy)


    We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

  15. Renormalization group flow of the Higgs potential (United States)

    Gies, Holger; Sondenheimer, René


    We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability. This article is part of the Theo Murphy meeting issue `Higgs cosmology'.

  16. Field renormalization in photonic crystal waveguides

    DEFF Research Database (Denmark)

    Colman, Pierre


    A novel strategy is introduced in order to include variations of the nonlinearity in the nonlinear Schro¨dinger equation. This technique, which relies on renormalization, is in particular well adapted to nanostructured optical systems where the nonlinearity exhibits large variations up to two...... Schro¨dinger equation is an occasion for physics-oriented considerations and unveils the potential of photonic crystal waveguides for the study of new nonlinear propagation phenomena....

  17. Renormalization group flows and continual Lie algebras

    CERN Document Server

    Bakas, Ioannis


    We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches...

  18. Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula (United States)

    Bischoff, Jan-Moritz; Jeckelmann, Eric


    We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

  19. Functional renormalization group study of fluctuation effects in fermionic superfluids

    Energy Technology Data Exchange (ETDEWEB)

    Eberlein, Andreas


    This thesis is concerned with ground state properties of two-dimensional fermionic superfluids. In such systems, fluctuation effects are particularly strong and lead for example to a renormalization of the order parameter and to infrared singularities. In the first part of this thesis, the fermionic two-particle vertex is analysed and the fermionic renormalization group is used to derive flow equations for a decomposition of the vertex in charge, magnetic and pairing channels. In the second part, the channel-decomposition scheme is applied to various model systems. In the superfluid state, the fermionic two-particle vertex develops rich and singular dependences on momentum and frequency. After simplifying its structure by exploiting symmetries, a parametrization of the vertex in terms of boson-exchange interactions in the particle-hole and particle-particle channels is formulated, which provides an efficient description of the singular momentum and frequency dependences. Based on this decomposition of the vertex, flow equations for the effective interactions are derived on one- and two-loop level, extending existing channel-decomposition schemes to (i) the description of symmetry breaking in the Cooper channel and (ii) the inclusion of those two-loop renormalization contributions to the vertex that are neglected in the Katanin scheme. In the second part, the superfluid ground state of various model systems is studied using the channel-decomposition scheme for the vertex and the flow equations. A reduced model with interactions in the pairing and forward scattering channels is solved exactly, yielding insights into the singularity structure of the vertex. For the attractive Hubbard model at weak coupling, the momentum and frequency dependence of the two-particle vertex and the frequency dependence of the self-energy are determined on one- and two-loop level. Results for the suppression of the superfluid gap by fluctuations are in good agreement with the literature

  20. BRST renormalization of the first order Yang-Mills theory (United States)

    Frenkel, J.; Taylor, John C.


    We examine the renormalization of the first order formulation of the Yang-Mills theory, by using the BRST identities. These preserve the gauge invariance of the theory and enable a recursive proof of renormalizability to higher orders in perturbation theory. The renormalization involves non-linear mixings as well as re-scalings of the fields and sources, which lead to a renormalized action at all orders.

  1. Generalized geometry, T-duality, and renormalization group flow (United States)

    Streets, Jeffrey


    We interpret the physical B-field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural ;Ricci flow; for generalized geometry. Next we show that the B-field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain new long time existence results for the B-field renormalization group flow.

  2. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

    Directory of Open Access Journals (Sweden)

    Huan-Yu Bi


    Full Text Available The Principle of Maximum Conformality (PMC eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I; the other, more recent, method (PMC-II uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e− and the Higgs partial width Γ(H→bb¯. Both methods lead to the same resummed (‘conformal’ series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi}-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  3. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale (United States)

    Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin


    The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e- and the Higgs partial width Γ (H → b b bar). Both methods lead to the same resummed ('conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi }-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  4. Applications of noncovariant gauges in the algebraic renormalization procedure

    CERN Document Server

    Boresch, A; Schweda, Manfred


    This volume is a natural continuation of the book Algebraic Renormalization, Perturbative Renormalization, Symmetries and Anomalies, by O Piguet and S P Sorella, with the aim of applying the algebraic renormalization procedure to gauge field models quantized in nonstandard gauges. The main ingredient of the algebraic renormalization program is the quantum action principle, which allows one to control in a unique manner the breaking of a symmetry induced by a noninvariant subtraction scheme. In particular, the volume studies in-depth the following quantized gauge field models: QED, Yang-Mills t

  5. Emergent space-time via a geometric renormalization method (United States)

    Rastgoo, Saeed; Requardt, Manfred


    We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of space-time can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the spirit of the Wilsonian renormalization group (RG). Furthermore, we introduce a physically relevant notion of dimension on the spaces of interest in our analysis, which, e.g., for regular lattices reduces to the ordinary lattice dimension. We show that this dimension is stable under the proposed coarse graining procedure as long as the latter is sufficiently local, i.e., quasi-isometric, and discuss the conditions under which this dimension is an integer. We comment on the possibility that the limit space may turn out to be fractal in case the dimension is noninteger. At the end of the paper we briefly mention the possibility that our network carries a translocal far order that leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local.

  6. Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model (United States)

    Heller, Urs M.


    An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.

  7. Charge transport properties of a twisted DNA molecule: A renormalization approach

    Energy Technology Data Exchange (ETDEWEB)

    Almeida, M.L. de; Ourique, G.S.; Fulco, U.L. [Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Albuquerque, E.L., E-mail: [Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Moura, F.A.B.F. de; Lyra, M.L. [Instituto de Física, Universidade Federal de Alagoas, 57072-900 Maceió-AL (Brazil)


    In this work we study the charge transport properties of a nanodevice consisting of a finite segment of the DNA molecule sandwiched between two metallic electrodes. Our model takes into account a nearest-neighbor tight-binding Hamiltonian considering the nucleobases twist motion, whose solutions make use of a two-steps renormalization process to simplify the algebra, which can be otherwise quite involved. The resulting variations of the charge transport efficiency are analyzed by numerically computing the main features of the electron transmittance spectra as well as their I × V characteristic curves.

  8. Implicit vs explicit renormalization and effective interactions

    Energy Technology Data Exchange (ETDEWEB)

    Ruiz Arriola, E., E-mail: [Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Fisica Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Szpigel, S., E-mail: [Faculdade de Computação e Informática, Universidade Presbiteriana Mackenzie (Brazil); Timóteo, V.S., E-mail: [Grupo de Óptica e Modelagem Numérica – GOMNI, Faculdade de Tecnologia, Universidade Estadual de Campinas – UNICAMP (Brazil)


    Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the first method is numerically involved, the second one can be solved almost analytically. In both cases we compare the outcoming effective interactions for the two nucleon system as functions of the cut-off scale and find a strikingly wide energy region where both approaches overlap, corresponding to relevant scales in light nuclei Λ≲200 MeV. This amounts to a great simplification in the determination of the effective interaction parameters.

  9. Functional renormalization group approach to neutron matter

    Directory of Open Access Journals (Sweden)

    Matthias Drews


    Full Text Available The chiral nucleon-meson model, previously applied to systems with equal number of neutrons and protons, is extended to asymmetric nuclear matter. Fluctuations are included in the framework of the functional renormalization group. The equation of state for pure neutron matter is studied and compared to recent advanced many-body calculations. The chiral condensate in neutron matter is computed as a function of baryon density. It is found that, once fluctuations are incorporated, the chiral restoration transition for pure neutron matter is shifted to high densities, much beyond three times the density of normal nuclear matter.

  10. Renormalization group flow of the Holst action

    Energy Technology Data Exchange (ETDEWEB)

    Daum, J.-E., E-mail: [University of Mainz, D-55099 Mainz (Germany); Reuter, M. [University of Mainz, D-55099 Mainz (Germany)


    The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under spacetime diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three-parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way.

  11. Perturbative and nonperturbative renormalization in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)


    We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)

  12. Tensor renormalization group methods for spin and gauge models (United States)

    Zou, Haiyuan

    The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

  13. Nonperturbative renormalization group treatment of amplitude fluctuations for |φ| 4 topological phase transitions (United States)

    Defenu, Nicolò; Trombettoni, Andrea; Nándori, István; Enss, Tilman


    The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional |φ| 4 models can be performed in several representations, and the amplitude-phase (AP) Madelung parametrization is a natural way to study the contribution of density fluctuations to nonuniversal quantities. We introduce a functional renormalization group scheme in AP representation where amplitude fluctuations are integrated first to yield an effective sine-Gordon model with renormalized superfluid stiffness. By a mapping between the lattice X Y and continuum |φ| 4 models, our method applies to both on equal footing. Our approach correctly reproduces the existence of a line of fixed points and of universal thermodynamics and it allows to estimate universal and nonuniversal quantities of the two models, finding good agreement with available Monte Carlo results. The presented approach is flexible enough to treat parameter ranges of experimental relevance.

  14. Terahertz Measurement Of The Quasiparticle Mass Renormalization In Lead And Chromium

    CERN Document Server

    Gilmore, M A


    We study the optical conductivity of lead and chromium as a function of frequency and temperature using terahertz time-domain spectroscopy (THz-TDS). The optical conductivity is interpreted in terms of the extended Drude model (EDM), where the optical scattering rate and renormalized mass of the carriers take on frequency as well as temperature dependence. Within the EDM framework, the theory of electron-phonon scattering yields expressions for the optical scattering rate and mass enhancement, dependent upon the transport-weighted Eliashberg spectral function. This thesis presents THz- TDS measurements of thin films of Pb and Cr. We compare results for the optical scattering rate and quasiparticle mass renormalization to theory and find a strong agreement.

  15. Renormalization group approach to relativistic cosmology (United States)

    Carfora, Mauro; Piotrkowska, Kamilla


    We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a ``3+1'' formalism and invokes the coarse-graining arguments, provided and supported by the real-space renormalization group (RG) methods, in parallel with lattice models of statistical mechanics. Block variables are introduced and the recursion relations written down explicitly enabling us to characterize the corresponding RG flow. To leading order, the RG flow is provided by the Ricci-Hamilton equations studied in connection with the geometry of three-manifolds. The possible relevance of the Ricci-Hamilton flow in implementing the averaging in cosmology has been previously advocated, but the physical motivations behind this suggestion were not clear. The RG interpretation provides us with such physical motivations. The properties of the Ricci-Hamilton flow make it possible to study a critical behavior of cosmological models. This criticality is discussed and it is argued that it may be related to the formation of sheetlike structures in the universe. We provide an explicit expression for the renormalized Hubble constant and for the scale dependence of the matter distribution. It is shown that the Hubble constant is affected by nontrivial scale-dependent shear terms, while the spatial anisotropy of the metric influences significantly the scale dependence of the matter distribution.

  16. A numerical renormalization group approach to non-equilibrium Green functions for quantum impurity models

    Energy Technology Data Exchange (ETDEWEB)

    Anders, Frithjof B [Institut fuer Theoretische Physik, Universitaet Bremen, PO Box 330 440, D-28334 Bremen (Germany)], E-mail:


    We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group (NRG). Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfils the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion U>0 is switched on at t = 0, and the asymptotic steady-state spectral functions are obtained for various values of U as well as magnetic field strength H and temperature T. These benchmark tests show excellent agreement between the time-evolved and the directly calculated equilibrium NRG spectra for finite U. This method could be used for calculating steady-state non-equilibrium spectral functions at finite bias through interacting nanodevices.

  17. Renormalization of the Abelian–Higgs model in the Rξ and Unitary gauges and the physicality of its scalar potential

    Directory of Open Access Journals (Sweden)

    Nikos Irges


    Full Text Available We perform an old school, one-loop renormalization of the Abelian–Higgs model in the Unitary and Rξ gauges, focused on the scalar potential and the gauge boson mass. Our goal is to demonstrate in this simple context the validity of the Unitary gauge at the quantum level, which could open the way for an until now (mostly avoided framework for loop computations. We indeed find that the Unitary gauge is consistent and equivalent to the Rξ gauge at the level of β-functions. Then we compare the renormalized, finite, one-loop Higgs potential in the two gauges and we again find equivalence. This equivalence needs not only a complete cancellation of the gauge fixing parameter ξ from the Rξ gauge potential but also requires its ξ-independent part to be equal to the Unitary gauge result. We follow the quantum behavior of the system by plotting Renormalization Group trajectories and Lines of Constant Physics, with the former the well known curves and with the latter, determined by the finite parts of the counter-terms, particularly well suited for a comparison with non-perturbative studies.

  18. Complete renormalization group improvement - avoiding factorization and renormalization scale dependence in QCD predictions

    Energy Technology Data Exchange (ETDEWEB)

    Maxwell, C.J. E-mail:; Mirjalili, A. E-mail:


    For moments of leptoproduction structure functions we show that all dependence on the renormalization and factorization scales disappears provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of effective charges. A direct and simple method for extracting {lambda}{sub MS-bar} from experimental data is advocated.

  19. Hilbert space renormalization for the many-electron problem. (United States)

    Li, Zhendong; Chan, Garnet Kin-Lic


    Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.

  20. Renormalization group approach to density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Kemler, Sandra; Braun, Jens [Institut fuer Kernphysik, TU Darmstadt (Germany)


    We study a two-point particle irreducible (2PPI) approach to many-body physics which relies on a renormalization group (RG) flow equation for the associated effective action. This approach relates to Density Functional Theory and can in principle be used to study ground-state properties of non-relativistic many-body systems from microscopic interactions, such as (heavy) nuclei. We apply our formalism to a 0+1-dimensional model, namely the quantum anharmonic oscillator and use the well-known exact solution to benchmark our approximations of the full RG flow. Moreover, we present flow equations for specific types of 1+1-dimensional field theories which allow us study the ground-state properties of self-bound systems of spinless fermions which can also be viewed as toy models of nuclei.

  1. Nonlinear relativistic plasma resonance: Renormalization group approach

    Energy Technology Data Exchange (ETDEWEB)

    Metelskii, I. I., E-mail: [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)


    An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

  2. From plasticity to a renormalization group. (United States)

    Ball, R C; Blumenfeld, R


    The marginally rigid state is a candidate paradigm for what makes granular material a state of matter distinct from both liquid and solid. The coordination number is identified as a discriminating characteristic, and for rough-surfaced particles we show that the low values predicted are indeed approached in simple two-dimensional experiments. We show calculations of the stress transmission, suggesting that this is governed by local linear equations of constraint between the stress components. These constraints can in turn be related to the generalized forces conjugate to the motion of grains rolling over each other. The lack of a spatially coherent way of imposing a sign convention on these motions is a problem for scaling up the equations, which leads us to attempt a renormalization-group calculation. Finally, we discuss how perturbations propagate through such systems, suggesting a distinction between the behaviour of rough and smooth grains.

  3. Renormalization group theory impact on experimental magnetism

    CERN Document Server

    Köbler, Ulrich


    Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are calle...

  4. Semihard processes with BLM renormalization scale setting

    Energy Technology Data Exchange (ETDEWEB)

    Caporale, Francesco [Instituto de Física Teórica UAM/CSIC, Nicolás Cabrera 15 and U. Autónoma de Madrid, E-28049 Madrid (Spain); Ivanov, Dmitry Yu. [Sobolev Institute of Mathematics and Novosibirsk State University, 630090 Novosibirsk (Russian Federation); Murdaca, Beatrice; Papa, Alessandro [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, Arcavacata di Rende, I-87036 Cosenza (Italy)


    We apply the BLM scale setting procedure directly to amplitudes (cross sections) of several semihard processes. It is shown that, due to the presence of β{sub 0}-terms in the NLA results for the impact factors, the obtained optimal renormalization scale is not universal, but depends both on the energy and on the process in question. We illustrate this general conclusion considering the following semihard processes: (i) inclusive production of two forward high-p{sub T} jets separated by large interval in rapidity (Mueller-Navelet jets); (ii) high-energy behavior of the total cross section for highly virtual photons; (iii) forward amplitude of the production of two light vector mesons in the collision of two virtual photons.

  5. Fundamentals of the exact renormalization group (United States)

    Rosten, Oliver J.


    Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a review of the concepts underpinning the framework and the circumstances under which it is expected to be useful. A particular emphasis is placed on the intuitive picture provided for both renormalization in quantum field theory and universality associated with second order phase transitions. A qualitative discussion of triviality, asymptotic freedom and asymptotic safety is presented. Focusing on scalar field theory, the construction of assorted flow equations is considered using a general approach, whereby different ERGs follow from field redefinitions. It is recalled that Polchinski’s equation can be cast as a heat equation, which provides intuition and computational techniques for what follows. The analysis of properties of exact solutions to flow equations includes a proof that the spectrum of the anomalous dimension at critical fixed-points is quantized. Two alternative methods for computing the β-function in λϕ4 theory are considered. For one of these it is found that all explicit dependence on the non-universal differences between a family of ERGs cancels out, exactly. The Wilson-Fisher fixed-point is rediscovered in a rather novel way. The discussion of nonperturbative approximation schemes focuses on the derivative expansion, and includes a refinement of the arguments that, at the lowest order in this approximation, a function can be constructed which decreases monotonically along the flow. A new perspective is provided on the relationship between the renormalizability of the Wilsonian effective action and of correlation functions, following which the construction of manifestly gauge invariant ERGs is sketched, and some new insights are given. Drawing these strands together suggests a new approach to quantum field theory.

  6. Renormalization group improved Higgs inflation with a running kinetic term

    Directory of Open Access Journals (Sweden)

    Fuminobu Takahashi


    Full Text Available We study a Higgs inflation model with a running kinetic term, taking account of the renormalization group evolution of relevant coupling constants. Specifically we study two types of the running kinetic Higgs inflation, where the inflaton potential is given by the quadratic or linear term potential in a frame where the Higgs field is canonically normalized. We solve the renormalization group equations at two-loop level and calculate the scalar spectral index and the tensor-to-scalar ratio. We find that, even if the renormalization group effects are included, the quadratic inflation is ruled out by the CMB observations, while the linear one is still allowed.

  7. Ultrasoft renormalization of the potentials in vNRQCD

    Energy Technology Data Exchange (ETDEWEB)

    Stahlhofen, Maximilian Horst


    The effective field theory vNRQCD allows to describe among others the production of top-antitop pairs in electron-positron collisions at threshold, i.e. with very small relative velocity {upsilon} << 1 of the quarks. Potentially large logarithms {proportional_to} ln {upsilon} are systematically summed up and lead to a scale dependence of the Wilson coefficients of the theory. The missing contributions to the cross section {sigma}(e{sup +}e{sup -} {yields} t anti t) in the resonance region at NNLL level are the so-called mixing contributions to the NNLL anomalous dimension of the S-wave production/annihilation current of the topquark pair. To calculate these one has to know the NLL renormalization group running of so-called potentials (4-quark operators). The dominant contributions to the anomalous dimension of these potentials come from vNRQCD diagrams with ultrasoft gluon loops. The aim of this thesis is to derive the complete ultrasoft NLL running of the relevant potentials. For that purpose the UV divergent parts of about 10{sup 4} two-loop diagrams are determined. Technical and conceptional issues are discussed. Some open questions related to the calculation of the non-Abelian two-loop diagrams arise. Preliminary results are analysed with regard to the consequences for the mentioned cross section and its theoretical uncertainty. (orig.)

  8. Renormalization of tracer turbulence leading to fractional differential operators

    Energy Technology Data Exchange (ETDEWEB)

    Sanchez, Raul [ORNL; Carreras, Benjamin A [ORNL; Newman, David E [University of Alaska; Lynch, Vickie E [ORNL; van Milligen, B. Ph. [Asociacion EURATOM-CIEMAT


    For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides with a first step towards establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

  9. One-loop renormalization of the Polyakov string functional (United States)

    Cohen, E.; Kluberg-Stern, H.; Navelet, H.; Peschanski, R.


    This paper studies the divergences of the bosonic string coupled to background fields, the graviton, the dilaton and the tachyon fields. These divergences are computed to first order in the string tension parameter for the topologies of the sphere and the torus. In our modular invariant regularization, depending on a dimensionful parameter ɛ, quadratic divergences are present and they modify the renormalization scheme. As an alternative to the Fischler-Susskind mechanism, which leads to a contribution to the target-space cosmological constant from the torus, it is possible to absorb the main divergences in a renormalization of the string coupling constant which is related to the renormalization of the dilaton background field. The contribution from the torus leads to new effects which are not σ-model counterterms. If certain factorization properties apply for the partition function of higher-order topologies, this scheme could indicate the existence of a solution without target space metric renormalization at this order.

  10. Massive Axial Gauge in the Exact Renormalization Group Approach (United States)

    Panza, P.; Soldati, R.

    The Exact Renormalization Group (ERG) approach to massive gauge theories in the axial gauge is studied and the smoothness of the massless limit is analysed for a formally gauge invariant quantity such as the Euclidean Wilson loop.

  11. Renormalization and power counting of chiral nuclear forces

    Energy Technology Data Exchange (ETDEWEB)

    Long, Bingwei [JLAB


    I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.

  12. Renormalization Group in the uniqueness region weak Gibbsianity and convergence.

    CERN Document Server

    Bertini, L; Olivieri, E


    We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. %We discuss the %Gibbs property of the renormalized measure and the convergence of %renormalized potential under iteration of the map. We prove weak Gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense. Since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system: the correlation length or the critical length for metastability, or both. Thus, to perturbatively treat the problem we have to use a scale--adapted expansion. Moreover, such a model below the critical temperature resembles a disordered system in presence of Griffiths' singularity. Then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached.

  13. Renormalization and 3-manifolds which fiber over the circle (AM-142)

    CERN Document Server

    McMullen, Curtis T


    Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitativ

  14. Renormalization group and continuum limit of quantum cellular automata

    Energy Technology Data Exchange (ETDEWEB)

    Zimboras, Zoltan [Quantum Information Theory Group, ISI, Torino (Italy)


    We develop a renormalization group formalism for quantum cellular automata (reminiscent of the algebraic renormalization group of Buchholz and Verch). Using this formalism, we can define the continuum limit for certain automata. As a particular example, we show that the continuum limit of the so-called ''Glider Clifford cellular automaton'' is the 1+1 dimensional relativistic QFT of free Majorana fermions.

  15. Solving renormalization group equations with the Lambert W function (United States)

    Sonoda, H.


    It has been known for some time that 2-loop renormalization group equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed point to construct renormalization group invariant physical parameters such as a coupling constant and a physical squared mass. As a further application, we speculate a possible exact effective potential for the O(N) linear sigma model in four dimensions.

  16. Investigation of renormalization effects in high temperature cuprate superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Zabolotnyy, Volodymyr B.


    It has been found that the self-energy of high-T{sub C} cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} and YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T{sub C} suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)

  17. Finite Divergence

    DEFF Research Database (Denmark)

    Hansen, Michael Edberg; Pandya, P. K.; Chaochen, Zhou


    Real-time and hybrid systems have been studied so far under the assumption of finite variability. In this paper, we consider models in which systems exhibiting finite divergence can also be analysed. In such systems, the state of the system can change infinitely often in a finite time. This kind...... of behaviour arises in many representations of hybrid systems, and also in theories of nonlinear systems. The aim is to provide a theory where pathological behaviour such as finite divergence can be analysed-if only to prove that it does not occur in systems of interest. Finite divergence is studied using...

  18. Renormalization group improvement and constituent quark model

    Energy Technology Data Exchange (ETDEWEB)

    Mirjalili, A. [Physics Department, Yazd University, Yazd (Iran, Islamic Republic of); School of Particles and Accelerators, IPM - Institute for Studies in Theoretical Physics and Mathematics, P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail:; Khorramian, Ali N. [Physics Department, Semnan University, Semnan (Iran, Islamic Republic of); School of Particles and Accelerators, IPM - Institute for Studies in Theoretical Physics and Mathematics, P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail:; Atashbar Tehrani, S. [Physics Department, Semnan University, Semnan (Iran, Islamic Republic of); School of Particles and Accelerators, IPM - Institute for Studies in Theoretical Physics and Mathematics, P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail:


    The scale dependence in perturbative QCD remains on obstacle to making precise tests of the theory. To over come the scale ambiguity while people are usually using the standard MS-bar approach with a physical choice of renormalization scale, we try to employ the approach of complete RG-improvement. In this approach all ultraviolet logarithms involving the dimensionful parameter, Q, on which the observable depends are resummed, thereby building the correct Q-dependence. Based on these two approaches, sea quark densities in the nucleon are analyzed. To achieve the asymmetry of these densities, chiral quark model is used. To avoid from the unaccepted Q{sup 2} behavior of sea densities inside the constituent quark, we assume that the free parameter which exists in the vertex function of boson-quark splitting function, is Q{sup 2}-dependence. Using un-symmetrized sea densities of the nucleon, the Gottfried sum rule is calculated in these two approaches. The result of the latter one is very close to the reported experimental value.

  19. Renormalization group approach to superfluid neutron matter

    Energy Technology Data Exchange (ETDEWEB)

    Hebeler, K.


    In the present thesis superfluid many-fermion systems are investigated in the framework of the Renormalization Group (RG). Starting from an experimentally determined two-body interaction this scheme provides a microscopic approach to strongly correlated many-body systems at low temperatures. The fundamental objects under investigation are the two-point and the four-point vertex functions. We show that explicit results for simple separable interactions on BCS-level can be reproduced in the RG framework to high accuracy. Furthermore the RG approach can immediately be applied to general realistic interaction models. In particular, we show how the complexity of the many-body problem can be reduced systematically by combining different RG schemes. Apart from technical convenience the RG framework has conceptual advantage that correlations beyond the BCS level can be incorporated in the flow equations in a systematic way. In this case however the flow equations are no more explicit equations like at BCS level but instead a coupled set of implicit equations. We show on the basis of explicit calculations for the single-channel case the efficacy of an iterative approach to this system. The generalization of this strategy provides a promising strategy for a non-perturbative treatment of the coupled channel problem. By the coupling of the flow equations of the two-point and four-point vertex self-consistency on the one-body level is guaranteed at every cutoff scale. (orig.)

  20. Renormalization of aperiodic model lattices: spectral properties

    CERN Document Server

    Kroon, L


    Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue-Morse, period-doubling and Rudin-Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schroedinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue-Morse sequence and the period-doubli...

  1. Renormalization Group Approach in Newtonian Cosmology (United States)

    Sota, Y.; Kobayashi, T.; Maeda, K.; Nakamichi, A.; Kurokawa, T.; Morikawa, M.

    There are many evidences that the matter distribution of the Universe show fractal well beyond the scale of hundred Mpc. This fractal matter distribution clearly conflicts with the widely assumed cosmological model in which the matter distribution asymptotically becomes homogeneous in larger scale. If this fractal distribution of matter, however, turns out to be true and the local density fluctuations do not reduce in larger scale, we have to change the present cosmological model of the Universe which is globally described by FRW space-time. Here, we analyze the global behavior of such fluctuation-dominated Universe by applying the renormalization group (RG) method. We derive the flow of the RG equations and clarify the properties of fixed points by using the model of Newtonian cosmology with dust fluid. This model allows the scale-invariance and a well defined procedure of space averaging, both of which make our RG analysis easier. Based on this RG analysis, we would like to argue (a) how the large fluctuations in all scales affect the global structure of the Universe, (b) how the age problem of the Universe is solved and (c) the nature of dark matter in fractal Universe.

  2. General Covariance from the Quantum Renormalization Group

    CERN Document Server

    Shyam, Vasudev


    The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the $D + 1$ dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the $D$ dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Po...

  3. Renormalized Wick expansion for a modified PQCD

    Energy Technology Data Exchange (ETDEWEB)

    Cabo Montes de Oca, Alejandro [Instituto de Cibernetica, Matematica y Fisica, Group of Theoretical Physics, Vedado, La Habana (Cuba); Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)


    The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m{sub q} and m{sub g} associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m{sub q} and m{sub g} is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum. (orig.)

  4. Holographic renormalization as a canonical transformation

    CERN Document Server

    Papadimitriou, Ioannis


    The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equati...

  5. Some aspects of N = 1 SYM renormalization

    Directory of Open Access Journals (Sweden)

    Stepanyantz Konstantin


    Full Text Available Using the BRST invariant version of the higher covariant derivative regularization, we demonstrate that in N = 1 supersymmetric gauge theories the three-point vertices with two ghost legs and a single leg of the quantum gauge superfield are finite in all orders. This theorem is proved by the help of the Slavnov–Taylor identities and the supergraph technique. Its correctness is verified by explicit one-loop calculation. Using finiteness of the considered vertices we express the NSVZ relation in terms of the anomalous dimensions of the gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields.

  6. Nonequilibrium dynamics of active matter with correlated noise: A dynamical renormalization group study (United States)

    Kachan, Devin; Levine, Alex; Bruinsma, Robijn


    Biology is rife with examples of active materials - soft matter systems driven into nonequilibrium steady states by energy input at the micro scale. For example, solutions of active micron scale swimmers produce active fluids showing phenomena reminiscent of turbulent convection at low Reynolds number; cytoskeletal networks driven by endogenous molecular motors produce active solids whose mechanics and low frequency strain fluctuations depend sensitively on motor activity. One hallmark of these systems is that they are driven at the micro scale by temporally correlated forces. In this talk, we study how correlated noise at the micro scale leads to novel long wavelength and long time scale dynamics at the macro scale in a simple model system. Specifically, we study the fluctuations of a ϕ4 scalar field obeying model A dynamics and driven by noise with a finite correlation time τ. We show that the effective dynamical system at long length and time scales is driven by white noise with a renormalized amplitude and renormalized transport coefficients. We discuss the implications of this result for a broad class of active matter systems driven at the micro scale by colored noise.

  7. Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction. (United States)

    Liu, X M; Cheng, W W; Liu, J-M


    We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions.

  8. Renormalization-group flow of the effective action of cosmological large-scale structures

    CERN Document Server

    Floerchinger, Stefan


    Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input ...

  9. Strong-disorder renormalization group study of aperiodic quantum Ising chains (United States)

    Oliveira Filho, Fleury J.; Faria, Maicon S.; Vieira, André P.


    We employ an adaptation of a strong-disorder renormalization group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground-state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.

  10. Difficulties of AN Infrared Extension of Differential Renormalization (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.

    We investigate the possibility of generalizing the differential renormalization of D. Z. Freedman, K. Johnson and J. I. Latorre in an invariant fashion to theories with infrared divergencies via an infrared widetilde R operation. Two-dimensional σ models and the four-dimensional ɸ4-theory diagrams with exceptional momenta are used as examples, while dimensional renormalization serves as a test scheme for comparison. We write the basic differential identities of the method simultaneously in co-ordinate and momentum space, introducing two scales which remove ultraviolet and infrared singularities. A consistent set of Fourier-transformation formulae is derived. However, the values for tadpole-type Feynman integrals in higher orders of perturbation theory prove to be ambiguous, depending on the order of evaluation of the subgraphs. In two dimensions, even earlier than this ambiguity manifests itself, renormalization-group calculations based on the infrared extension of differential renormalization lead to incorrect results. We conclude that the procedure of extended differential renormalization does not perform the infrared widetilde R operation in a self-consistent way.

  11. Renormalization group and the deep structure of the proton

    CERN Document Server

    Petermann, Andreas


    The spirit of the renormalization group approach lies entirely in the observation that in a specific theory the renormalized constants such as the couplings, the masses, are arbitrary mathematical parameters which can be varied by changing arbitrarily the renormalization prescription. Given a scale of mass mu , prescriptions can be chosen by doing subtractions of the relevant amplitudes at the continuously varying points mu e/sup t/, t being an arbitrary real parameter. A representation of such a renormalization group transformation mu to mu + mu e/sup t/ is the transformation g to g(t) of the renormalized coupling into a continuously varying coupling constant, the so-called 'running coupling constant'. If, for the theory under investigation there exists a domain of the t space where g(t) is small, then because it is not known how to handle field theory beyond the perturbative approach attention must be focused on the experimental range in which the g(t) 'runs' with small values. The introduction of couplings...

  12. Gauge-independent renormalization of the N2HDM (United States)

    Krause, Marcel; López-Val, David; Mühlleitner, Margarete; Santos, Rui


    The Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) is an interesting benchmark model for a Higgs sector consisting of two complex doublet and one real singlet fields. Like the Next-to-Minimal Supersymmetric extension (NMSSM) it features light Higgs bosons that could have escaped discovery due to their singlet admixture. Thereby, the model allows for various different Higgs-to-Higgs decay modes. Contrary to the NMSSM, however, the model is not subject to supersymmetric relations restraining its allowed parameter space and its phenomenology. For the correct determination of the allowed parameter space, the correct interpretation of the LHC Higgs data and the possible distinction of beyond-the-Standard Model Higgs sectors higher order corrections to the Higgs boson observables are crucial. This requires not only their computation but also the development of a suitable renormalization scheme. In this paper we have worked out the renormalization of the complete N2HDM and provide a scheme for the gauge-independent renormalization of the mixing angles. We discuss the renormalization of the Z_2 soft breaking parameter m 12 2 and the singlet vacuum expectation value v S . Both enter the Higgs self-couplings relevant for Higgs-to-Higgs decays. We apply our renormalization scheme to different sample processes such as Higgs decays into Z bosons and decays into a lighter Higgs pair. Our results show that the corrections may be sizable and have to be taken into account for reliable predictions.

  13. Exact renormalization flow and domain walls from holography (United States)

    Ketov, Sergei V.


    The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in N=2 supergravity background are interpreted as the exact renormalization group flow equations in two dimensions. Our geometrical description of the renormalization flow is manifestly covariant under general reparametrization of the 2d coupling constants. An explicit exact solution to the 2d renormalization flow, based on its dual holographic description in terms of the Zamolodchikov metric, is considered in the particular case of the four-dimensional NLSM target space described by the SU(2)-invariant (Weyl) anti-self-dual Einstein metrics. The exact regular (Tod-Hitchin) solutions to these metrics are governed by the Painlevé VI equation, and describe domain walls.

  14. Renormalization group theory of the critical properties of the interacting bose fluid

    NARCIS (Netherlands)

    Creswick, Richard J.; Wiegel, F.W.


    Starting from a functional integral representation of the partition function we apply the renormalization group to the interacting Bose fluid. A closed form for the renormalization equation is derived and the critical exponents are calculated in 4-ε dimensions.

  15. Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time (United States)

    Antonov, N. V.; Hnatič, M.; Kapustin, A. S.; Lučivjanský, T.; Mižišin, L.


    The direct bond percolation process (Gribov process) is studied in the presence of random velocity fluctuations generated by the Gaussian self-similar ensemble with finite correlation time. We employ the renormalization group in order to analyze a combined effect of the compressibility and finite correlation time on the long-time behavior of the phase transition between an active and an absorbing state. The renormalization procedure is performed to the one-loop order. Stable fixed points of the renormalization group and their regions of stability are calculated in the one-loop approximation within the three-parameter (ɛ ,y ,η ) expansion. Different regimes corresponding to the rapid-change limit and frozen velocity field are discussed, and their fixed points' structure is determined in numerical fashion.

  16. Thermal geometry from CFT at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Gan, Wen-Cong, E-mail: [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)


    We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

  17. Thermal geometry from CFT at finite temperature

    Directory of Open Access Journals (Sweden)

    Wen-Cong Gan


    Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

  18. Peripheral NN scattering from subtractive renormalization of chiral interactions

    Energy Technology Data Exchange (ETDEWEB)

    Batista, E. F. [Departamento de Ciências Exatas e Naturais, Universidade Estadual do Sudoeste da Bahia, 45700-000 Itapetinga - BA (Brazil); Szpigel, S. [Centro de Rádio-Astronomia e Astrofísica Mackenzie, Escola de Engenharia, Universidade Presbiteriana Mackenzie, 01302-907 São Paulo - SP (Brazil); Timóteo, V. S. [Grupo de Óptica e Modelagem NumérIca - GOMNI, Faculdade de Tecnologia - FT, Universidade Estadual de Campinas - UNICAMP, 13484-332 Limeira - SP (Brazil)


    We apply five subtractions in the Lippman-Schwinger (LS) equation in order to perform a non-perturbative renormalization of chiral N3LO nucleon-nucleon interactions. Here we compute the phase shifts for the uncoupled peripheral waves at renormalization scales between 0.1 fm{sup −1} and 1 fm{sup −1}. In this range, the results are scale invariant and provide an overall good agreement with the Nijmegen partial wave analysis up to at least E{sub lab} = 150 MeV, with a cutoff at Λ = 30 fm{sup −1}.

  19. Computing the effective action with the functional renormalization group

    DEFF Research Database (Denmark)

    Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław


    The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action Γ k. The ordinary effective action Γ 0 can be obtained by integrating the flow equation from an ultraviolet scale k= Λ down to k= 0. We give several examples of such...... of QED and of Yang–Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity....

  20. Renormalization group approach to matrix models via noncommutative space

    Energy Technology Data Exchange (ETDEWEB)

    Kuroki, T. [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Furo-cho, Chikusa-ku, Nagoya Aichi 464-8602 (Japan); Kawamoto, S. [National Center for Theoretical Sciences, Hsinchu 30013 (China); Tomino, D. [Department of Physics, Tunghai University, Taichung 40704 (China)


    We develop a new method for analyzing the large-N limit of matrix models. We assign the concept of energy to each matrix element and integrate the most highest energy to get a new matrix model which has reduced rank. By regarding this procedure as a renormalization group, we deduce the critical exponents in the large-N limit by elaborating fixed points of renormalization group transformation. For consistency of our method, we compare our result to that obtained by another method and find nice agreement. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  1. Parton distribution function with nonperturbative renormalization from lattice QCD (United States)

    Chen, Jiunn-Wei; Ishikawa, Tomomi; Jin, Luchang; Lin, Huey-Wen; Yang, Yi-Bo; Zhang, Jian-Hui; Zhao, Yong; Lattice Parton Physics Project LP3


    We present lattice results for the isovector unpolarized parton distribution with nonperturbative regularization-invariant momentum-subtraction scheme (RI/MOM) renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-x dependence of a momentum-dependent quasidistribution is calculated on the lattice and matched to the ordinary light cone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.

  2. Finite Automata


    Rogač, Luka Viktor


    In this diploma work the concept of formal language is presented, introducing the ideas related to the concept of formal language and operations over languages. Informal and formal recognition of the concept of the finite state automata is given together with the similarities and differences between deterministic and nondeterministic finite state automata. The concept of regular expression and regular language is described, enabling a transparent and shorter form at writing of the language...

  3. On the renormalization group flow of f(R)-gravity

    NARCIS (Netherlands)

    Machado, P.F.; Saueressig, F.


    We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \\int d^dx \\sqrt{g} f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently

  4. Running with rugby balls: bulk renormalization of codimension-2 branes (United States)

    Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.


    We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

  5. Renormalization Group Flows, Cycles, and c-Theorem Folklore (United States)

    Curtright, Thomas L.; Jin, Xiang; Zachos, Cosmas K.


    Monotonic renormalization group flows of the “c” and “a” functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.

  6. Renormalization group flows, cycles, and c-theorem folklore. (United States)

    Curtright, Thomas L; Jin, Xiang; Zachos, Cosmas K


    Monotonic renormalization group flows of the "c" and "a" functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.

  7. Rota-Baxter algebras and the Hopf algebra of renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Ebrahimi-Fard, K.


    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  8. Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces

    Directory of Open Access Journals (Sweden)

    Hossein Soleimani


    Full Text Available In this paper we show that by renorming an ordered Banach space, every cone $P$ can be converted to a normal cone with constant $K=1$ and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

  9. Galilean invariance and vertex renormalization in turbulence theory. (United States)

    McComb, W D


    The Navier-Stokes equation is invariant under Galilean transformation of the instantaneous velocity field. However, the total velocity transformation is effected by transformation of the mean velocity alone. For a constant mean velocity, the equation of motion for the fluctuating velocity is automatically Galilean invariant in the comoving frame, and vertex renormalization is not constrained by this symmetry.

  10. Renormalization of one-pion exchange and power counting

    NARCIS (Netherlands)

    Nogga, A; Timmermans, RGE; van Kolck, U


    The renormalization of the chiral nuclear interactions is studied. In leading order, the cutoff dependence is related to the singular tensor interaction of the one-pion exchange potential. In S waves and in higher partial waves where the tensor force is repulsive this cutoff dependence can be

  11. On Newton-Cartan local renormalization group and anomalies

    Energy Technology Data Exchange (ETDEWEB)

    Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); INFN Sezione di Perugia,Via A. Pascoli, 06123 Perugia (Italy); Baiguera, Stefano; Filippini, Francesco [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento,38123 Povo (Italy)


    Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.

  12. Holographic torus entanglement and its renormalization group flow (United States)

    Bueno, Pablo; Witczak-Krempa, William


    We study the universal contributions to the entanglement entropy (EE) of 2 +1 -dimensional and 3 +1 -dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti-de Sitter-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2 +1 dimensions, in the simple limit where the torus becomes a thin one-dimensional ring, the EE reduces to a shape-independent constant 2 γ . This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the renormalization group flow of γ by defining a renormalized EE that (1) is applicable to general QFTs, (2) resolves the failure of the area law subtraction, and (3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of nonuniqueness of such renormalized EEs both in 2 +1 dimensions and 3 +1 dimensions.

  13. Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange

    Energy Technology Data Exchange (ETDEWEB)

    Higa, R; Valderrama, M Pavon; Arriola, E Ruiz


    The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.

  14. Simple perturbative renormalization scheme for supersymmetric gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)


    We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/ -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.

  15. Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

    Energy Technology Data Exchange (ETDEWEB)

    Chankowski, Piotr H. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Lewandowski, Adrian [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Meissner, Krzysztof A. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland)


    We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional (MS)-bar scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the (MS)-bar scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

  16. Renormalization group and phase transitions in spin, gauge, and QCD like theories (United States)

    Liu, Yuzhi

    In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete beta functions. The motivation of calculating the discrete beta functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare

  17. Numerical Calculation of Scaling Exponents of Percolation Process in the Framework of Renormalization Group Approach

    Directory of Open Access Journals (Sweden)

    Adzhemyan L. Ts.


    Full Text Available The renormalization group theory is used to the study of the directed bond percolation (Gribov process near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ε-expansion where ε is the deviation from the upper critical dimension dc = 4. Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the R operation, and for computational purposes we choose the null momentum subtraction scheme.

  18. Renormalization-group approach to the vulcanization transition (United States)

    Peng; Goldbart


    The vulcanization transition-the cross-link-density-controlled equilibrium phase transition from the liquid to the amorphous solid state-is explored analytically from a renormalization-group perspective. The analysis centers on a minimal model which has previously been shown to yield a rich and informative picture of vulcanized matter at the mean-field level, including a connection with mean-field percolation theory (i.e., random graph theory). This minimal model accounts for both the thermal motion of the constituents and the quenched random constraints imposed on their motion by the cross-links, as well as particle-particle repulsion which suppresses density fluctuations and plays a pivotal role in determining the symmetry structure (and hence properties) of the model. A correlation function involving fluctuations of the amorphous solid order parameter, the behavior of which signals the vulcanization transition, is examined, its physical meaning is elucidated, and the associated susceptibility is constructed and analyzed. A Ginzburg criterion for the width (in cross-link density) of the critical region is derived and is found to be consistent with a prediction due to de Gennes. Inter alia, this criterion indicates that the upper critical dimension for the vulcanization transition is 6. Certain universal critical exponents characterizing the vulcanization transition are computed, to lowest nontrivial order, within the framework of an expansion around the upper critical dimension. This expansion shows that the connection between vulcanization and percolation extends beyond mean-field theory, surviving the incorporation of fluctuations in the sense that pairs of physically analogous quantities (one percolation related and one vulcanization related) are found to be governed by identical critical exponents, at least to first order in the departure from the upper critical dimension (and presumably beyond). The relationship between the present approach to vulcanized

  19. Absence of a consistent classical equation of motion for a mass-renormalized point charge. (United States)

    Yaghjian, Arthur D


    The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self-electromagnetic force on an extended charged sphere of radius a are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self-force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, a transition force must be included during each of these two transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solution to the equation of motion without the transition forces. Although the exact time dependence of each transition force is not known, the effect of each transition force on the solution to the equation of motion can be determined to within a single unknown constant, namely the change in velocity of the charge across the transition interval. For the extended charged sphere, the changes in velocity across the transition intervals can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, regardless of the values chosen for the changes in the velocity across the transition intervals, renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.

  20. Finite superstrings

    CERN Document Server

    Restuccia, A; Taylor, J G


    This is the first complete account of the construction and finiteness analysis of multi-loop scattering amplitudes for superstrings, and of the guarantee that for certain superstrings (in particular the heterotic one), the symmetries of the theory in the embedding space-time are those of the super-poincaré group SP10 and that the multi-loop amplitudes are each finite. The book attempts to be self-contained in its analysis, although it draws on the works of many researchers. It also presents the first complete field theory for such superstrings. As such it demonstrates that gravity can be quant

  1. Density Matrix Renormalization Group Approach to Two-Fluid Open Many-Fermion Systems

    Energy Technology Data Exchange (ETDEWEB)

    Rotureau, J. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL); Michel, N. [Kyoto University, Japan; Nazarewicz, Witold [ORNL; Ploszajczak, M. [Grand Accelerateur National d' Ions Lourds (GANIL); Dukelsky, J. [Instituto de Estructura de la Materia, CSIC, Madrid, Spain


    We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow Shell Model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground state eigenvalue and discuss different truncation schemes within DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.

  2. Renormalized Stress-Energy Tensor of an Evaporating Spinning Black Hole. (United States)

    Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten


    We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.

  3. Topologically twisted renormalization group flow and its holographic dual (United States)

    Nakayama, Yu


    Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (also known as topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a nontrivial fixed point, it generically gives rise to a scale invariant Euclidean field theory without conformal invariance. Motivated by an ansatz studied in cosmological models some time ago, we develop a holographic dual description of such renormalization group flows in the context of AdS /CFT . We argue that the nontrivial fixed points require fine-tuning of the bulk theory, in general, but remarkably we find that the O (3 ) Yang-Mills theory coupled with the four-dimensional Einstein gravity in the minimal manner supports such a background with the Euclidean anti-de Sitter metric.

  4. BOOK REVIEW: Renormalization Methods---A Guide For Beginners (United States)

    Cardy, J.


    The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard phi4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent

  5. Renormalization group flow of f(R) gravity (United States)

    Machado, Pedro F.; Saueressig, Frank


    We use the functional renormalization group equation for quantum gravity to construct a nonperturbative flow equation for modified gravity theories of the form S=∫ddxgf(R). Based on this equation we show that certain gravitational interaction monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The nonperturbative RG flow of nonlocal extensions of the Einstein-Hilbert truncation including ∫ddxgln⁡(R) and ∫ddxgR-n interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some R-n truncations all physical trajectories emanate from a non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the ln⁡(R) truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.

  6. Cyclic renormalization and automorphism groups of rooted trees

    CERN Document Server

    Bass, Hyman; Rockmore, Daniel; Tresser, Charles


    The theme of the monograph is an interplay between dynamical systems and group theory. The authors formalize and study "cyclic renormalization", a phenomenon which appears naturally for some interval dynamical systems. A possibly infinite hierarchy of such renormalizations is naturally represented by a rooted tree, together with a "spherically transitive" automorphism; the infinite case corresponds to maps with an invariant Cantor set, a class of particular interest for its relevance to the description of the transition to chaos and of the Mandelbrot set. The normal subgroup structure of the automorphism group of such "spherically homogeneous" rooted trees is investigated in some detail. This work will be of interest to researchers in both dynamical systems and group theory.

  7. Renormalization out of equilibrium in a superrenormalizable theory

    CERN Document Server

    Garny, Mathias


    We discuss the renormalization of the initial value problem in Nonequilibrium Quantum Field Theory within a simple, yet instructive, example and show how to obtain a renormalized time evolution for the two-point functions of a scalar field and its conjugate momentum at all times. The scheme we propose is applicable to systems that are initially far from equilibrium and compatible with non-secular approximation schemes which capture thermalization. It is based on Kadanoff-Baym equations for non-Gaussian initial states, complemented by usual vacuum counterterms. We explicitly demonstrate how various cutoff-dependent effects peculiar to nonequilibrium systems, including time-dependent divergences or initial-time singularities, are avoided by taking an initial non-Gaussian three-point vacuum correlation into account.

  8. More on the renormalization group limit cycle in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Evgeny Epelbaum; Hans-Werner Hammer; Ulf-G. Meissner; Andreas Nogga


    We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. We show that small increases in the up and down quark masses, corresponding to a pion mass around 200 MeV, can move QCD to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. At next-to-leading order in the chiral counting, we find three parameter sets where this effect occurs. For one of them, we study the structure of the three-nucleon system using both chiral and contact effective field theories in detail. Furthermore, we calculate the influence of the limit cycle on scattering observables.

  9. E-cigarette marketing and older smokers: road to renormalization. (United States)

    Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas


    To describe older smokers' perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking.

  10. Computing the effective action with the functional renormalization group

    Energy Technology Data Exchange (ETDEWEB)

    Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)


    The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 0} can be obtained by integrating the flow equation from an ultraviolet scale k = Λ down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. (orig.)

  11. A functional renormalization method for wave propagation in random media (United States)

    Lamagna, Federico; Calzetta, Esteban


    We develop the exact renormalization group approach as a way to evaluate the effective speed of the propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a non equilibrium field theory one, and then consider a sequence of models with a progressively lower infrared cutoff; in the limit where the cutoff is removed we recover the problem of interest. As a test of the formalism, we compute the effective dielectric constant of an homogeneous medium interspersed with randomly located, interpenetrating bubbles. A simple approximation to the renormalization group equations turns out to be equivalent to a self-consistent two-loops evaluation of the effective dielectric constant.

  12. Holographic entanglement entropy of N =2* renormalization group flow (United States)

    Pang, Da-Wei


    The N =2* theory is obtained by deforming N =4 supersymmetric Yang-Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the N =2* theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large R behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where R denotes the size of the entangling region. A term proportional to 1 /R is found for both cases, which can be attributed to the emergent CFT5 in the IR.

  13. The proton-proton scattering without Coulomb force renormalization

    Directory of Open Access Journals (Sweden)

    Glöckle W.


    Full Text Available We demonstrate numerically that proton-proton (pp scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. We numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS equation for an exponentially screened Coulomb potential. For the limit of large screening radii we confirm analytically predicted properties for off-shell, half-shell and on-shell elements of the Coulomb t-matrix.

  14. BPHZ renormalization in configuration space for the A4-model

    Directory of Open Access Journals (Sweden)

    Steffen Pottel


    Full Text Available Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.

  15. Ising Spin Glasses and Renormalization Group Theory: the Binder cumulant


    Lundow, P. H.; Campbell, I. A.


    Numerical data on scaling of the normalized Binder cumulant and the normalized correlation length are shown for the Thermodynamic limit regime, first for canonical Ising ferromagnet models and then for a range of Ising spin glass models. A fundamental Renormalization Group Theory rule linking the critical exponents for the two observables is well obeyed in the Ising models, but not for the Ising spin glasses in dimensions three and four. We conclude that there is a violation of a standard Jos...

  16. Charge renormalization for effective interactions of colloids at water interfaces


    Frydel, D.; Dietrich, S.; Oettel, M.


    We analyze theoretically the electrostatic interaction of surface-charged colloids at water interfaces with special attention to the experimentally relevant case of large charge densities on the colloid-water interface. Whereas linear theory predicts an effective dipole potential the strength of which is proportional to the square of the product of charge density and screening length, nonlinear charge renormalization effects change this dependence to a weakly logarithmic one. These results ap...

  17. Renormalization group method for Farley-Buneman fluctuations: basic results

    Directory of Open Access Journals (Sweden)

    A. M. Hamza


    Full Text Available Sudan and Keskinen in [1979] derived a set of equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the E x B or gradient-drift instability. This problem is of fundamental importance in ionospheric physics. The nonlinear nature of the equations makes it very hard to write a closed form solution. In this paper we propose to use 'Dynamical Renormalization Group' methods to study the long-- wavelength, long-time behaviour of density correlations generated in this ionospheric plasma stirred by a Gaussian random force characterized by a correlation function (fk fk k. The effect of the small scales on the large scale dynamics in the limit k -> 0 and infinite 'Reynolds' number, can be expressed in the form of renormalized coefficients; in our case renormalized diffusion. If one assumes the power spectra to be given by the kolmogorov argument of cascading of energy, then one can not only derive a subgrid model based on the results of RNG, and this has been done by Hamza and Sudan [1995], but one can also extract the skewness of the spectra as we do in this paper.

  18. Renormalized spacetime is two-dimensional at the Planck scale

    CERN Document Server

    Padmanabhan, T; Kothawala, Dawood


    Quantum field theory distinguishes between the bare variables -- which we introduce in the Lagrangian -- and the renormalized variables which incorporate the effects of interactions. This suggests that the renormalized, physical, metric tensor of spacetime (and all the geometrical quantities derived from it) will also be different from the bare, classical, metric tensor in terms of which the bare gravitational Lagrangian is expressed. We provide a physical ansatz to relate the renormalized metric tensor to the bare metric tensor such that the spacetime acquires a zero-point-length $\\ell _{0}$ of the order of the Planck length $L_{P}$. This prescription leads to several remarkable consequences. In particular, the Euclidean volume $V_D(\\ell,\\ell _{0})$ in a $D$-dimensional spacetime of a region of size $\\ell $ scales as $V_D(\\ell, \\ell_{0}) \\propto \\ell _{0}^{D-2} \\ell^2$ when $\\ell \\sim \\ell _{0}$, while it reduces to the standard result $V_D(\\ell,\\ell _{0}) \\propto \\ell^D$ at large scales ($\\ell \\gg \\ell _{0}...

  19. Power counting and Wilsonian renormalization in nuclear effective field theory (United States)

    Valderrama, Manuel Pavón


    Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

  20. One-loop renormalization of a gravity-scalar system

    Energy Technology Data Exchange (ETDEWEB)

    Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)


    Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the ''mass'' term. One-loop calculations lead to renormalization of the cosmological and Newton constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information. (orig.)

  1. Finite-time stability and finite-time stabilization (United States)

    Bhat, Sanjay Purushottam

    While non-Lipschitzian effects such as Coulomb friction abound in nature, most of the available techniques for feedback stabilization yield closed-loop systems with Lipschitzian dynamics. The convergence in such systems is at best exponential with infinite settling time. In this dissertation, we are interested in finite-settling-time behavior, that is, finite-time stability. The object of this dissertation is to provide a rigorous foundation for the theory of finite-time stability of continuous autonomous systems and motivate a closer examination of finite-time stability as a possible objective in control design. Accordingly, the notion of finite-time stability is precisely formulated and properties of the settling-time function are studied. Lyapunov and converse Lyapunov results involving scalar differential inequalities are obtained. It is shown that, under certain conditions, finite-time-stable systems possess better disturbance rejection and robustness properties. As an application of these ideas, we consider the finite-time stabilization of the translational and rotational double integrators. In the case of the rotational double integrator, the topology of the cylindrical state space renders continuous global stabilization impossible and hence the closed-loop system possesses saddle points. Because of the non-Lipschitzian character of the feedback law, these saddle points are, in fact, finite-time repellers--equilibria from which solutions can spontaneously and unpredictably depart. It is generally believed that models obtained from classical dynamics are completely deterministic. We present a counterexample to this widely held notion. The counterexample consists of a particle moving along a nonsmooth (once, but not twice, differentiable) constraint in a uniform gravitational field. The equation of motion obtained by applying classical Lagrangian dynamics contains non-Lipschitzian terms and, consequently, the dynamics of the system exhibit a finite-time saddle

  2. Quantum renormalization group approach to quantum coherence and multipartite entanglement in an XXZ spin chain

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)


    We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.

  3. Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)


    We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.

  4. Setting the renormalization scale in pQCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

    Energy Technology Data Exchange (ETDEWEB)

    Ma, Hong -Hao [Chongqing Univ., Chongqing (People' s Republic of China); Wu, Xing -Gang [Chongqing Univ., Chongqing (People' s Republic of China); Ma, Yang [Chongqing Univ., Chongqing (People' s Republic of China); Brodsky, Stanley J. [Stanford Univ., Stanford, CA (United States); Mojaza, Matin [KTH Royal Inst. of Technology and Stockholm Univ., Stockholm (Sweden)


    A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R

  5. Finite-temperature study of eight-flavor SU(3) gauge theory

    CERN Document Server

    Schaich, David; Rinaldi, Enrico


    We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 \\lesssim 20$ on lattice volumes as large as $48^3 \\times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.

  6. Renormalization group methods in subsurface hydrology: overview and applications in hydraulic conductivity upscaling (United States)

    Hristopulos, Dionissios T.


    The renormalization group (RG) approach is a powerful theoretical framework, more suitable for upscaling strong heterogeneity than low-order perturbation expansions. Applications of RG methods in subsurface hydrology include the calculation of (1) macroscopic transport parameters such as effective and equivalent hydraulic conductivity and dispersion coefficients, and (2) anomalous exponents characterizing the dispersion of contaminants due to long-range conductivity correlations or broad (heavy-tailed) distributions of the groundwater velocity. First, we review the main ideas of RG methods and their hydrological applications. Then, we focus on the hydraulic conductivity in saturated porous media with isotropic lognormal heterogeneity, and we present an RG calculation based on the replica method. The RG analysis gives rigorous support to the exponential conjecture for the effective hydraulic conductivity [Water Resour. Res. 19 (1) (1983) 161]. Using numerical simulations in two dimensions with a bimodal conductivity distribution, we demonstrate that the exponential expression is not suitable for all types of heterogeneity. We also introduce an RG coarse-grained conductivity and investigate its applications in estimating the conductivity of blocks or flow domains with finite size. Finally, we define the fractional effective dimension, and we show that it justifies fractal exponents in the range 1-2/ d⩽ α<1 (where d is the actual medium dimension) in the geostatistical power average.

  7. Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

    KAUST Repository

    Kumar, Manoranjan


    An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.

  8. Renormalized dynamics of the Dean-Kawasaki model (United States)

    Bidhoodi, Neeta; Das, Shankar P.


    We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ (x ,t ) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ . The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ ,θ } , linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D0 to DR is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997), 10.1007/s002570050396]. DR sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with DR=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.

  9. The density matrix renormalization group and nuclear structure

    Energy Technology Data Exchange (ETDEWEB)

    Pittel, S.; Thakur, B. [Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716 (United States); Sandulescu, N. [Institute of Physics and Nuclear Engineering, 76900 Bucharest (Romania)


    We briefly review the Density Matrix Renormalization Group (DMRG) method and its potential use in large-scale nuclear shell-model calculations. We propose the use of angular-momentum-conserving variant of the method (the JDMRG) and report the first test results of such an approach for the nucleus {sup 48}Cr The positive results of these calculations have motivated us to search for an even more efficient means of implementing the DMRG strategy and the status of these efforts is also described. (Author)

  10. (Non)-renormalization of the chiral vortical effect coefficient

    Energy Technology Data Exchange (ETDEWEB)

    Golkar, Siavash; Son, Dam T. [Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago,5640 South Ellis Ave., Chicago, IL 60637 (United States)


    We show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D, dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula ∑{sub n=1}{sup ∞}n=−1/12. We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large N limit.

  11. Renormalization and applications of baryon distribution amplitudes QCD

    Energy Technology Data Exchange (ETDEWEB)

    Rohrwild, Juergen Holger


    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N{sup *} distribution amplitudes. (orig.)

  12. Renormalization and applications of baryon distribution amplitudes in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Rohrwild, Juergen Holger


    Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N* distribution amplitudes. (orig.)

  13. Tensor renormalization group analysis of CP(N-1) model

    CERN Document Server

    Kawauchi, Hikaru


    We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\\theta$-term is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$. The numerical computation including the $\\theta$-term is left for future challenges.

  14. Entanglement renormalization, quantum error correction, and bulk causality

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Isaac H. [IBM T.J. Watson Research Center,1101 Kitchawan Rd., Yorktown Heights, NY (United States); Kastoryano, Michael J. [NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen (Denmark)


    Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

  15. Perturbative dynamics of open quantum systems by renormalization group method (United States)

    Kukita, Shingo


    We analyze perturbative dynamics of a composite system consisting of a quantum mechanical system and an environment by the renormalization group (RG) method. The solution obtained from the RG method has no secular terms and approximates the exact solution for a long time interval. Moreover, the RG method causes a reduction of the dynamics of the composite system under some assumptions. We show that this reduced dynamics is closely related to a quantum master equation for the quantum mechanical system. We compare this dynamics with the exact dynamics in an exactly solvable spin-boson model.

  16. Renormalizing the kinetic energy operator in elementary quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Coutinho, F A B [Faculdade de Medicina, Universidade de Sao Paulo e LIM 01-HCFMUSP, 05405-000 Sao Paulo (Brazil); Amaku, M [Faculdade de Medicina Veterinaria e Zootecnia, Universidade de Sao Paulo, 05508-970 Sao Paulo (Brazil)], E-mail:


    In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form {psi}(r) = u(r)/r, where u(0) {ne} 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

  17. Renormalization of Long Wavelength Spin Waves in the 2d Ferromagnet Rb2CrCl4

    DEFF Research Database (Denmark)

    Lindgård, Per-Anker; Als-Nielsen, Jens Aage; Hutchings, M. T.


    Rb2CrCl4 is a nearly 2d-ferromagnetic, optically transparent insulator isomorphous with K2CuF4. High resolution neutron scattering data for temperatures below Tc = 52.4 K of the low energy long wavelength spin waves are presented and a Hartree-Fock analysis yields Hamiltonian parameters and accou......Rb2CrCl4 is a nearly 2d-ferromagnetic, optically transparent insulator isomorphous with K2CuF4. High resolution neutron scattering data for temperatures below Tc = 52.4 K of the low energy long wavelength spin waves are presented and a Hartree-Fock analysis yields Hamiltonian parameters...... and accounts for the renormalization. No evidence of a Bose condensate is found. A spin canting angle θ ≈ 2° is predicted....

  18. Unitary networks from the exact renormalization of wave functionals (United States)

    Fliss, Jackson R.; Leigh, Robert G.; Parrikar, Onkar


    The exact renormalization group (ERG) for O (N ) vector models (at large N ) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on AdSd +1. This was established in the sense that at large N the generating functional of correlation functions of single-trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the O (N ) vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared recently in holographic contexts. In particular, the ERG tensor network appears to share the general structure of cMERA but differs in important ways. We comment on possible holographic implications.

  19. Nonperturbative Renormalization Group and Bose-Einstein Condensation (United States)

    Blaizot, Jean-Paul

    These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature T_c of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have been discussed at this school on effective theories and renormalization group. Effective theories are used first in order to obtain a simple hamiltonian describing the atomic interactions: because the typical atomic interaction potentials are short range, and the systems that we consider are dilute, these potentials can be replaced by a contact interaction whose strength is determined by the s-wave scattering length. Effective theories are used next in order to obtain a simple formula for the shift in T_c: this comes from the fact that near T_c the physics is dominated by low momentum modes whose dynamics is most economically described in terms of classical fields. The ingredients needed to calculate the shift of T_c can be obtained from this classical field theory. Finally the renormalization group is used both to obtain a qualitative understanding, and also as a non perturbative tool to evaluate quantitatively the shift in T_c.

  20. Holographic renormalization group and cosmology in theories with quasilocalized gravity

    Energy Technology Data Exchange (ETDEWEB)

    Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John


    We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.

  1. Spatial dependence of entanglement renormalization in XY model (United States)

    Usman, M.; Ilyas, Asif; Khan, Khalid


    In this article, a comparative study of the renormalization of entanglement in one-, two- and three-dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the quantum renormalization group (QRG) method using numerical techniques. Adopting the Kadanoff's block approach, numerical results for the concurrence are obtained for the spin {-}1/2 XY model in all the spatial dimensions. The results show similar qualitative behavior as we move from the lower to the higher dimensions in space, but the number of iterations reduces for achieving the QPT in the thermodynamic limit. We find that in the two-dimensional and three-dimensional spin {-}1/2 XY model, maximum value of the concurrence reduce by the factor of 1 / n (n=2,3) with reference to the maximum value of one-dimensional case. Moreover, we study the scaling behavior and the entanglement exponent. We compare the results for one-, two- and three-dimensional cases and illustrate how the system evolves near the critical point.

  2. Two-loop renormalization in the standard model, part I. Prolegomena

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)


    In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)

  3. Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions

    DEFF Research Database (Denmark)

    Altenkamp, Lukas; Dittmaier, Stefan; Rzehak, Heidi


    . The renormalization group equations for the M S ¯ parameters are solved in each scheme, so that a consistent renormalization scale variation can be performed. We have implemented all Feynman rules including counterterms and the renormalization conditions into a FeynArts model file, so that amplitudes and squared...

  4. Algebraic renormalization perturbative twisted considerations on topological Yang-Mills theory and on N=2 supersymmetric gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Fucito, F.; Tanzini, A. [Rome Univ. 2 (Italy). Dipt. di Fisica; Vilar, L.C.Q.; Ventura, O.S.; Sasaki, C.A.G. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Sorella, S.P. [Universidade do Estado (UERJ), Rio de Janeiro, RJ (Brazil). Inst. de Fisica


    The aim of these notes is to provide a simple and pedagogical (as much as possible) introduction to what is nowadays commonly called Algebraic Renormalization. As the same itself let it understand, the Algebraic Renormalization gives a systematic set up in order to analyse the quantum extension of a given set of classical symmetries. The framework is purely algebraic, yielding a complete characterization of all possible anomalies and invariant counterterms without making use of any explicit computation of the Feynman diagrams. This goal is achieved by collecting, with the introduction of suitable ghost fields, all the symmetries into a unique operation summarized by a generalized Slavnov-Taylor (or master equation) identity which is the starting point for the quantum analysis. The Slavnov-Taylor identity allows to define a nilpotent operator whose cohomology classes in the space of the integrated local polynomials in the fields and their derivatives with dimensions bounded by power counting give all nontrivial anomalies and counterterms. I other words, the proof of the renormalizability is reduced to the computation of some cohomology classes. (author) 28 refs., 2 figs.

  5. Low-energy. beta. -function in a finite super-Yang-Mills model with multiple mass scales

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.; Helayel-Neto, J.A. (International Centre for Theoretical Physics, Trieste (Italy))


    We compute the one-loop contribution to the low-energy light-fermion gauge coupling in a finite supersymmetric gauge theory with two mass scales: a heavy mass that breaks an initial N=4 supersymmetry down to N=2, but respects the finiteness, and a light mass that, for simplicity, is set to zero. We find that coupling grows with the mass of the heavy intermediate states. Hence the latter do not decouple at low energies, leading to large logarithms that invalidate low-energy perturbation theory. Consequently, further manipulations are required to obtain a meaningful perturbative expansion. Enforcing decoupling through finite renormalizations, that absorb the heavy mass effects into a redefinition of the parameters of the lagrangian, introduces an arbitrary subtraction mass The requirement that the S-matrix elements be independent of leads to a non-trivial renormalization-group equation for the low-energy theory, with a non-vanishing ..beta..-function.

  6. Dimension 7 operators in the b{yields}s transition

    Energy Technology Data Exchange (ETDEWEB)

    Chalons, G. [Karlsruhe Univ. (T.H.) (Germany). Inst. fuer Theoretische Teilchenphysik; Domingo, F. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)


    We extend the low-energy effective field theory relevant for b{yields}s transitions up to operators of mass-dimension 7 and compute the associated anomalous-dimension matrix. We then compare our findings to the known results for dimension 6 operators and derive a solution for the renormalization group equations involving operators of dimension 7. We finally apply our analysis to a particularly simple case where the Standard Model is extended by an electroweak-magnetic operator and consider limits on this scenario from the decays B{sub s}{yields}{mu}{sup +}{mu}{sup -} and B{yields}K{nu} anti {nu}.

  7. Resummation and renormalization in effective theories of particle physics

    CERN Document Server

    Jakovac, Antal


    Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to vario...

  8. Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory

    Directory of Open Access Journals (Sweden)

    Jutho Haegeman


    Full Text Available We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a “half-shift”: translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

  9. Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory (United States)

    Haegeman, Jutho; Swingle, Brian; Walter, Michael; Cotler, Jordan; Evenbly, Glen; Scholz, Volkher B.


    We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

  10. Extracting Supersymmetry-Breaking Effects from Wave-Function Renormalization

    CERN Document Server

    Giudice, Gian Francesco


    We show that in theories in which supersymmetry breaking is communicated by renormalizable perturbative interactions, it is possible to extract the soft terms for the observable fields from wave-function renormalization. Therefore all the information about soft terms can be obtained from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram. This method greatly simplifies calculations which are rather involved if performed in terms of component fields. For illustrative purposes we reproduce known results of theories with gauge-mediated supersymmetry breaking. We then use our method to obtain new results of phenomenological importance. We calculate the next-to-leading correction to the Higgs mass parameters, the two-loop soft terms induced by messenger-matter superpotential couplings, and the soft terms generated by messengers belonging to vector supermultiplets.

  11. Functional renormalization group study of the Anderson-Holstein model (United States)

    Laakso, M. A.; Kennes, D. M.; Jakobs, S. G.; Meden, V.


    We present a comprehensive study of the spectral and transport properties in the Anderson-Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron-phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson-Holstein quantum dot and find clear signatures of the presence of the phonon mode.

  12. Renormalization Group Running of Newton's G: The Static Isotropic Case

    CERN Document Server

    Hamber, H W; Hamber, Herbert W.; Williams, Ruth M.


    Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is argued, related to the observed effective cosmological constant. Several analogies between the proposed vacuum condensate picture of quantum gravitation, and non-perturbative aspects of vacuum condensation in strongly coupled non-abelian gauge theories are developed. In contrast to phenomenological approaches, the underlying functional integral formulation of the theory severely constrains possible scenarios for the renormalization group evolution of couplings. The expected running of Newton's constant $G$ is compared to known vacuum polarization induced effects in QED and QCD. The general analysis is then extended to a set of covariant non-local effective field equati...

  13. Anomalous contagion and renormalization in networks with nodal mobility (United States)

    Manrique, Pedro D.; Qi, Hong; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F.


    A common occurrence in everyday human activity is where people join, leave and possibly rejoin clusters of other individuals —whether this be online (e.g. social media communities) or in real space (e.g. popular meeting places such as cafes). In the steady state, the resulting interaction network would appear static over time if the identities of the nodes are ignored. Here we show that even in this static steady-state limit, a non-zero nodal mobility leads to a diverse set of outbreak profiles that is dramatically different from known forms, and yet matches well with recent real-world social outbreaks. We show how this complication of nodal mobility can be renormalized away for a particular class of networks.

  14. Improved quasi parton distribution through Wilson line renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Jiunn-Wei [Department of Physics, Center for Theoretical Sciences, and Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 106, Taiwan (China); Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Ji, Xiangdong [INPAC, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240 (China); Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Zhang, Jian-Hui, E-mail: [Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg (Germany)


    Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV) power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a “mass” counterterm in the auxiliary z-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.

  15. Dimensional reduction of Markov state models from renormalization group theory. (United States)

    Orioli, S; Faccioli, P


    Renormalization Group (RG) theory provides the theoretical framework to define rigorous effective theories, i.e., systematic low-resolution approximations of arbitrary microscopic models. Markov state models are shown to be rigorous effective theories for Molecular Dynamics (MD). Based on this fact, we use real space RG to vary the resolution of the stochastic model and define an algorithm for clustering microstates into macrostates. The result is a lower dimensional stochastic model which, by construction, provides the optimal coarse-grained Markovian representation of the system's relaxation kinetics. To illustrate and validate our theory, we analyze a number of test systems of increasing complexity, ranging from synthetic toy models to two realistic applications, built form all-atom MD simulations. The computational cost of computing the low-dimensional model remains affordable on a desktop computer even for thousands of microstates.

  16. Renormalization group flows of the N -component Abelian Higgs model (United States)

    Fejős, G.; Hatsuda, T.


    Flows of the couplings of a theory of an N -component (complex) scalar field coupled to electrodynamics are investigated using the functional renormalization group formalism in d dimensions in covariant gauges. We find charged fixed points for any number of components in d =3 , in accordance with the findings of [G. Fejos and T. Hatsuda, Phys. Rev. D 93, 121701 (2016), 10.1103/PhysRevD.93.121701] for N =1 . It is argued that the appropriate choice of the regulator matrix is indispensable to obtain such a result. Ward-Takahashi identities are analyzed in the presence of the regulator, and their compatibility with the flow equation is investigated in detail.

  17. Renormalized stress-energy tensor for stationary black holes

    CERN Document Server

    Levi, Adam


    We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the $t$-splitting variant of the method, which was first presented for $\\left\\langle\\phi^{2}\\right\\rangle_{ren}$, to compute the RSET in a stationary, asymptotically-flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally-coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.

  18. High Precision Renormalization Group Study of the Roughening Transition

    CERN Document Server

    Hasenbusch, M; Pinn, K


    We confirm the Kosterlitz-Thouless scenario of the roughening transition for three different Solid-On-Solid models: the Discrete Gaussian model, the Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with standard (cosine) action. The method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are performed using efficient cluster algorithms. We obtain high precision estimates for the critical couplings and other non-universal quantities. For the XY model with cosine action our critical coupling estimate is $\\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and $K_R^{ASOS}=0.8061(3)$, respectively.

  19. Holographic Renormalization of general dilaton-axion gravity

    CERN Document Server

    Papadimitriou, Ioannis


    We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Improved Holographic QCD with arbitrary dilaton potential. In particular, we derive the generalized Fefferman-Graham asymptotic expansions and provide a proof of the holographic Ward identities.

  20. Momentum-subtraction renormalization techniques in curved space-time

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.


    Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.

  1. Assessing notions of denormalization and renormalization of smoking in light of e-cigarette regulation. (United States)

    Sæbø, Gunnar; Scheffels, Janne


    The rationale for 'denormalization' of smoking in tobacco policies has been challenged by the emergence of e-cigarettes and the need to regulate e-cigarette use and promotion. Our aim is to assess the research status on e-cigarettes' contribution to 'renormalization' of smoking and to clarify how renormalization of smoking can be appraised at the conceptual and empirical level. Combining conceptual analysis and narrative review, the paper brings out three dimensions of denormalization/renormalization of smoking ('unacceptability/acceptability'; 'invisibility/visibility'; 'phasing out behaviour/maintaining behaviour') and an inherent duality of the e-cigarette as a smoking-like device and a smoking alternative. These analytical dimensions are applied qualitatively to consider the literature identified by searching the Web of Science database for 'e-cigarettes AND renormalization' (and variants thereof). Theoretically, normative changes in smoking acceptability, increased visibility of e-cigarettes and use, and observations of actual use (prevalence, dual use, gateway) can all be applied to illustrate processes of renormalization. However, only acceptability measures and user measures can be said to be empirical tests of renormalization effects. Visibility measures are only based on logical assumptions of a possible renormalization; they are not in themselves indicative of any "real" renormalization effects and can just as well be understood as possible consequences of normalization of e-cigarettes. Just as a downward trend in smoking prevalence is the litmus test of whether denormalization policy works, stagnating or rising smoking prevalence should be the main empirical indicator of renormalization. Copyright © 2017 Elsevier B.V. All rights reserved.

  2. Renormalization of massive Feynman amplitudes and homogeneity (based on a joint work with Raymond Stora)

    Energy Technology Data Exchange (ETDEWEB)

    Nikolov, Nikolay M., E-mail:


    We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which characterize the presence of additional scales due to renormalization, to the massive case.

  3. Renormalizations in supersymmetric and nonsupersymmetric non-abelian Chern-Simons field theories with matter (United States)

    Avdeev, L. V.; Kazakov, D. I.; Kondrashuk, I. N.


    We explicitly carry out the renormalization of non-abelian Chern-Simons field theories with matter in (2 + 1) dimensions. All the renormalization constants are calculated to the leading two-loop order both in terms of component fields and N = 1 superfields for the fundamental representation of the SU( n), Sp( n) and SO( n) groups. Renormalization-group fixed points are found, and their stability properties are examined. It is shown that the N = 2 supersymmetry is realized as an infrared fixed-point solution, where the ultraviolet divergencies cancel.

  4. Renormalizations in supersymmetric and nonsupersymmetric non-abelian Chern-Simons field theories with matter

    Energy Technology Data Exchange (ETDEWEB)

    Avdeev, L.V.; Kazakov, D.I.; Kondrashuk, I.N. (Lab. of Theoretical Physics, Joint Inst. for Nuclear Research, Dubna (Russia))


    We explicitly carry out the renormalization of non-abelian Chern-Simons field theories with matter in (2+1) dimensions. All the renormalization constants are calculated to the leading two-loop order both in terms of component fields and N=1 superfields for the fundamental representation of the SU(n), Sp(n) and SO(n) groups. Renormalization-group fixed points are found, and their stability properties are examined. It is shown that the N=2 supersymmetry is realized as an infrared fixed-point solution, where the ultraviolet divergencies cancel. (orig.).

  5. Direct Observation of Electrostatically Driven Band Gap Renormalization in a Degenerate Perovskite Transparent Conducting Oxide

    Energy Technology Data Exchange (ETDEWEB)

    Lebens-Higgins, Z.; Scanlon, D. O.; Paik, H.; Sallis, S.; Nie, Y.; Uchida, M.; Quackenbush, N. F.; Wahila, M. J.; Sterbinsky, G. E.; Arena, Dario A.; Woicik, J. C.; Schlom, D. G.; Piper, L. F. J.


    We have directly measured the band gap renormalization associated with the Moss-Burstein shift in the perovskite transparent conducting oxide (TCO), La-doped BaSnO 3 , using hard x-ray photoelectron spectroscopy. We determine that the band gap renormalization is almost entirely associated with the evolution of the conduction band. Our experimental results are supported by hybrid density functional theory supercell calculations. We determine that unlike conventional TCOs where interactions with the dopant orbitals are important, the band gap renormalization in La - BaSnO 3 is driven purely by electrostatic interactions.

  6. Renormalization-group theory for the eddy viscosity in subgrid modeling (United States)

    Zhou, YE; Vahala, George; Hossain, Murshed


    Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

  7. A low-cost approach to electronic excitation energies based on the driven similarity renormalization group (United States)

    Li, Chenyang; Verma, Prakash; Hannon, Kevin P.; Evangelista, Francesco A.


    We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.

  8. Renormalized quark-antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD (United States)

    Głazek, Stanisław D.; Gómez-Rocha, María; More, Jai; Serafin, Kamil


    In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space-time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit-Fermi spin couplings in the effective quark-antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.

  9. The Γ-Limit of the Two-Dimensional Ohta-Kawasaki Energy. Droplet Arrangement via the Renormalized Energy (United States)

    Goldman, Dorian; Muratov, Cyrill B.; Serfaty, Sylvia


    This is the second in a series of papers in which we derive a Γ-expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small "droplets" of the minority phase in a "sea" of the majority phase. In our previous paper, we computed the Γ-limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order Γ-limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg-Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Thus, without appealing to the Euler-Lagrange equation, we establish for all configurations which have "almost minimal energy" the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of Γ-equivalence, the obtained results also yield an expansion of the minimal energy and a characterization of the zero super-level sets of the minimizers for the original Ohta-Kawasaki energy. This leads to the expectation of seeing triangular lattices of droplets as energy minimizers.

  10. Renormalization in the cauchy problem for the Korteweg-de Vries equation (United States)

    Zakharov, S. V.


    We consider the Cauchy problem for the Korteweg-de Vries equation with a small parameter at the highest derivative and a large gradient of the initial function. We construct an asymptotic solution of this problem by the renormalization method.

  11. Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation


    Zakharov, Sergei V.


    The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.

  12. Renormalization group flows for the second Z{sub 5} parafermionic field theory

    Energy Technology Data Exchange (ETDEWEB)

    Dotsenko, Vladimir S. [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589. Universite Pierre et Marie Curie, Paris VI (France) and CNRS, Universite Denis Diderot, Paris VII, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:; Estienne, Benoit [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589. Universite Pierre et Marie Curie, Paris VI (France) and CNRS, Universite Denis Diderot, Paris VII, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:


    Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry Z{sub 5}. New fixed points are found and classified.

  13. Renormalizations in softly broken N = 1 theories: Slavnov-Taylor identities (United States)

    Kondrashuk, Igor


    Slavnov-Taylor identities have been applied to perform explicitly the renormalization procedure for the softly broken N = 1 SYM. The result is in accordance with the previous results obtained at the level of the supergraph technique.

  14. Renormalizations in softly broken N=1 theories: Slavnov-Taylor identities


    Kondrashuk, Igor


    Slavnov-Taylor identities have been applied to perform explicitly the renormalization procedure for the softly broken N=1 SYM. The result is in accordance with the previous results obtained at the level of supergraph technique.

  15. Renormalizations in softly broken N=1 theories: Slavnov-Taylor identities

    Energy Technology Data Exchange (ETDEWEB)

    Kondrashuk, Igor [SISSA-ISAS and INFN, Sezione di Trieste, Trieste (Italy)]. E-mail:


    Slavnov-Taylor identities have been applied to perform explicitly the renormalization procedure for the softly broken N=1 SYM. The result is in accordance with the previous results obtained at the level of the supergraph technique. (author)

  16. yield indicators

    African Journals Online (AJOL)

    YIELD INDICATORS. P. NTAWURUHUNGA, P.R. RUBAIHAYOI, J.B.A. WHYTE, A.G.O. DIXONZ and use. osnzu1. International Institute of Tropical Agriculture, East and Southern Africa, Centre, PO. Box 7878, l Kampala ... most important sources of food energy in several ... efficiency in selecting and identifying cassava.

  17. Finite BRST Mapping in Higher-Derivative Models (United States)

    Moshin, Pavel Yu.; Upadhyay, Sudhaker; Castro, Ricardo A.


    We continue the study of finite field-dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry is then applied to a number of well-established quantum gauge theories in a form which incudes higher-derivative terms. Specifically, we examine the corresponding versions of the Maxwell theory, non-Abelian vector field theory, and gravitation theory. We present a systematic mapping between different forms of gauge-fixing, including those with higher-derivative terms, for which these theories have better renormalization properties. In doing so, we also provide the independence of the S-matrix from a particular gauge-fixing with higher derivatives. Following this method, a higher-derivative quantum action can be constructed for any gauge theory in the FFBRST framework.

  18. Accuracy of topological entanglement entropy on finite cylinders. (United States)

    Jiang, Hong-Chen; Singh, Rajiv R P; Balents, Leon


    Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.

  19. Renormalization of domain-wall bilinear operators with short-distance current correlators (United States)

    Tomii, M.; Cossu, G.; Fahy, B.; Fukaya, H.; Hashimoto, S.; Kaneko, T.; Noaki, J.; Jlqcd Collaboration


    We determine the renormalization constants for flavor nonsinglet fermion bilinear operators of Möbius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the nonperturbative lattice calculation reproduces the perturbatively calculated counterpart at short distances. The perturbative expansion is precise as the coefficients are available up to O (αs4). We employ 2 +1 -flavor lattice ensembles at three lattice spacings in the range 0.044-0.080 fm.

  20. Dirac relation and renormalization group equations for electric and magnetic fine structure constants

    CERN Document Server

    Laperashvili, L V


    The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $\\alpha $ and magnetic $\\tilde \\alpha $ - were obtained. It was shown that the Dirac relation is valid for the renormalized $\\alpha $ and $\\tilde perturbatively only in the small region: $0.25 \\stackrel{<}{\\sim} \\alpha, relation: $\\alpha {\\tilde \\alpha} = \\frac 14 $.

  1. Nuclear Spectroscopy with the In-Medium Similarity Renormalization Group (United States)

    Parzuchowski, Nathan Michael

    The in-medium similarity renormalization group (IMSRG) is an ab initio many-body method which features soft polynomial scaling with system size and a Hermitian framework to create Hamiltonians tailored for use with low-level approximations such as Hartree-Fock (HF) theory or the random phase approximation (RPA). The flexibility that comes with these characteristics has made the IMSRG a mainstay in contemporary nuclear structure theory. However, spectroscopy with IMSRG calculations has been limited to scalar observables in nuclei accessible with shell model machinery, where the IMSRG is used to construct effective valence-space interactions. In this thesis, we present two novel developments which have greatly extended the IMSRG's capability to perform spectroscopic calculations. First is the introduction of the equations-of-motion IMSRG (EOM-IMSRG), which uses an approximate, but systematically improvable diagonalization scheme in conjunction with the IMSRG to produce spectra and wave functions. The method does not suffer the model-space limitations of the shell model, but sacrifices some accuracy due to the approximate diagonalization. We benchmark this new method with the well established equations-of-motion coupled cluster and full configuration interaction methods, where we demonstrate that the method is indeed viable for closed-shell systems, encouraging expansion to open shells using a multireference formalism. We also introduce a perturbative framework to add systematic corrections to the EOM-IMSRG, showing results for closed shell nuclei and quantum dots. The second development is a generalized effective operator formalism for the IMSRG, capable of consistently evolving non-scalar operators relevant for electroweak transitions and moments. This general framework is applicable to both the EOM-IMSRG and the valence-space IMSRG approaches. We benchmark electromagnetic transition strengths and moments using both of these methods, also comparing with the quasi

  2. All-order renormalization of propagator matrix for fermionic system with flavor mixing

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics


    We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.

  3. Anatomy of the magnetic catalysis by renormalization-group method

    Directory of Open Access Journals (Sweden)

    Koichi Hattori


    Full Text Available We first examine the scaling argument for a renormalization-group (RG analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger–Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu–Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

  4. Quantum renormalization group for ground-state fidelity (United States)

    Langari, A.; Rezakhani, A. T.


    Ground-state fidelity (GSF) and quantum renormalization group (QRG) theory have proven to be useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method for calculating GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances the characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field (ITF) and the anisotropic spin-1/2 Heisenberg (XXZ) model. Explicitly, we find the scaling behavior of the GSF for the ITF model in both small- and large-size limits, the corresponding critical exponents, the exact value of the GSF in the thermodynamic limit and a closed form for the GSF for arbitrary size and system parameters. In the case of the XXZ model, we also present an analytic expression for the GSF, which captures well the criticality of the model, hence excluding doubts that GSF might be an insufficient tool for signaling criticality in this model.

  5. Driven similarity renormalization group: Third-order multireference perturbation theory. (United States)

    Li, Chenyang; Evangelista, Francesco A


    A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N(6)) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F2, H2O2, C2H6, and N2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (ΔST=ET-ES) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic ΔST is 3.9 kcal mol(-1), a value that is within 0.1 kcal mol(-1) from multireference coupled cluster results.

  6. Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model

    Energy Technology Data Exchange (ETDEWEB)

    Friederich, Simon


    Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)

  7. Anatomy of the magnetic catalysis by renormalization-group method (United States)

    Hattori, Koichi; Itakura, Kazunori; Ozaki, Sho


    We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu-Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.

  8. Finite volume treatment of $\\pi\\pi$ scattering in the $\\rho$ channel

    CERN Document Server

    Albaladejo, M; Oller, J A; Roca, L


    We make a theoretical study of $\\pi\\pi$ scattering with quantum numbers $J^{PC}=1^{--}$ in a finite box. To calculate physical observables for infinite volume from lattice QCD, the finite box dependence of the potentials is not usually considered. We quantify such effects by means of two different approaches for vector-isovector $\\pi\\pi$ scattering based on Unitarized Chiral Perturbation Theory results: the Inverse Amplitude Method and another one based on the $N/D$ method. We take into account finite box effects stemming from higher orders through loops in the crossed $t,u-$channels as well as from the renormalization of the coupling constants. The main conclusion is that for $\\pi\\pi$ phase shifts in the isovector channel one can safely apply L\\"uscher based methods for finite box sizes of $L$ greater than $2 m_\\pi^{-1}$.

  9. Finite Coverings by Cones

    NARCIS (Netherlands)

    Tijs, S.H.; Reijnierse, J.H.


    This paper considers analogues of statements concerning compactness and finite coverings, in which the roles of spheres are replaced by cones. Furthermore, one of the finite covering results provides an application in Multi-Objective Programming; infinite sets of alternatives are reduced to finite

  10. Automatic calculation of supersymmetric renormalization group equations and loop corrections (United States)

    Staub, Florian


    SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/ CompHep or FeynArts/ FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one- and two-loop level. Furthermore, it calculates the one-loop self-energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates. Program summaryProgram title: SARAH Catalogue identifier: AEIB_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, No. of lines in distributed program, including test data, etc.: 97 577 No. of bytes in distributed program, including test data, etc.: 2 009 769 Distribution format: tar.gz Programming language: Mathematica Computer: All systems that Mathematica is available for Operating system: All systems that Mathematica is available for Classification: 11.1, 11.6 Nature of problem: A supersymmetric model is usually characterized by the particle content, the gauge sector and the superpotential. It is a time consuming process to obtain all necessary information for phenomenological studies from these basic ingredients. Solution method: SARAH calculates the complete Lagrangian for a given model whose

  11. On higher order geometric and renormalization group flows (United States)

    Prabhu, Kartik; Das, Sanjit; Kar, Sayan


    Renormalization group (RG) flows of the bosonic nonlinear σ-model are governed, perturbatively, at different orders of α', by perturbatively evaluated β-functions. In regions where {α'}/{Rc2}≪1 ( {1}/{Rc2} represents the curvature scale), the flow equations at various orders in α' can be thought of as approximating the full, non-perturbative RG flow. On the other hand, taking a different viewpoint, we may consider the above-mentioned RG flow equations as viable geometric flows in their own right, without any reference to the RG aspect. Looked at as purely geometric flows where higher order terms appear, we no longer have the perturbative restrictions (small curvatures). In this paper, we perform our analysis from both these perspectives using specific target manifolds such as S2, H2, unwarped S2×H2 and simple warped products. We analyse and solve the higher order RG flow equations within the appropriate perturbative domains and find the corrections arising due to the inclusion of higher order terms. Such corrections, within the perturbative regime, are shown to be small and they provide an estimate of the error that arises when higher orders are ignored. We also investigate higher order geometric flows on the same manifolds and figure out generic features of geometric evolution, the appearance of singularities and solitons. The aim, in this context, is to demonstrate the role of higher order terms in modifying the flow. One interesting aspect of our analysis is that, separable solutions of the higher order flow equations for simple warped spacetimes (of the kind used in bulk-brane models with a single extra dimension), correspond to constant curvature anti de Sitter (AdS) spacetimes, modulo an overall flow parameter dependent scale factor. The functional form of this scale factor (that we obtain) changes on the inclusion of successive higher order terms in the flow.

  12. Random Vector and Matrix Theories: A Renormalization Group Approach (United States)

    Zinn-Justin, Jean


    Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly. However, the somewhat paradoxical situation is that either models can be solved exactly or little can be said. Since the solved models display critical points and universal properties, it is tempting to use renormalization group ideas to determine universal properties, without solving models explicitly. Initiated by Br\\'ezin and Zinn-Justin, the approach has led to encouraging results, first for matrix integrals and then quantum mechanics with matrices, but has not yet become a universal tool as initially hoped. In particular, general quantum field theories with matrix fields require more detailed investigations. To better understand some of the encountered difficulties, we first apply analogous ideas to the simpler O(N) symmetric vector models, models that can be solved quite generally in the large N limit. Unlike other attempts, our method is a close extension of Br\\'ezin and Zinn-Justin. Discussing vector and matrix models with similar approximation scheme, we notice that in all cases (vector and matrix integrals, vector and matrix path integrals in the local approximation), at leading order, non-trivial fixed points satisfy the same universal algebraic equation, and this is the main result of this work. However, its precise meaning and role have still to be better understood.

  13. Scaling and renormalization group in replica-symmetry-breaking space: evidence for a simple analytical solution of the Sherrington-Kirkpatrick model at zero temperature. (United States)

    Oppermann, R; Sherrington, D


    Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0infinity, where x/T --> a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.

  14. Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

    CERN Document Server

    Elizalde, E; Pozdeeva, E O; Vernov, S Yu


    The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, $n_s$ and $r$, are close to the corresponding ones in the $R^2$ and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.

  15. Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Elizalde, Emilio; Odintsov, Sergei D. [Instituto de Ciencias del Espacio (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Campus UAB, Carrer de Can Magrans, s/n, Cerdanyola del Vallès, Barcelona, 08193 Spain (Spain); Pozdeeva, Ekaterina O.; Vernov, Sergey Yu., E-mail:, E-mail:, E-mail:, E-mail: [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 (Russian Federation)


    The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, n{sub s} and r, are close to the corresponding ones in the R{sup 2} and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.

  16. One-loop renormalization of the NMSSM in SloopS. II. The Higgs sector (United States)

    Bélanger, G.; Bizouard, V.; Boudjema, F.; Chalons, G.


    We present a full one-loop renormalization of the Higgs sector of the next-to-minimal-supersymmetric-Standard-Model (NMSSM) and its implementation within sloops, a code for the automated computations of one-loop processes in theories beyond the Standard Model. The present work is the sequel to the study we performed on the renormalization of the sectors of the NMSSM comprising neutralinos, charginos, and sfermions, thereby completing the full one-loop renormalization of the NMSSM. We have investigated several renormalization schemes based on alternative choices (on-shell or DR ¯ ) of the physical parameters. Special attention is paid to the issue of the mixing between physical fields. To weigh the impact of the different renormalization schemes, the partial widths for the decays of the Higgs bosons into supersymmetric particles are computed at one loop. In many decays large differences between the schemes are found. We discuss the origin of these differences. In particular, we study two contrasting scenarios. The first model is MSSM-like with a small value for the mixing between the doublet and singlet Higgs superfields while the second model has a moderate value for this mixing. We critically discuss the issue of the reconstruction of the underlying parameters and their counterterms in the case of a theory with a large number of parameters, such as the NMSSM, from a set of physical parameters. In the present study this set corresponds to the minimum set of masses for the implementation of the on-shell schemes.

  17. Renormalization group calculations for wetting transitions of infinite order and continuously varying order: local interface Hamiltonian approach. (United States)

    Indekeu, J O; Koga, K; Hooyberghs, H; Parry, A O


    We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with β(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.

  18. Functional renormalization-group approach to the Pokrovsky-Talapov model via the modified massive Thirring fermions (United States)

    Nosov, P. A.; Kishine, Jun-ichiro; Ovchinnikov, A. S.; Proskurin, I.


    We consider a possibility of the topological Kosterlitz-Thouless (KT) transition in the two-dimensional Pokrovsky-Talapov model with a finite misfit parameter and discuss its relevance to the theory of critical behavior in thin films of monoaxial chiral helimagnets. For this purpose, the initial model is reformulated in terms of the two-dimensional relativistic model of massive Thirring fermions and the Wetterich's functional renormalization-group (RG) approach is employed. In the new formalism, the misfit parameter corresponds to an effective gauge field that can be included in the RG scheme on an equal footing with the other parameters of the theory. Our main result is that the presence of the misfit parameter, which may be attributed to the Dzyaloshinskii-Moriya interaction in the magnetic system, rules out the KT transition. To support this finding, we provide an additional intuitive explanation of the KT scenario breakdown by using the mapping onto the Coulomb gas model. In the framework of the model, the misfit parameter has a meaning of an effective in-plane electric field that prevents a formation of bound vortex-antivortex pairs.

  19. Carrier plasmon induced nonlinear band gap renormalization in two-dimensional semiconductors. (United States)

    Liang, Yufeng; Yang, Li


    In reduced-dimensional semiconductors, doping-induced carrier plasmons can strongly couple with quasiparticle excitations, leading to a significant band gap renormalization. However, the physical origin of this generic effect remains obscure. We develop a new plasmon-pole theory that efficiently and accurately captures this coupling. Using monolayer MoS(2) and MoSe(2) as prototype two-dimensional (2D) semiconductors, we reveal a striking band gap renormalization above 400 meV and an unusual nonlinear evolution of their band gaps with doping. This prediction significantly differs from the linear behavior that is observed in one-dimensional structures. Notably, our predicted band gap renormalization for MoSe(2) is in excellent agreement with recent experimental results. Our developed approach allows for a quantitative understanding of many-body interactions in general doped 2D semiconductors and paves the way for novel band gap engineering techniques.

  20. Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition (United States)

    José, Jorge V.


    In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

  1. Introduction to real-space renormalization-group methods in critical and chaotic phenomena (United States)

    Hu, Bambi


    The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. Seminal concepts such as scaling and universality, and their characterization by critical exponents are discussed. The basic ideas of the renormalization group are then explained. A survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given. The Hamiltonian formulation of classical statistical systems into quantum mechanical systems by the method of the transfer matrix is introduced. Quantum renormalization-group methods of truncation and projection, and their application to the transcribed quantum mechanical Ising model in a transverse field are illustrated. Finally, the quantum cumulant-expansion method as applied to the one-dimensional quantum mechanical XY model is discussed. The second part of the article is devoted to the subject of bifurcations and transitions to chaos. The three most commonly discussed kinds of bifurcations: the pitchfork, tangent and Hopf bifurcations, and the associated routes to chaos: period doubling, intermittency and quasiperiodicity are discussed. Period doubling based on the logistic map is explained in detail. Universality and its expression in terms of functional renormalization-group equations is discussed. The Liapunov characteristic exponent and its analogy to the order parameter are introduced. The effect of external noise and its universal scaling feature are shown. The simplest characterizations of the Hénon strange attractor are intuitively illustrated. The purpose of this article is primarily pedagogical. The similarity between critical and chaotic phenomena is a recurrent

  2. Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Di Giustino, Leonardo; /SLAC


    A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 2}): The purpose of the running coupling in any gauge theory is to sum all terms involving the {beta} function; in fact, when the renormalization scale is set properly, all non-conformal {beta} {ne} 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with {beta} = 0. The resulting scale-fixed predictions using the 'principle of maximum conformality' (PMC) are independent of the choice of renormalization scheme - a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD {beta} function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

  3. Renormalized molecular levels in a Sc3N@C-80 molecular electronic device

    DEFF Research Database (Denmark)

    Larade, Brian; Taylor, Jeremy Philip; Zheng, Q. R.


    We address several general questions about quantum transport through molecular systems by an ab initio analysis of a scandium-nitrogen doped C-80 metallofullerene device. Charge transfer from the Sc3N is found to drastically change the current-voltage characteristics: the current through the Sc3N...... @ C-80 device is double that through a bare C-80 device. We provide strong evidence that transport in such molecular devices is mediated by molecular electronic states which have been renormalized by the device environment, such as the electrodes and external bias V-b. The renormalized molecular...

  4. Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

    Energy Technology Data Exchange (ETDEWEB)

    Groh, Kai


    The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

  5. Periodically driven random quantum spin chains: real-space renormalization for Floquet localized phases (United States)

    Monthus, Cécile


    When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding strong disorder renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.

  6. Renormalization of gauge theories in the background-field approach arXiv

    CERN Document Server

    Barvinsky, Andrei O.; Herrero-Valea, Mario; Sibiryakov, Sergey M.; Steinwachs, Christian F.

    Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. In other words, the renormalization procedure for these gauge theories is compatible with their gauge invariance. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. We illustrate our general approach with several explicit examples.

  7. Finite element procedures

    CERN Document Server

    Bathe, Klaus-Jürgen


    Finite element procedures are now an important and frequently indispensable part of engineering analyses and scientific investigations. This book focuses on finite element procedures that are very useful and are widely employed. Formulations for the linear and nonlinear analyses of solids and structures, fluids, and multiphysics problems are presented, appropriate finite elements are discussed, and solution techniques for the governing finite element equations are given. The book presents general, reliable, and effective procedures that are fundamental and can be expected to be in use for a long time. The given procedures form also the foundations of recent developments in the field.

  8. Finite Discrete Gabor Analysis

    DEFF Research Database (Denmark)

    Søndergaard, Peter Lempel


    frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

  9. Fractional finite Fourier transform. (United States)

    Khare, Kedar; George, Nicholas


    We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

  10. Universal Finite Size Corrections and the Central Charge in Non-solvable Ising Models (United States)

    Giuliani, Alessandro; Mastropietro, Vieri


    We investigate a non-solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all and λ 0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.

  11. Finite-size scaling at quantum transitions (United States)

    Campostrini, Massimo; Pelissetto, Andrea; Vicari, Ettore


    We develop the finite-size scaling (FSS) theory at quantum transitions. We consider various boundary conditions, such as open and periodic boundary conditions, and characterize the corrections to the leading FSS behavior. Using renormalization-group (RG) theory, we generalize the classical scaling ansatz to describe FSS in the quantum case, classifying the different sources of scaling corrections. We identify nonanalytic corrections due to irrelevant (bulk and boundary) RG perturbations and analytic contributions due to regular backgrounds and analytic expansions of the nonlinear scaling fields. To check the general predictions, we consider the quantum XY chain in a transverse field. For this model exact or numerically accurate results can be obtained by exploiting its fermionic quadratic representation. We study the FSS of several observables, such as the free energy, the energy differences between low-energy levels, correlation functions of the order parameter, etc., confirming the general predictions in all cases. Moreover, we consider bipartite entanglement entropies, which are characterized by the presence of additional scaling corrections, as predicted by conformal field theory.

  12. Finite Control in Korean (United States)

    Lee, Kum Young


    This thesis explores finite control in Korean. An overview of the previous studies of control shows that the mainstream literature on control has consistently argued that referential dependence between an overt matrix argument and an embedded null subject is characteristic of non-finite clauses which contain a PRO subject. Moreover, although some…

  13. Finite Boltzmann schemes

    NARCIS (Netherlands)

    Sman, van der R.G.M.


    In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

  14. Designs and finite geometries

    CERN Document Server


    Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

  15. Finite Virtual State Machines


    Senhadji Navarro, Raouf; García Vargas, Ignacio


    This letter proposes a new model of state machine called Finite Virtual State Machine (FVSM). A memory-based architecture and a procedure for generating FVSM implementations from Finite State Machines (FSMs) are presented. FVSM implementations provide advantages in speed over conventional RAM-based FSM implementations. The results of experiments prove the feasibility of this approach.

  16. Renormalization-group calculations of ground-state and transport properties of ultrasmall tunnel junctions

    DEFF Research Database (Denmark)

    Frota, H.O.; Flensberg, Karsten


    We have done a numerical renormalization-group calculation for a Hamiltonian modeling charging effect in ultrasmall tunnel junctions. We find that the conductance is enhanced by the quantum charge fluctuations allowing tunneling below the charging energy gap. However, in all cases the conductance...

  17. Renormalization group flows for the second Z{sub N} parafermionic field theory for N odd

    Energy Technology Data Exchange (ETDEWEB)

    Dotsenko, Vladimir S. [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589, Universite Pierre et Marie Curie, Paris-6 (France) and CNRS, Universite Denis Diderot, Paris-7, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:; Estienne, Benoit [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589, Universite Pierre et Marie Curie, Paris-6 (France) and CNRS, Universite Denis Diderot, Paris-7, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail:


    Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry Z{sub N}, for N odd. New fixed points are found and classified.

  18. Electron-Phonon Renormalization of Electronic Band Structures of C Allotropes and BN Polymorphs (United States)

    Tutchton, Roxanne M.; Marchbanks, Christopher; Wu, Zhigang

    The effect of lattice vibration on electronic band structures has been mostly neglected in first-principles calculations because the electron-phonon (e-ph) renormalization of quasi-particle energies is often small (Career Award (Grant No. DE-SC0006433). Computations were carried out at the Golden Energy Computing Organization at CSM and the National Energy Research Scientific Computing Center (NERSC).

  19. Phase behavior of charged colloids : many-body effects, charge renormalization and charge regulation

    NARCIS (Netherlands)

    Zoetekouw, Bastiaan


    The main topic of this thesis is Poisson–Boltzmann theory for suspensions of charged colloids in two of its approximations: cell-type approximations that explicitly take into account non-linear effects near the colloidal surfaces, such as charge renormalization, at the expense of neglecting any

  20. Surprising convergence of the Monte Carlo renormalization group for the three-dimensional Ising model. (United States)

    Ron, Dorit; Brandt, Achi; Swendsen, Robert H


    We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.

  1. Setting the renormalization scale in QCD: The principle of maximum conformality

    DEFF Research Database (Denmark)

    Brodsky, S. J.; Di Giustino, L.


    A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormali...

  2. A density matrix renormalization group study of low-lying excitations ...

    Indian Academy of Sciences (India)


    Abstract. Symmetrized density-matrix-renormalization-group calculations have been carried out, within. Pariser–Parr–Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited C2 symmetry and spin parity of the system to obtain excited states of ...

  3. Existence of Renormalized Solutions for p(x-Parabolic Equation with three unbounded nonlinearities

    Directory of Open Access Journals (Sweden)

    Youssef Akdim


    Full Text Available In this article, we study the existence of renormalized solution for the nonlinear $p(x$-parabolic problem of the form:\\\\ $\\begin{cases} \\frac{\\partial b(x,u}{\\partial t} - div (a(x,t,u,\

  4. Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence

    NARCIS (Netherlands)

    Haro, S. de; Skenderis, K.; Solodukhin, S.N.


    We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity actionin a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We

  5. On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity

    Directory of Open Access Journals (Sweden)

    Charles Traina


    functions on the lattice generated by . Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, ℬ, of and a nonnegative, finite set function defined on ℬ.

  6. Finite size effects in the static structure factor of dusty plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Davletov, A. E., E-mail:; Yerimbetova, L. T.; Mukhametkarimov, Ye. S.; Ospanova, A. K. [Department of Physics and Technology, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040 Almaty (Kazakhstan)


    Based on the previously developed pseudopotential model of the dust particles interaction, which takes into account both the finite size and screening effects, the equilibrium distribution functions are investigated in a broad range of plasma parameters. The treatment stems entirely from the renormalization theory of plasma particles interactions which leads to the so-called generalized Poisson-Boltzmann equation. In particular, an analytical expression for the static structure factor of the dust particles is proposed and its non-monotonic behavior in the hyper-netted chain approximation is found in a specified domain of plasma parameters to indicate the formation of short- or even long-range order in the system.

  7. Spin-orbit interaction and asymmetry effects on Kondo ridges at finite magnetic field

    DEFF Research Database (Denmark)

    Grap, Stephan; Andergassen, Sabine; Paaske, Jens


    We study electron transport through a serial double quantum dot with Rashba spin-orbit interaction (SOI) and Zeeman field of amplitude B in the presence of local Coulomb repulsion. The linear conductance as a function of a gate voltage Vg equally shifting the levels on both dots shows two B=0 Kondo......-right asymmetric level-lead couplings and detuned on-site energies lead to a simultaneous breaking of left-right and bonding-antibonding state symmetry. In this case, the finite-B Kondo ridges in the Vg-B plane are bent with respect to the Vg axis. For the Kondo ridge to develop, different level renormalizations...

  8. Density-matrix renormalization study of the Hubbard model on a Bethe lattice

    Energy Technology Data Exchange (ETDEWEB)

    Lepetit, M.B.; Cousy, M.; Pastor, G.M. [Toulouse-3 Univ., 31 (France). Lab. de Physique Quantique


    The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization left angle S{sub z}(i) right angle, its fluctuations left angle S{sub z}(i){sup 2} right angle - left angle S{sub z}(i) right angle {sup 2} and various spin correlation functions left angle S{sub z}(i)S{sub z}(j) right angle - left angle S{sub z}(i) right angle left angle S{sub z}(j) right angle are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments left angle S{sub z}(i) right angle increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors [ left angle S{sub z}(0) right angle {approx_equal}- left angle S{sub z}(1) right angle ]. At large U/t, left angle S{sub z}(i) right angle is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ vertical stroke left angle S{sub z}(i) right angle vertical stroke {approx_equal}0.35 for U/t{yields}+{infinity}]. left angle S{sub z}(i){sup 2} right angle - left angle S{sub z}(i) right angle {sup 2} shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of left angle S{sub z}(i){sup 2} right angle with increasing U/t and the formation of important permanent moments left angle S{sub z}(i) right angle at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. (orig.)

  9. Real-Space Renormalization-Group Approach to the Integer Quantum Hall Effect (United States)

    Cain, Philipp; Römer, Rudolf A.

    We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent ν that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as RL and RH is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD). This distribution is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with ν = 2.37±0.02. Away from the transition it crosses over towards the Poisson distribution. We next investigate the plateau-to-insulator transition at strong magnetic fields. For a fully quantum coherent situation, we find a quantized Hall insulator with RH≈h/e2 up to RL 20h/e2 when interpreting the results in terms of most probable value of the distribution function P(RH). Upon further increasing RL→∞, the Hall insulator with diverging Hall resistance R H∝ R Lκ is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure for the distributions P(RL) and P(RH). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law r-α. Similar to the classical percolation, we observe an enhancement of ν with decreasing α. These results exemplify the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization

  10. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C


    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  11. Applications of the complex-mass renormalization scheme in effective field theory; Anwendungen des Komplexe-Masse-Renormierungsschemas in effektiver Feldtheorie

    Energy Technology Data Exchange (ETDEWEB)

    Bauer, Torsten


    In the first part of the this doctoral thesis the perturbative unitarity in the complex-mass scheme (CMS) is analysed. To that end a procedure for calculating cutting rules for loop integrals containing propagators with finite widths is presented. A toy-model Lagrangian describing the interaction of a heavy vector boson with a light fermion is used to demonstrate that the CMS respects unitarity order by order in perturbation theory provided that the renormalized coupling constant remains real. The second part of the thesis deals with various applications of the CMS to chiral effective field theory (EFT). In particular, mass and width of the delta resonance, elastic electromagnetic form factors of the Roper resonance, form factors of the nucleon-to-Roper transition, pion-nucleon scattering, and pion photo- and electroproduction for center-of-mass energies in the region of the Roper mass are calculated. By choosing appropriate renormalization conditions, a consistent chiral power counting scheme for EFT with resonant degrees of freedom can be established. This allows for a systematic investigation of the above processes in terms of an expansion in small quantities. The obtained results can be applied to the extrapolation of corresponding simulations in the context of lattice QCD to the physical value of the pion mass. Therefore, in addition to the Q{sup 2} dependence of the form factors, also the pion-mass dependence of the magnetic moment and electromagnetic radii of the Roper resonance is explored. Both a partial wave decomposition and a multipole expansion are performed for pion-nucleon scattering and pion photo- and electroproduction, respectively. In this connection the P11 partial wave as well as the M{sub 1-} and S{sub 1-} multipoles are fitted via non-linear regression to empirical data.


    Energy Technology Data Exchange (ETDEWEB)



    The author discusses quarkonium spectral functions at finite temperature reconstructed using the Maximum Entropy Method. The author shows in particular that the J/{psi} survives in the deconfined phase up to 1.5T{sub c}.

  13. Finite BMS transformations

    Energy Technology Data Exchange (ETDEWEB)

    Barnich, Glenn [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Troessaert, Cédric [Centro de Estudios Científicos (CECs),Arturo Prat 514, Valdivia (Chile)


    The action of finite BMS and Weyl transformations on the gravitational data at null infinity is worked out in three and four dimensions in the case of an arbitrary conformal factor for the boundary metric induced on Scri.

  14. Advanced finite element technologies

    CERN Document Server

    Wriggers, Peter


    The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.

  15. PyR@TE. Renormalization group equations for general gauge theories (United States)

    Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.


    Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer

  16. Biset functors for finite groups

    CERN Document Server

    Bouc, Serge


    This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.

  17. Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality. (United States)

    Andreev, Oleg


    We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.

  18. Material and Doping Dependence of the Nodal and Anti-Nodal Dispersion Renormalizations in Single- and Multi-Layer Cuprates

    Energy Technology Data Exchange (ETDEWEB)

    Johnston, S.; /Waterloo U. /SLAC; Lee, W.S.; /Stanford U., Geballe Lab. /SLAC; Nowadnick, E.A.; /SLAC /Stanford U., Phys. Dept.; Moritz, B.; /SLAC /North Dakota U.; Shen, Z.-X.; /Stanford U., Geballe Lab. /SLAC /Stanford U., Phys. Dept. /Stanford U., Appl. Phys. Dept.; Devereaux, T.P.; /Stanford U., Geballe Lab. /SLAC


    In this paper we present a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. Specifically, we discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice and review how materials dependence, such as the number of CuO{sub 2} layers, and doping dependence can be understood straightforwardly in terms of several aspects of electron-phonon coupling in layered correlated materials.

  19. A novel functional renormalization group framework for gauge theories and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Codello, Alessandro


    In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for k{yields}{infinity} and the standard effective action for k{yields}0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NL{sigma}M) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or

  20. Magnetism in atomically thin quasi two-dimensional materials: Renormalized spin wave theory (United States)

    Li, Zhenglu; Cao, Ting; Louie, Steven G.

    In this work, we apply renormalized spin wave theory to the magnetic behavior of atomically thin two-dimensional crystals. We find that magnon-magnon interaction plays an important role in renormalizing the magnetic transition temperature, and the magnetic behavior is largely dependent on the magnetic anisotropy and the thickness of the crystal in the two-dimensional limit. Our method is applicable to general magnetic crystals with input spin interaction parameters mapped out from either ab initio calculations or extracted from experiments. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, and by the National Science Foundation. Computational resources have been provided by NERSC and XSEDE.

  1. Flexoelectricity and thermal fluctuations of lipid bilayer membranes: Renormalization of flexoelectric, dielectric, and elastic properties (United States)

    Liu, L. P.; Sharma, P.


    Thermal fluctuations renormalize the bending elasticity of lipid bilayers. This well-studied effect is a cornerstone in the study of several membrane biophysical phenomena. Analogously, nearly all membranes are endowed with an electromechanical coupling called flexoelectricity that admits membrane polarization due to curvature changes. Flexoelectricity is found to be important in a number of biological functions, including hearing, ion transport, and in some situations where mechanotransduction is necessary. Very little is known about the interplay between thermal fluctuations and flexoelectricity. In this work, we explore how the apparent flexoelectricity is altered due to thermal fluctuations and, further, how the elastic and dielectric properties are renormalized due to flexoelectricity. We find that the apparent bending rigidity is softened by flexoelectricity and discuss the ramifications for interpreting existing experimental work.

  2. Gauge- and Renormalization-Group-Invariant Formulation of the Higgs-Boson Resonance

    CERN Document Server

    Papavassiliou, J; Papavassiliou, Joannis; Pilaftsis, Apostolos


    A gauge- and renormalization-group- invariant approach implemented by the pinch technique is formulated for resonant transitions involving the Higgs boson. The lineshape of the Higgs boson is shown to consist of two distinct and physically meaningful contributions: a process-independent resonant part and a process-dependent non-resonant background, which are separately gauge independent, invariant under the renormalization group, satisfy naive, tree-level Ward identities, and respect the optical and equivalence theorem individually. The former process-independent quantity serves as the natural extension of the concept of the effective charge to the case of the Higgs scalar, and constitutes a common ingredient of every Born-improved amplitude. The difference in the phenomenological predictions obtained within our approach and those found with other methods is briefly discussed.

  3. Energy Renormalization for Coarse-Graining the Dynamics of a Model Glass-Forming Liquid. (United States)

    Xia, Wenjie; Song, Jake; Hansoge, Nitin K; Phelan, Frederick R; Keten, Sinan; Douglas, Jack F


    Coarse-grained modeling achieves the enhanced computational efficiency required to model glass-forming materials by integrating out "unessential" molecular degrees of freedom, but no effective temperature transferable coarse-graining method currently exists to capture dynamics. We address this fundamental problem through an energy-renormalization scheme, in conjunction with the localization model of relaxation relating the Debye-Waller factor ⟨u 2 ⟩ to the structural relaxation time τ. Taking ortho-terphenyl as a model small-molecule glass-forming liquid, we show that preserving ⟨u 2 ⟩ (at picosecond time scale) under coarse-graining by renormalizing the cohesive interaction strength allows for quantitative prediction of both short- and long-time dynamics covering the entire temperature range of glass formation. Our findings provide physical insights into the dynamics of cooled liquids and make progress for building temperature-transferable coarse-grained models that predict key properties of glass-forming materials.

  4. Renormalization effects and phonon density of states in high temperature superconductors

    Directory of Open Access Journals (Sweden)

    Vinod Ashokan


    Full Text Available Using the versatile double time thermodynamic Green's function approach based on many body theory the renormalized frequencies, phonon energy line widths, shifts and phonon density of states (PDOS are investigated via a newly formulated Hamiltonian (does not include BCS type Hamiltonian that includes the effects of electron-phonon, anharmonicities and that of isotopic impurities. The automatic appearance of pairons, temperature, impurity and electron-phonon coupling of renormalized frequencies, widths, shifts and PDOS emerges as a characteristic feature of present theory. The numerical investigations on PDOS for the YBa2Cu3O7 − δ crystal predicts several new feature of high temperature superconductors (HTS and agreements with experimental observations.

  5. Renormalization group summation of Laplace QCD sum rules for scalar gluon currents

    Directory of Open Access Journals (Sweden)

    Farrukh Chishtie


    Full Text Available We employ renormalization group (RG summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter μ2 once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.

  6. On the perturbative renormalization of four-quark operators for new physics

    Energy Technology Data Exchange (ETDEWEB)

    Papinutto, M. [Roma Univ. (Italy). Dipt. di Fisica; INFN, Sezione di Roma (Italy); Pena, C. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC; Preti, D. [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC


    We discuss the renormalization properties of the full set of ΔF = 2 operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schroedinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all ΔF = 1,2 operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard MS and RI-MOM schemes. Large truncation effects are found for some of the operators considered. (orig.)

  7. On the perturbative renormalization of four-quark operators for new physics (United States)

    Papinutto, M.; Pena, C.; Preti, D.


    We discuss the renormalization properties of the full set of Δ F=2 operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schrödinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all Δ F=1,2 operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard {\\overline{MS}} and RI-MOM schemes. Large truncation effects are found for some of the operators considered.

  8. Critical Exponents, Scaling Law, Universality and Renormalization Group Flow in Strong Coupling QED (United States)

    Kondo, Kei-Ichi

    The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

  9. Real-space renormalization-group studies of low-dimensional quantum antiferromagnets

    Energy Technology Data Exchange (ETDEWEB)

    Lepetit, M. (Laboratoire de Physique Quantique, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX (France)); Manousakis, E. (Department of Physics, Center for Materials Research and Technology Supercomputer Computations Research Isntitute, Florida State University, Tallahassee, Florida 32306 (United States))


    We study the ground state of one- and two-dimensional (square-lattice) spin-1/2 quantum antiferromagnets using a numerical real-space renormalization-group (RG) approach. In our RG approach we consider blocks of various sizes but with an odd number of sites; we retain only the doublet ground state and we integrate out the higher-energy states by means of second-order quasidegenerate perturbation theory. That is, we assume that the role of the excited states of a block, in the RG iteration process, is to renormalize the effective coupling parameters between blocks. We compute the ground-state energy of a spin-1/2 linear chain for various block sizes and find close agreement with the Bethe-ansatz exact solution. In the case of the spin-1/2 square-lattice quantum antiferromagnet, the obtained ground-state energy is in reasonable agreement with the available numerical estimates.

  10. A renormalization approach to describe charge transport in quasiperiodic dangling backbone ladder (DBL)-DNA molecules

    Energy Technology Data Exchange (ETDEWEB)

    Sarmento, R.G. [Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Fulco, U.L. [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Albuquerque, E.L., E-mail: [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Caetano, E.W.S. [Instituto Federal de Educacao, Ciencia e Tecnologia do Ceara, 60040-531 Fortaleza, CE (Brazil); Freire, V.N. [Departamento de Fisica, Universidade Federal do Ceara, 60455-760 Fortaleza, CE (Brazil)


    Highlights: → One-step renormalization approach to describe the DBL-DNA molecule. → Electronic tight-binding Hamiltonian model. → A quasiperiodic sequence to mimic the DNA nucleotides arrangement. → Electronic transmission spectra. → I-V characteristics. -- Abstract: We study the charge transport properties of a dangling backbone ladder (DBL)-DNA molecule focusing on a quasiperiodic arrangement of its constituent nucleotides forming a Rudin-Shapiro (RS) and Fibonacci (FB) Poly (CG) sequences, as well as a natural DNA sequence (Ch22) for the sake of comparison. Making use of a one-step renormalization process, the DBL-DNA molecule is modeled in terms of a one-dimensional tight-binding Hamiltonian to investigate its transmissivity and current-voltage (I-V) profiles. Beyond the semiconductor I-V characteristics, a striking similarity between the electronic transport properties of the RS quasiperiodic structure and the natural DNA sequence was found.

  11. Thermodynamics of the two-dimensional XY model from functional renormalization

    CERN Document Server

    Jakubczyk, Pawel


    We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $\\phi^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.

  12. Nonperturbative renormalization group for scalar fields in de Sitter space: beyond the local potential approximation

    CERN Document Server

    Guilleux, Maxime


    Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local potential approximation employed in earlier works. In particular, we consider the derivative expansion, a systematic expansion in powers of field derivatives, appropriate for long wavelength modes, that we generalize to the relevant case of a curved metric with Lorentzian signature. The method is illustrated with a detailed discussion of the so-called local potential approximation prime which, on the top of the full effective potential, includes a running (but field-independent) field renormalization. We explicitly compute the associated anomalous dimension for O(N) theories. We find that it can take large values along the flow, leading to sizable differences as compared to the local potential approximation. However, it does not prevent the phenomenon of gravitationally induc...

  13. Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

    Energy Technology Data Exchange (ETDEWEB)

    Kawamoto, Shoichi [Department of Physics, Chung-Yuan Christian University, Chung-Li 320, Taiwan, R.O.C. (China); Kuroki, Tsunehide [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe,Nagoya University, Nagoya 464-8602 (Japan)


    In the previous study Kawamoto, D. Tomino and T. Kuroki, Large-N renormalization group on fuzzy sphere, Int. J. Mod. Phys. Conf. Ser. 21 (2013) 151., we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative nature of the geometry. We aim at formulating renormalization group equations including such nonlocal interactions and finding existence of nontrivial field theory with antipodal interactions on the fuzzy sphere. We find several nontrivial fixed points and calculate the scaling dimensions associated with them. We also consider the noncommutative plane limit and then no consistent fixed point is found. This contrast between the fuzzy sphere limit and the noncommutative plane limit would be manifestation in our formalism of the claim given by Chu, Madore and Steinacker that the former does not have UV/IR mixing, while the latter does.

  14. Tachyonic instability of the scalar mode prior to the QCD critical point based on the functional renormalization-group method in the two-flavor case (United States)

    Yokota, Takeru; Kunihiro, Teiji; Morita, Kenji


    We establish and elucidate the physical meaning of the appearance of an acausal mode in the sigma mesonic channel, found in the previous work by the present authors, when the system approaches the Z2 critical point. The functional renormalization-group method is applied to the two-flavor quark-meson model with varying current quark mass mq even away from the physical value at which the pion mass is reproduced. We first determine the whole phase structure in the three-dimensional space (T ,μ ,mq) consisting of temperature T , quark chemical potential μ and mq, with the tricritical point, O(4) and Z2 critical lines being located; they altogether make a winglike shape quite reminiscent of those known in the condensed matters with a tricritical point. We then calculate the spectral functions ρσ ,π(ω ,p ) in the scalar and pseudoscalar channel around the critical points. We find that the sigma mesonic mode becomes tachyonic with a superluminal velocity at finite momenta before the system reaches the Z2 point from the lower density, even for mq smaller than the physical value. One of the possible implications of the appearance of such a tachyonic mode at finite momenta is that the assumed equilibrium state with a uniform chiral condensate is unstable toward a state with an inhomogeneous σ condensate. No such anomalous behavior is found in the pseudoscalar channel. We find that the σ -to-2 σ coupling due to finite mq plays an essential role for the drastic modification of the spectral function.

  15. Dynamical density matrix renormalization group study of photoexcited states in one-dimensional Mott insulators


    Matsueda, H.; Tohyama, T.; Maekawa, S.


    One-dimensional Mott insulators exhibit giant nonlinear optical response. Based on the dynamical density matrix renormalization group method, photoexcited states and optical response in the insulators are studied as functions of the on-site and the nearest neighbor Coulomb interactions, $U$ and $V$, respectively. We find that the lowest optically-allowed and forbidden excited states, which have odd and even parities, respectively, are degenerate for $V/t\\ltsim 2$ with $t$ being the hopping in...

  16. A non-renormalization theorem for chiral primary 3-point functions

    CERN Document Server

    Baggio, Marco; Papadodimas, Kyriakos


    In this note we prove a non-renormalization theorem for the 3-point functions of 1/2 BPS primaries in the four-dimensional N = 4 SYM and chiral primaries in two dimensional N =(4,4) SCFTs. Our proof is rather elementary: it is based on Ward identities and the structure of the short multiplets of the superconformal algebra and it does not rely on superspace techniques. We also discuss some possible generalizations to less supersymmetric multiplets.

  17. Tracing the evolution of nuclear forces under the similarity renormalization group


    Johnson, Calvin W.


    I examine the evolution of nuclear forces under the similarity renormalization group (SRG) using traces of the many-body configuration-space Hamiltonian. While SRG is often said to “soften” the nuclear interaction, I provide numerical examples which paint a complementary point of view: the primary effect of SRG, using the kinetic energy as the generator of the evolution, is to shift downward the diagonal matrix elements in the model space, while the off-diagonal elements undergo significantly...

  18. Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

    Directory of Open Access Journals (Sweden)

    Segun Goh

    Full Text Available Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare bus stops are transformed into a (renormalized "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

  19. Density matrix renormalization group approach for many-body open quantum systems. (United States)

    Rotureau, J; Michel, N; Nazarewicz, W; Płoszajczak, M; Dukelsky, J


    The density matrix renormalization group (DMRG) approach is extended to complex-symmetric density matrices characteristic of many-body open quantum systems. Within the continuum shell model, we investigate the interplay between many-body configuration interaction and coupling to open channels in case of the unbound nucleus (7)He. It is shown that the extended DMRG procedure provides a highly accurate treatment of the coupling to the nonresonant scattering continuum.

  20. A renormalization group study of persistent current in a quasiperiodic ring

    Energy Technology Data Exchange (ETDEWEB)

    Dutta, Paramita [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India); Maiti, Santanu K., E-mail: [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata-700 108 (India); Karmakar, S.N. [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India)


    We propose a real-space renormalization group approach for evaluating persistent current in a multi-channel quasiperiodic Fibonacci tight-binding ring based on a Green's function formalism. Unlike the traditional methods, the present scheme provides a powerful tool for the theoretical description of persistent current with a very high degree of accuracy in large periodic and quasiperiodic rings, even in the micron scale range, which emphasizes the merit of this work.

  1. Real-space renormalization group study of the Hubbard model on a non-bipartite lattice

    Directory of Open Access Journals (Sweden)

    R. D. Levine


    Full Text Available Abstract: We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t ≈ 12.5.

  2. A renormalization operator for 1D maps under quasi-periodic perturbations (United States)

    Jorba, À.; Rabassa, P.; Tatjer, J. C.


    This paper concerns the reducibility loss of (periodic) invariant curves of quasi-periodically forced one-dimensional maps and its relationship with the renormalization operator. Let gα be a one-parametric family of one-dimensional maps with a cascade of period doubling bifurcations. Between each of these bifurcations, there exists a parameter value αn such that gα_n has a superstable periodic orbit of period 2n. Consider a quasi-periodic perturbation (with only one frequency) of the one-dimensional family of maps, and let us call ε the perturbing parameter. For ε small enough, the superstable periodic orbits of the unperturbed map become attracting invariant curves (depending on α and ε) of the perturbed system. Under a suitable hypothesis, it is known that there exist two reducibility loss bifurcation curves around each parameter value (αn, 0), which can be locally expressed as (α_n^+(\\varepsilon), \\varepsilon) and (α_n^-(\\varepsilon), \\varepsilon) . We propose an extension of the classic one-dimensional (doubling) renormalization operator to the quasi-periodic case. We show that this extension is well defined and the operator is differentiable. Moreover, we show that the slopes of reducibility loss bifurcation \\frac{d}{d\\varepsilon} α_n^+/-(0) can be written in terms of the tangent map of the new quasi-periodic renormalization operator. In particular, our result applies to the families of quasi-periodic forced perturbations of the Logistic Map typically encountered in the literature. We also present a numerical study that demonstrates that the asymptotic behaviour of \\{\\frac{d}{d\\varepsilon} α_n^+/-(0)\\}n≥ 0 is governed by the dynamics of the proposed quasi-periodic renormalization operator.

  3. An Exact Renormalization Group analysis of 3-d Well Developed turbulence

    CERN Document Server

    Tomassini, P


    We take advantage of peculiar properties of three dimensional incompressible turbulence to introduce a nonstandard Exact Renormalization Group method. A Galilean invariance preserving regularizing procedure is utilized and a field truncation is adopted to test the method. Results are encouraging: the energy spectrum E(k) in the inertial range scales with exponent -1.666+/- 0.001 and the Kolmogorov constant C_K, computed for several (realistic) shapes of the stirring force correlator, agrees with experimental data.

  4. Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions (United States)

    Lee, Yu-Wen; Lee, Yu-Li


    We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group (RG) method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type I) or Fermi lines (type II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work we study the effects of Coulomb interactions, following the spirit of Shankar [Rev. Mod. Phys. 66, 129 (1994), 10.1103/RevModPhys.66.129], by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

  5. Egalitarian Improvement to Democracy: Quark renormalization constants in N_f=2 QCD

    CERN Document Server

    Petrov, K


    We present our results on the non-perturbative evaluation of the renormalization constant for the quark field, $Z_q$, in Landau gauge within RI-MOM scheme. Using three lattice spacing we are able to isolate lattice artefacts of various origin, both perturbative and non-perturbative. In particular, the existence of the dimension-two gluon-condensate is discussed, and confirmed.

  6. Application of renormalization group theory to the large-eddy simulation of transitional boundary layers (United States)

    Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.


    An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.

  7. Exponential and power-law renormalization in phonon-assisted tunneling (United States)

    Khedri, A.; Costi, T. A.; Meden, V.


    We investigate the spinless Anderson-Holstein model routinely employed to describe the basic physics of phonon-assisted tunneling in molecular devices. Our focus is on small to intermediate electron-phonon coupling; we complement a recent strong coupling study [Phys. Rev. B 87, 075319 (2013), 10.1103/PhysRevB.87.075319]. The entire crossover from the antiadiabatic regime to the adiabatic one is considered. Our analysis using the essentially analytical functional renormalization group approach backed up by numerical renormalization group calculations goes beyond lowest order perturbation theory in the electron-phonon coupling. In particular, we provide an analytic expression for the effective tunneling coupling at particle-hole symmetry valid for all ratios of the bare tunnel coupling and the phonon frequency. It contains the exponential polaronic as well as the power-law renormalization in the electron-phonon interaction; the latter can be traced back to x-ray edgelike physics. In the antiadiabatic and the adiabatic limit this expression agrees with the known ones obtained by mapping to an effective interacting resonant level model and lowest order perturbation theory, respectively. Away from particle-hole symmetry, we discuss and compare results from several approaches for the zero temperature electrical conductance of the model.

  8. Irreversibility of the renormalization group flow in non-unitary quantum field theory (United States)

    Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Ravanini, Francesco


    We show irreversibility of the renormalization group flow in non-unitary but {{ P}T} -invariant quantum field theory in two space-time dimensions. In addition to unbroken PT -symmetry and a positive energy spectrum, we assume standard properties of quantum field theory including a local energy-momentum tensor and relativistic invariance. This generalizes Zamolodchikov’s c-theorem to {{ P}T} -symmetric Hamiltonians. Our proof follows closely Zamolodchikov’s arguments. We show that a function ceff(s) of the renormalization group parameter s exists which is non-negative and monotonically decreasing along renormalization group flows. Its value at a critical point is the ‘effective central charge’ entering the specific free energy. At least in rational models, this equals ceff=c-24Δ , where c is the central charge and Δ is the lowest primary field dimension in the conformal field theory which describes the critical point. Dedicated to John Cardy on the occasion of his 70th birthday.

  9. Effective lactation yield

    NARCIS (Netherlands)

    Kok, Akke; Middelaar, van C.E.; Engel, B.; Knegsel, van A.T.M.; Hogeveen, H.; Kemp, B.; Boer, de I.J.M.


    To compare milk yields between cows or management strategies, lactations are traditionally standardized to 305-d yields. The 305-d yield, however, gives no insight into the combined effect of additional milk yield before calving, decreased milk yield after calving, and a possible shorter calving

  10. A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

    Energy Technology Data Exchange (ETDEWEB)

    Lindesay, James V


    We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.

  11. Finite element analysis

    CERN Document Server


    Finite element analysis is an engineering method for the numerical analysis of complex structures. This book provides a bird's eye view on this very broad matter through 27 original and innovative research studies exhibiting various investigation directions. Through its chapters the reader will have access to works related to Biomedical Engineering, Materials Engineering, Process Analysis and Civil Engineering. The text is addressed not only to researchers, but also to professional engineers, engineering lecturers and students seeking to gain a better understanding of where Finite Element Analysis stands today.

  12. Finite-State Complexity and the Size of Transducers

    Directory of Open Access Journals (Sweden)

    Cristian Calude


    Full Text Available Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our main result, we show that the state-size hierarchy with respect to a standard encoding is infinite. We consider also hierarchies yielded by more general computable encodings.

  13. Hybrid finite difference/finite element immersed boundary method. (United States)

    E Griffith, Boyce; Luo, Xiaoyu


    The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

  14. Algorithms for finite rings

    NARCIS (Netherlands)

    Ciocanea Teodorescu I.,


    In this thesis we are interested in describing algorithms that answer questions arising in ring and module theory. Our focus is on deterministic polynomial-time algorithms and rings and modules that are finite. The first main result of this thesis is a solution to the module isomorphism problem in

  15. Inside finite elements

    CERN Document Server

    Weiser, Martin


    All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.

  16. Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics (United States)

    Klein, Bertram


    Finite-volume effects in Quantum Chromodynamics (QCD) have been a subject of much theoretical interest for more than two decades. They are in particular important for the analysis and interpretation of QCD simulations on a finite, discrete space-time lattice. Most of these effects are closely related to the phenomenon of spontaneous breaking of the chiral flavor symmetry and the emergence of pions as light Goldstone bosons. These long-range fluctuations are strongly affected by putting the system into a finite box, and an analysis with different methods can be organized according to the interplay between pion mass and box size. The finite volume also affects critical behavior at the chiral phase transition in QCD. In the present review, I will be mainly concerned with modeling such finite volume effects as they affect the thermodynamics of the chiral phase transition for two quark flavors. I review recent work on the analysis of finite-volume effects which makes use of the quark-meson model for dynamical chiral symmetry breaking. To account for the effects of critical long-range fluctuations close to the phase transition, most of the calculations have been performed using non-perturbative Renormalization Group (RG) methods. I give an overview over the application of these methods to a finite volume. The method, the model and the results are put into the context of related work in random matrix theory for very small volumes, chiral perturbation theory for larger volumes, and related methods and approaches. They are applied towards the analysis of finite-volume effects in lattice QCD simulations and their interpretation, mainly in the context of the chiral phase transition for two quark flavors.

  17. Shear Yielding and Shear Jamming of Dense Hard Sphere Glasses. (United States)

    Urbani, Pierfrancesco; Zamponi, Francesco


    We investigate the response of dense hard sphere glasses to a shear strain in a wide range of pressures ranging from the glass transition to the infinite-pressure jamming point. The phase diagram in the density-shear strain plane is calculated analytically using the mean-field infinite-dimensional solution. We find that just above the glass transition, the glass generically yields at a finite shear strain. The yielding transition in the mean-field picture is a spinodal point in presence of disorder. At higher densities, instead, we find that the glass generically jams at a finite shear strain: the jamming transition prevents yielding. The shear yielding and shear jamming lines merge in a critical point, close to which the system yields at extremely large shear stress. Around this point, highly nontrivial yielding dynamics, characterized by system-spanning disordered fractures, is expected.

  18. Simplifying Nondeterministic Finite Cover Automata

    Directory of Open Access Journals (Sweden)

    Cezar Câmpeanu


    Full Text Available The concept of Deterministic Finite Cover Automata (DFCA was introduced at WIA '98, as a more compact representation than Deterministic Finite Automata (DFA for finite languages. In some cases representing a finite language, Nondeterministic Finite Automata (NFA may significantly reduce the number of states used. The combined power of the succinctness of the representation of finite languages using both cover languages and non-determinism has been suggested, but never systematically studied. In the present paper, for nondeterministic finite cover automata (NFCA and l-nondeterministic finite cover automaton (l-NFCA, we show that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets. Moreover, we show how we can adapt the methods used to reduce, or minimize the size of NFAs/DFCAs/l-DFCAs, for simplifying NFCAs/l-NFCAs.

  19. Finiteness in Hinuq

    Directory of Open Access Journals (Sweden)

    Diana Forker


    Full Text Available Hinuq (Nakh-Daghestanian language family, Caucasus, Russia has a rich system of verbal forms. In independent/main clauses there are seven synthetic TAM forms, 20 periphrastic TAM forms, and two heterogeneous TAM forms that cannot be attributed clearly to one of these two groups. In dependent clauses there are about twenty forms that serve adverbial function, attributive function (i.e. headed and headless relative clauses or complement function. To these forms belong suffixed forms that are traditionally called participles, adverbial participles, Infinitive and Masdar. In this paper I analyze Hinuq verb forms and clause types with respect to categories and phenomena that have been associated with finiteness. I will explore which of the criteria actually apply to Hinuq and whether they form a cluster that could be subsumed under the notion of finiteness.

  20. Particle debonding using different yield criteria

    DEFF Research Database (Denmark)

    Legarth, Brian Nyvang; Kuroda, Mitsutoshi


    Effects of plastic anisotropy in relation to debonding of rigid inclusions embedded in an elastic-viscoplastic metal are studied. Full finite strain analyses are carried out for plane cells assuming plane stress or plane strain. The overall stress strain response is calculated, when the cell...... extent and shape of the particular yield function considered. The required overall straining of the cell for debonding initiation is related to the extent of the yield surfaces, since a high yield stress promotes debonding. Additionally, the maximum overall stress level for the cell is lower for the Hill...... [Hill, R., 1948. Proc. Roy. Soc. London Ser. A 193, 281-297] and Barlat et al. [Barlat, F., Lege, D.J., Brem, J.C., 1991. Int. J. Plasticity 7, 693-712] materials than that predicted by the other three yield functions. In all cases analyzed the non-normality flow rule hastens the particle...

  1. Yield stress materials in soft condensed matter (United States)

    Bonn, Daniel; Denn, Morton M.; Berthier, Ludovic; Divoux, Thibaut; Manneville, Sébastien


    A comprehensive review is presented of the physical behavior of yield stress materials in soft condensed matter, which encompasses a broad range of materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear flow behavior in response to external mechanical forces due to the existence of a finite force threshold for flow to occur: the yield stress. Both the physical origin and rheological consequences associated with this nonlinear behavior are discussed and an overview is given of experimental techniques available to measure the yield stress. Recent progress is discussed concerning a microscopic theoretical description of the flow dynamics of yield stress materials, emphasizing, in particular, the role played by relaxation time scales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and nonlocal effects in confined geometries.

  2. Confinement at Finite Temperature (United States)

    Cardoso, Nuno; Bicudo, Pedro; Cardoso, Marco


    We show the flux tubes produced by static quark-antiquark, quark-quark and quark-gluon charges at finite temperature. The sources are placed on the lattice with fundamental and adjoint Polyakov loops. We compute the squared strengths of the chromomagnetic and chromoelectric fields above and below the critical temperature. Our results are for pure gauge SU(3) gauge theory, they are invariant and all computations are done with GPUs using CUDA.

  3. Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables

    Directory of Open Access Journals (Sweden)

    Khellat M.R.


    Full Text Available We first consider the idea of renormalization group-induced estimates, in the context of optimization procedures, for the Brodsky-Lepage-Mackenzie approach to generate higher-order contributions to QCD perturbative series. Secondly, we develop the deviation pattern approach (DPA in which through a series of comparisons between lowerorder RG-induced estimates and the corresponding analytical calculations, one could modify higher-order RG-induced estimates. Finally, using the normal estimation procedure and DPA, we get estimates of αs4 corrections for the Bjorken sum rule of polarized deep-inelastic scattering and for the non-singlet contribution to the Adler function.

  4. Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group


    Vian, F


    The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived f...

  5. Renormalization of Molecular Quasiparticle Levels at Metal-Molecule Interfaces: Trends across Binding Regimes

    DEFF Research Database (Denmark)

    Thygesen, Kristian Sommer; Rubio, Angel


    When an electron or a hole is added into an orbital of an adsorbed molecule the substrate electrons will rearrange in order to screen the added charge. This polarization effect reduces the electron addition and removal energies of the adsorbed molecule relative to those of the free molecule. Using...... a microscopic model of the metal-molecule interface, we illustrate the basic features of this renormalization mechanism through systematic GW, Hartree-Fock, and Kohn-Sham calculations for the molecular energy levels as function of the model parameters. We identify two different polarization mechanisms: (i...

  6. Implementation and assessment of the renormalization group (Rng) k - {epsilon} model in gothic

    Energy Technology Data Exchange (ETDEWEB)

    Analytis, G.Th. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)


    In GOTHIC, the standard k - {epsilon} model is used to model turbulence. In an attempt to enhance the turbulence modelling capabilities of the code for simulation of mixing driven by highly buoyant discharges, we implemented the Renormalization Group (RNG) k - {epsilon} model. This model which for the time being, is only implemented in the ''gas'' phase, was tested with different simple test-problems and its predictions were compared to the corresponding ones obtained when the standard k - {epsilon} model was used. (author)

  7. Tensor renormalization group analysis of ${\\rm CP}(N-1)$ model in two dimensions

    CERN Document Server

    Kawauchi, Hikaru


    We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of CP($N-1$) model is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$.

  8. Tracing the evolution of nuclear forces under the similarity renormalization group

    Directory of Open Access Journals (Sweden)

    Calvin W. Johnson


    Full Text Available I examine the evolution of nuclear forces under the similarity renormalization group (SRG using traces of the many-body configuration-space Hamiltonian. While SRG is often said to “soften” the nuclear interaction, I provide numerical examples which paint a complementary point of view: the primary effect of SRG, using the kinetic energy as the generator of the evolution, is to shift downward the diagonal matrix elements in the model space, while the off-diagonal elements undergo significantly smaller changes. By employing traces, I argue that this is a very natural outcome as one diagonalizes a matrix, and helps one to understand the success of SRG.

  9. Dimensional regularization in position space and a forest formula for regularized Epstein-Glaser renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Keller, Kai Johannes


    The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established. (orig.)

  10. The Schrödinger functional a renormalization probe for non-abelian gauge theories

    CERN Document Server

    Lüscher, Martin; Weisz, P; Wolff, U; L\\"{u}scher, Martin; Narayanan, Rajamani; Weisz, Peter; Wolff, Ulli


    Following Symanzik we argue that the Schr\\"odinger functional in lattice gauge theories without matter fields has a well-defined continuum limit. Due to gauge invariance no extra counter terms are required. The Schr\\"odinger functional is, moreover, accessible to numerical simulations. It may hence be used to study the scaling properties of the theory and in particular the evolution of the renormalized gauge coupling from low to high energies. A concrete proposition along this line is made and the necessary perturbative analysis of the Schr\\"odinger functional is carried through to 1-loop order.

  11. Thermodynamics of isotropic and anisotropic layered magnets: renormalization group approach and 1/N expansion


    Irkhin, V. Yu.; Katanin, A. A.


    The O(N) model of layered antiferro- and ferromagnets with a weak interlayer coupling and/or easy-axis anisotropy is considered. A renormalization group (RG) analysis in this model is performed, the results for N=3 being expected to agree with those of the 1/M expansion in the CP^{M-1} model at M=2. The quantum and classical cases are considered. A crossover from an isotropic 2D-like to 3D Heisenberg (or 2D Ising) regime is investigated within the 1/N expansion. Analytical results for the tem...

  12. Renormalization Group Equations of d=6 Operators in the Standard Model Effective Field Theory

    CERN Multimedia

    CERN. Geneva


    The one-loop renormalization group equations for the Standard Model (SM) Effective Field Theory (EFT) including dimension-six operators are calculated. The complete 2499 × 2499 one-loop anomalous dimension matrix of the d=6 Lagrangian is obtained, as well as the contribution of d=6 operators to the running of the parameters of the renormalizable SM Lagrangian. The presence of higher-dimension operators has implications for the flavor problem of the SM. An approximate holomorphy of the one-loop anomalous dimension matrix is found, even though the SM EFT is not a supersymmetric theory.

  13. Anomalous swelling of multilamellar lipid bilayers in the transition region by renormalization of curvature elasticity

    DEFF Research Database (Denmark)

    Callisen, Thomas Hønger; Mortensen, Kell; Ipsen, John Hjorth


    Small-angle neutron scattering is used to determine the temperature dependence of the lamellar repeat distance in an aqueous multilamellar solution of phospholipid bilayers. A thermal anomaly in the swelling behavior is observed at the bilayer phase transition. The anomalous behavior can be suppr...... be suppressed by varying the lipid acyl-chain length or by alloying with a molecular stiffening agent. The experimental results are explained in terms of renormalization of the bilayer curvature elasticity and by using a theory of repulsive interlamellar undulation forces....

  14. {gamma} (2) modular symmetry, renormalization group flow and the quantum hall effect

    Energy Technology Data Exchange (ETDEWEB)

    Georgelin, Yvon [Groupe de Physique Theorique, Institut de Physique Nucleaire, Orsay (France); Masson, Thierry; Wallet, Jean-Christophe [Laboratoire de Physique Theorique (UMR 8627), Universitdede Paris-Sud, Orsay (France)


    We construct a family of holomorphic {beta}-functions whose renormalization group (RG) flow preserves the {gamma} (2) modular symmetry and reproduces the observed stability of the Hall plateaus. The semicircle law relating the longitudinal and Hall conductivities that has been experimentally observed is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependence of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occurring in the crossover of the permitted transitions is discussed. (author)

  15. Charge independence, charge symmetry breaking in the S-wave nucleon-nucleon interaction, and renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Alvaro Calle Cordon,Manuel Pavon Valderrama,Enrique Ruiz Arriola


    We study the interplay between charge symmetry breaking and renormalization in the NN system for S-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.

  16. Singular perturbation analysis of a reduced model for collective motion: a renormalization group approach. (United States)

    Lee, Chiu Fan


    In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion, we determine how the critical density depends on the form of the initial perturbation. Specifically, we employ a renormalization-group improved perturbative method to analyze the model equations and show analytically, up to first order in the perturbation parameter, how the critical density is modified by the strength of the initial angular perturbation in the system.

  17. Non-perturbative renormalization of the static vector current and its O(a)-improvement in quenched QCD

    Energy Technology Data Exchange (ETDEWEB)

    Palombi, F.


    We carry out the renormalization and the Symanzik O(a)-improvement programme for the static vector current in quenched lattice QCD. The scale independent ratio of the renormalization constants of the static vector and axial currents is obtained non-perturbatively from an axial Ward identity with Wilson-type light quarks and various lattice discretizations of the static action. The improvement coefficients c{sub V}{sup stat} and b{sub V}{sup stat} are obtained up to O(g{sub 4}{sup 0})-terms by enforcing improvement conditions respectively on the axial Ward identity and a three-point correlator of the static vector current. A comparison between the non-perturbative estimates and the corresponding one-loop results shows a non-negligible effect of the O(g{sub 4}{sup 0})-terms on the improvement coefficients but a good accuracy of the perturbative description of the ratio of the renormalization constants. (orig.)

  18. Renormalization: infinity in today microscopic physics; Renormalisation et groupe de renormalisation: les infinis en physique microscopique contemporaine

    Energy Technology Data Exchange (ETDEWEB)

    Zinn-Justin, J


    The expectations put in quantum electrodynamics were deceived when first calculations showed that divergencies, due to the pinpoint aspect of the electron, continued to exist. Later, as a consequence of new experimental data and theoretical progress, an empirical method called renormalization was proposed to allow the evaluation of expressions involving infinite terms. The development of this method opened the way to the theory of re-normalizing fields and gave so successful results that it was applied to all fundamental interactions except gravity. This theory allowed the standard model in weak, electromagnetic and strong interactions to be confronted successfully with experimental data during more than 25 years. This article presents the progressive evolution of ideas in the concept of renormalization. (A.C.)

  19. A renormalization group study of the three-color Ashkin-Teller model on a Wheatstone hierarchical lattice (United States)

    Teodoro, R.; Bezerra, C. G.; Mariz, A. M.; da Costa, F. A.; de Araújo, J. M.


    A three-color Ashkin-Teller model (3AT) is investigated by means of a Migdal-Kadanoff renormalization group approach on a Wheatstone bridge hierarchical lattice. The exact recursion relations for the renormalized couplings are obtained through a decimation procedure. The phase diagram of the model is obtained from the analysis of the fixed points and the flow generated by the renormalization group transformation. Four distinct phases are obtained along with nine critical points and are graphically represented in a phase diagram in terms of the dual transmissivity vector. The correlation length (νT)and crossover (ϕ) critical exponents are numerically calculated. It is found that seven of the critical points are in the Potts model universality class (q = 2, 4 e 8). The remaining critical points are in a universality class which may belong to a sort of Baxter's line. The results can be considered as an approximation to more realistic Bravais lattices.

  20. Optimal renormalization and the extraction of the strange quark mass from moments of the τ -decay spectral function (United States)

    Ananthanarayan, B.; Das, Diganta


    We introduce an optimal renormalization group analysis pertinent to the analysis of polarization functions associated with the s -quark mass relevant in τ -decay. The technique is based on the renormalization group invariance constraints which lead to closed form summation of all the leading and next-to-leading logarithms at each order in perturbation theory. The new perturbation series exhibits reduced sensitivity to the renormalization scale and improved behavior in the complex plane along the integration contour. Using improved experimental and theory inputs, we have extracted the value of the strange quark mass ms(2 GeV )=106.70 ±9.36 MeV and ms(2 GeV )=74.47 ±7.77 MeV from presently available ALEPH and OPAL data respectively. These determinations are in agreement with the determinations in other phenomenological methods and from the lattice.

  1. Skewness as measure of the invariance of instantaneous renormalized drop diameter distributions – Part 1: Convective vs. stratiform precipitation

    Directory of Open Access Journals (Sweden)

    M. Ignaccolo


    Full Text Available We investigate the variability of the shape of the renormalized drop diameter instantaneous distribution using of the third order central moment: the skewness. Disdrometer data, collected at Darwin Australia, are considered either as whole or as divided in convective and stratiform precipitation intervals. We show that in all cases the distribution of the skewness is strongly peaked around 0.64. This allows to identify a most common distribution of renormalized drop diameters and two main variations, one with larger and one with smaller skewness. The distributions shapes are independent from the stratiform vs. convective classification.

  2. Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality

    Directory of Open Access Journals (Sweden)

    Uwe C. Täuber


    Full Text Available The universal critical behavior of the driven-dissipative nonequilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex-valued Landau-Ginzburg functional, which captures the near critical nonequilibrium dynamics, and generalizes model A for classical relaxational dynamics with nonconserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional ε expansion about the upper critical dimension d_{c}=4 and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (subdiffusive model B with complex coefficients.

  3. Renormalization-Scheme Dependence of Padé Summation in QCD

    CERN Document Server

    Ellis, John R.; Karliner, Marek; Samuel, Mark A.; Ellis, John; Gardi, Einan; Karliner, Marek; Samuel, Mark A.


    We study the renormalization-scheme (RS) dependence of Padé Approximants (PA's), and compare them with the Principle of Minimal Sensitivity (PMS) and the Effective Charge (ECH) approaches. Although the formulae provided by the PA, PMS and ECH predictions for higher-order terms in a QCD perturbation expansion differ in general, their predictions can be very close numerically for a wide range of renormalization schemes. Using the Bjorken sum rule as a test case, we find that Padé Summation (PS) reduces drastically the RS dependence of the Bjorken effective charge. We use these results to estimate the theoretical error due to the choice of RS in the extraction of $\\alpha_s$ from the Bjorken sum rule, and use the available data at $Q^2=3 GeV^2$ to estimate $\\alpha_s(M_Z) = 0.117^{+0.004}_{-0.007} \\pm 0.002$, where the first error is experimental, and the second is theoretical.

  4. Turbulent mixing of a critical fluid: The non-perturbative renormalization

    Directory of Open Access Journals (Sweden)

    M. Hnatič


    Full Text Available Non-perturbative Renormalization Group (NPRG technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi〉∼(Pji⊥+αPji∥/kd+ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow, but there is a new nonequilibrium regime (universality class associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

  5. Bulk renormalization and particle spectrum in codimension-two brane worlds (United States)

    Salvio, Alberto


    We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).

  6. A functional renormalization group approach to electronic structure calculations for systems without translational symmetry

    CERN Document Server

    Seiler, Christian


    A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG-flow is organized in the energy-domain rather than in k-space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band-structure, such as disordered metals or molecules. The energy-domain FRG ({\\epsilon}FRG) presented here accounts for Fermi-liquid corrections to quasi-particle energies and particle-hole excitations. It goes beyond the state of the art GW-BSE, because in {\\epsilon}FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on...

  7. Inverse scattering theory: renormalization of the Lippmann-Schwinger equation for acoustic scattering in one dimension. (United States)

    Kouri, Donald J; Vijay, Amrendra


    The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the frequency. By contrast, it is well known that the Born-Neumann series for the Volterra integral equations in quantum scattering are absolutely convergent, independent of the strength of the coupling characterizing the interaction. The transformation of the Lippmann-Schwinger equation from a Fredholm to a Volterra structure by renormalization has been considered previously for quantum scattering calculations and electromagnetic scattering. In this paper, we employ the renormalization technique to obtain a Volterra equation framework for the inverse acoustic scattering series, proving that this series also converges absolutely in the entire complex plane of coupling constant and frequency values. The present results are for acoustic scattering in one dimension, but the method is general. The approach is illustrated by applications to two simple one-dimensional models for acoustic scattering.

  8. Comparative interpretations of renormalization inversion technique for reconstructing unknown emissions from measured atmospheric concentrations (United States)

    Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory


    The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.

  9. Renormalization of spectra by phase competition in the half-filled Hubbard-Holstein model (United States)

    Nowadnick, E. A.; Johnston, S.; Moritz, B.; Devereaux, T. P.


    We present electron and phonon spectral functions calculated from determinant quantum Monte Carlo simulations of the half-filled two-dimensional Hubbard-Holstein model on a square lattice. By tuning the relative electron-electron (e -e ) and electron-phonon (e -p h ) interaction strengths, we show the electron spectral function evolving between antiferromagnetic insulating, metallic, and charge-density-wave (CDW) insulating phases. The phonon spectra concurrently gain a strong momentum dependence and soften in energy upon approaching the CDW phase. In particular, we study how the e -e and e -p h interactions renormalize the spectra and find that the presence of both interactions suppresses the amount of renormalization at low energy, thus allowing the emergence of a metallic phase at intermediate coupling strengths. In addition, we find a modest enhancement of the d -wave pairing susceptibility in the metallic regime, although spin and charge correlations are still dominant at the temperatures considered in our study. These findings demonstrate the importance of considering the influence of multiple interactions in spectroscopically determining any one interaction strength in strongly correlated materials.

  10. Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model

    Energy Technology Data Exchange (ETDEWEB)

    Meloni, Davide [Dipartimento di Matematica e Fisica, Università di Roma Tre,Via della Vasca Navale 84, 00146 Rome (Italy); Ohlsson, Tommy; Riad, Stella [Department of Physics, School of Engineering Sciences,KTH Royal Institute of Technology - AlbaNova University Center,Roslagstullsbacken 21, 106 91 Stockholm (Sweden)


    We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10{sub H}, 120{sub H}, and 126{sub H} representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M{sub I}. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10{sub H} and 126{sub H} representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.

  11. Combinatorics of finite sets

    CERN Document Server

    Anderson, Ian


    Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. ""An excellent text for a topics course in discrete mathematics."" - Bulletin of the Ame

  12. Renormalized Volume (United States)

    Gover, A. Rod; Waldron, Andrew


    We develop a universal distributional calculus for regulated volumes of metrics that are suitably singular along hypersurfaces. When the hypersurface is a conformal infinity we give simple integrated distribution expressions for the divergences and anomaly of the regulated volume functional valid for any choice of regulator. For closed hypersurfaces or conformally compact geometries, methods from a previously developed boundary calculus for conformally compact manifolds can be applied to give explicit holographic formulæ for the divergences and anomaly expressed as hypersurface integrals over local quantities (the method also extends to non-closed hypersurfaces). The resulting anomaly does not depend on any particular choice of regulator, while the regulator dependence of the divergences is precisely captured by these formulæ. Conformal hypersurface invariants can be studied by demanding that the singular metric obey, smoothly and formally to a suitable order, a Yamabe type problem with boundary data along the conformal infinity. We prove that the volume anomaly for these singular Yamabe solutions is a conformally invariant integral of a local Q-curvature that generalizes the Branson Q-curvature by including data of the embedding. In each dimension this canonically defines a higher dimensional generalization of the Willmore energy/rigid string action. Recently, Graham proved that the first variation of the volume anomaly recovers the density obstructing smooth solutions to this singular Yamabe problem; we give a new proof of this result employing our boundary calculus. Physical applications of our results include studies of quantum corrections to entanglement entropies.

  13. Finite quantum gauge theories (United States)

    Modesto, Leonardo; Piva, Marco; Rachwał, Lesław


    We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).

  14. Yield stress fluids slowly yield to analysis

    NARCIS (Netherlands)

    Bonn, D.; Denn, M.M.


    We are surrounded in everyday life by yield stress fluids: materials that behave as solids under small stresses but flow like liquids beyond a critical stress. For example, paint must flow under the brush, but remain fixed in a vertical film despite the force of gravity. Food products (such as

  15. Stochastic delocalization of finite populations (United States)

    Geyrhofer, Lukas; Hallatschek, Oskar


    The localization of populations of replicating bacteria, viruses or autocatalytic chemicals arises in various contexts, such as ecology, evolution, medicine or chemistry. Several deterministic mathematical models have been used to characterize the conditions under which localized states can form, and how they break down due to convective driving forces. It has been repeatedly found that populations remain localized unless the bias exceeds a critical threshold value, and that close to the transition the population is characterized by a diverging length scale. These results, however, have been obtained upon ignoring number fluctuations (‘genetic drift’), which are inevitable given the discreteness of the replicating entities. Here, we study the localization/delocalization of a finite population in the presence of genetic drift. The population is modeled by a linear chain of subpopulations, or demes, which exchange migrants at a constant rate. Individuals in one particular deme, called ‘oasis’, receive a growth rate benefit, and the total population is regulated to have constant size N. In this ecological setting, we find that any finite population delocalizes on sufficiently long time scales. Depending on parameters, however, populations may remain localized for a very long time. The typical waiting time to delocalization increases exponentially with both population size and distance to the critical wind speed of the deterministic approximation. We augment these simulation results by a mathematical analysis that treats the reproduction and migration of individuals as branching random walks subject to global constraints. For a particular constraint, different from a fixed population size constraint, this model yields a solvable first moment equation. We find that this solvable model approximates very well the fixed population size model for large populations, but starts to deviate as population sizes are small. Nevertheless, the qualitative behavior of the

  16. Yield load solutions of heterogeneous welded joints

    Energy Technology Data Exchange (ETDEWEB)

    Kozak, D., E-mail: dkozak@sfsb.h [Mechanical Engineering Faculty in Slavonski Brod, Josip Juraj Strossmayer University of Osijek, Trg Ivane Brlic-Mazuranic 2, Hr-35000 Slavonski Brod (Croatia); Gubeljak, N. [Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor (Slovenia); Konjatic, P.; Sertic, J. [Mechanical Engineering Faculty in Slavonski Brod, Josip Juraj Strossmayer University of Osijek, Trg Ivane Brlic-Mazuranic 2, Hr-35000 Slavonski Brod (Croatia)


    The aim of this paper is to establish yield load solutions when the materials inhomogeneity within the weld is present, which is usually the case in repair welding. The effect of yield strength mismatch of welded joints performed with different geometry on the yield load value has been investigated in the context of single edge notched fracture toughness specimen subjected to bending SE(B) using the finite element method. The crack was located in the center of the weld and the two most important geometrical parameters were identified as: crack length ratio a/W as well as slenderness of the welded joint, which were systematically varied. One practical and four additional combinations of filler materials, with the same portion of overmatched part and undermatched part of the weld, were analyzed, and plane strain FE solutions for the case when the crack is located in the overmatched half of the heterogeneous weld were obtained.

  17. The Determining Finite Automata Process

    Directory of Open Access Journals (Sweden)

    M. S. Vinogradova


    Full Text Available The theory of formal languages widely uses finite state automata both in implementation of automata-based approach to programming, and in synthesis of logical control algorithms.To ensure unambiguous operation of the algorithms, the synthesized finite state automata must be deterministic. Within the approach to the synthesis of the mobile robot controls, for example, based on the theory of formal languages, there are problems concerning the construction of various finite automata, but such finite automata, as a rule, will not be deterministic. The algorithm of determinization can be applied to the finite automata, as specified, in various ways. The basic ideas of the algorithm of determinization can be most simply explained using the representations of a finite automaton in the form of a weighted directed graph.The paper deals with finite automata represented as weighted directed graphs, and discusses in detail the procedure for determining the finite automata represented in this way. Gives a detailed description of the algorithm for determining finite automata. A large number of examples illustrate a capability of the determinization algorithm.

  18. Yield Improvement in Steel Casting (Yield II)

    Energy Technology Data Exchange (ETDEWEB)

    Richard A. Hardin; Christoph Beckermann; Tim Hays


    This report presents work conducted on the following main projects tasks undertaken in the Yield Improvement in Steel Casting research program: Improvement of Conventional Feeding and Risering Methods, Use of Unconventional Yield Improvement Techniques, and Case Studies in Yield Improvement. Casting trials were conducted and then simulated using the precise casting conditions as recorded by the participating SFSA foundries. These results present a statistically meaningful set of experimental data on soundness versus feeding length. Comparisons between these casting trials and casting trials performed more than forty years ago by Pellini and the SFSA are quite good and appear reasonable. Comparisons between the current SFSA feeding rules and feeding rules based on the minimum Niyama criterion reveal that the Niyama-based rules are generally less conservative. The niyama-based rules also agree better with both the trials presented here, and the casting trails performed by Pellini an d the SFSA years ago. Furthermore, the use of the Niyama criterion to predict centerline shrinkage for horizontally fed plate sections has a theoretical basis according to the casting literature reviewed here. These results strongly support the use of improved feeding rules for horizontal plate sections based on the Niyama criterion, which can be tailored to the casting conditions for a given alloy and to a desired level of soundness. The reliability and repeatability of ASTM shrinkage x-ray ratings was investigated in a statistical study performed on 128 x-rays, each of which were rated seven different times. A manual ''Feeding and Risering Guidelines for Steel Castings' is given in this final report. Results of casting trials performed to test unconventional techniques for improving casting yield are presented. These use a stacked arrangement of castings and riser pressurization to increase the casting yield. Riser pressurization was demonstrated to feed a casting up to


    NARCIS (Netherlands)


    We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Our main results apply to local (in position space) RG maps acting on systems of bounded spins (compact

  20. Renormalization of the quasiparticle band gap in doped two-dimensional materials from many-body calculations (United States)

    Gao, Shiyuan; Yang, Li


    Doped free carriers can substantially renormalize electronic self-energy and quasiparticle band gaps of two-dimensional (2D) materials. However, it is still challenging to quantitatively calculate this many-electron effect, particularly at the low doping density that is most relevant to realistic experiments and devices. Here we develop a first-principles-based effective-mass model within the G W approximation and show a dramatic band-gap renormalization of a few hundred meV for typical 2D semiconductors. Moreover, we reveal the roles of different many-electron interactions: The Coulomb-hole contribution is dominant for low doping densities while the screened-exchange contribution is dominant for high doping densities. Three prototypical 2D materials are studied by this method: h -BN , Mo S2 , and black phosphorus, covering insulators to semiconductors. Especially, anisotropic black phosphorus exhibits a surprisingly large band-gap renormalization because of its smaller density-of-state that enhances the screened-exchange interactions. Our work demonstrates an efficient way to accurately calculate band-gap renormalization and provides quantitative understanding of doping-dependent many-electron physics of general 2D semiconductors.

  1. Structural vs electronic origin of renormalized band widths in TTF-TCNQ: An angular dependent NEXAFS study

    DEFF Research Database (Denmark)

    Sing, M; Meyer, J; Hoinkis, M


    in the topmost surface layer. We find that the tilt angles of the molecules with respect to the one-dimensional axis are essentially the same as in the bulk. Thus, we can rule out surface relaxation as the origin of the renormalized band widths which were inferred from the analysis of photoemission data within...

  2. Bond yield curve construction

    Directory of Open Access Journals (Sweden)

    Kožul Nataša


    Full Text Available In the broadest sense, yield curve indicates the market's view of the evolution of interest rates over time. However, given that cost of borrowing it closely linked to creditworthiness (ability to repay, different yield curves will apply to different currencies, market sectors, or even individual issuers. As government borrowing is indicative of interest rate levels available to other market players in a particular country, and considering that bond issuance still remains the dominant form of sovereign debt, this paper describes yield curve construction using bonds. The relationship between zero-coupon yield, par yield and yield to maturity is given and their usage in determining curve discount factors is described. Their usage in deriving forward rates and pricing related derivative instruments is also discussed.

  3. Numerical renormalization group studies of the partially brogen SU(3) Kondo model

    Energy Technology Data Exchange (ETDEWEB)

    Fuh Chuo, Evaristus


    The two-channel Kondo (2CK) effect with its exotic ground state properties has remained difficult to realize in physical systems. At low energies, a quantum impurity with orbital degree of freedom, like a proton bound in an interstitial lattice space, comprises a 3-level system with a unique ground state and (at least) doubly degenerate rotational excitations with excitation energy {Delta}{sub 0}. When immersed in a metal, electronic angular momentum scattering induces transitions between any two of these levels (couplings J), while the electron spin is conserved. We show by extensive numerical renormalization group (NRG) calculations that without fi ne-tuning of parameters this system exhibits a 2CK fixed point, due to Kondo correlations in the excited-state doublet whose degeneracy is stabilized by the host lattice parity, while the channel symmetry (electron spin) is guaranteed by time reversal symmetry. We find a pronounced plateau in the entropy at S(T{sub K}>{Delta}{sub 0})=k{sub B} ln 3, and the 2CK ground state value, S(0)=k{sub B} ln {radical}(2). This indicates a downward renormalization of the doublet below the non-interacting ground state, thus realizing the 2CK fixed point, in agreement with earlier conjectures. We mapped out the phase diagram of the model in the J-{Delta}{sub 0} plane. The Kondo temperature T{sub K} shows non-monotonic J-dependence, characteristic for 2CK systems. Beside the two-channel Kondo effect of the model, we also study the single-channel version, which is realized by applying a strong magnetic fi eld to the conduction band electrons so that their degeneracy is lifted and consequently having only one kind of electrons scattering off the impurity. This single-channel case is easier to analyze since the Hilbert space is not as large as that of the 2CK. We equally find a downward renormalization of the excited state energy by the Kondo correlations in the SU(2) doublet

  4. Scale Setting Using the Extended Renormalization Group and the Principle of Maximal Conformality: the QCD Coupling at Four Loops

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, Stanley J.; /SLAC; Wu, Xing-Gang; /SLAC /Chongqing U.


    A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC)/Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal {beta}{sub i} terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. Different schemes lead to different effective PMC/BLM scales, but the final results are scheme independent. Conversely, from the requirement of scheme independence, one not only can obtain scheme-independent commensurate scale relations among different observables, but also determine the scale displacements among the PMC/BLM scales which are derived under different schemes. In principle, the PMC/BLM scales can be fixed order-by-order, and as a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit application for determining the scale setting of R{sub e{sup +}e{sup -}}(Q) up to four loops is presented. By using the world average {alpha}{sub s}{sup {ovr MS}}(MZ) = 0.1184 {+-} 0.0007, we obtain the asymptotic scale for the 't Hooft associated with the {ovr MS} scheme, {Lambda}{sub {ovr MS}}{sup 'tH} = 245{sub -10}{sup +9} MeV, and the asymptotic scale for the conventional {ovr MS} scheme, {Lambda}{sub {ovr MS}} = 213{sub -8}{sup +19} MeV.

  5. Electronic Raman scattering and the renormalization of the electron spectrum in LuB{sub 12}

    Energy Technology Data Exchange (ETDEWEB)

    Ponosov, Yu. S., E-mail:; Streltsov, S. V., E-mail: [Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation); Levchenko, A. V.; Filippov, V. B. [National Academy of Sciences of Ukraine, Frantsevich Institute of Materials Science Problems (Ukraine)


    The electronic Raman scattering in LuB{sub 12} single crystals of various isotope compositions is studied in the temperature range 10–650 K. The shape and the energy position of spectral maxima depend on the direction and magnitude of a probe wavevector, the temperature, and the excitation symmetry and remain unchanged when the isotope composition changes. Experimental spectra are compared with the spectra simulated on the basis of a calculated electronic structure. The experimental results are successfully described when the electron spectrum renormalization effects caused by electron–phonon coupling are taken into account. This confirms that the origin of the observed spectra in LuB{sub 12} is due to Raman scattering by electrons. A comparison of the calculated and experimental data makes it possible to determine the coupling constant (λ{sub ep} = 0.32) that gives the correct superconducting transition temperature.

  6. On the robustness of the primordial power spectrum in renormalized Higgs inflation (United States)

    Bezrukov, Fedor; Pauly, Martin; Rubio, Javier


    We study the cosmological consequences of higher-dimensional operators respecting the asymptotic symmetries of the tree-level Higgs inflation action. The main contribution of these operators to the renormalization group enhanced potential is localized in a compact field range, whose upper limit is close to the end of inflation. The spectrum of primordial fluctuations in the so-called universal regime turns out to be almost insensitive to radiative corrections and in excellent agreement with the present cosmological data. However, higher-dimensional operators can play an important role in critical Higgs inflation scenarios containing a quasi-inflection point along the inflationary trajectory. The interplay of radiative corrections with this quasi-inflection point may translate into a sizable modification of the inflationary observables.

  7. Excitation Energies Through the Locally Renormalized Equation-of-Motion Formalism: Singles and Doubles Model

    Energy Technology Data Exchange (ETDEWEB)

    Kowalski, Karol


    The stationary conditions obtained from approximate coupled-cluster functional derived from the Numerator-Denominator connected Expansion (NDC) [K. Kowalski, P. Piecuch, J Chem. Phys. 122 (2005) 074107] are employed to calculate the linear response of cluster amplitudes. A simple scheme that involves singly and doubly excited amplitudes, termed locally renormalized equation-of-motion approach with singles and doubles (LR-EOMCCSD), is compared with other excited-state methods that include up to two-body operators in the wavefunction expansion. In particular, the impact of the local denominators on the excitation energies is discussed in detail. Several benchmark calculations on the CH+, C?, N?, O?, CIOCI molecules are presented to illustrate the performance of the LR-EOMCCSD approach.

  8. Density-matrix renormalization-group study of current and activity fluctuations near nonequilibrium phase transitions. (United States)

    Gorissen, Mieke; Hooyberghs, Jef; Vanderzande, Carlo


    Cumulants of a fluctuating current can be obtained from a free-energy-like generating function, which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the density-matrix renormalization group for stochastic systems. We calculate the variance of the current in the different phases, and at the phase transitions, of the totally asymmetric exclusion process. Our results can be described in the terms of a scaling ansatz that involves the dynamical exponent z . We also calculate the generating function of the dynamical activity (total number of configuration changes) near the absorbing-state transition of the contact process. Its scaling properties can be expressed in terms of known critical exponents.

  9. A renormalized Perelman-functional and a lower bound for the ADM-mass (United States)

    Haslhofer, Robert


    In the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning the regularity of Ricci-flat spaces and the non-uniqueness of the Ricci flow with conical initial data. In the second part, we define a geometric invariant λ for asymptotically flat manifolds with nonnegative scalar curvature. This invariant gives a quantitative lower bound for the ADM-mass from general relativity, motivates a Ricci flow proof of the rigidity statement in the positive mass theorem, and eventually leads to the discovery of a mass-decreasing flow in dimension three.

  10. About renormalization of the Yang - Mills theory and the approach to calculation of the heat kernel (United States)

    Ivanov, Aleksandr


    The quantum theory of Yang - Mills in four-dimensional space - time plays an important role in modern theoretical physics. Currently, this model contains many open problems, therefore, it is of great interest to mathematicians. This work consists of several parts, however, it only offers a new approach and, therefore, it is methodological. First of all, the diagram technique and the mathematical basis will be recalled in the first part. Then the process of renormalization will be explained. It is based on momentum cut-off regularization and described in [1] and [2]. However, this type of the regularization has several problems, as a result, only the first correction is calculated. After common constructions and observations, the first correction will be described in detail. Namely, the heat kernel will be considered since it plays a main role in this formalism. In particular, the method for calculating of coefficients of arbitrary order will be proposed.

  11. Phonon renormalization of the Nèel transition in KCuF3 (United States)

    Lee, J. C. T.; Yuan, S.; Rusydi, A.; Smadici, S.; Cooper, S. L.; Fradkin, E.; Abbamonte, P.


    Critical magnetic fluctuations in the one-dimensional antiferromagnet KCuF3, in the form of diffuse scattering around the magnetic (001) Bragg peak, have been studied with resonant soft x-ray scattering. Using x-rays near the Cu L3 edge to exploit the 2p -> 3d dipole transition, the (001) was directly observed at temperatures ranging from 23K to above the transition temperature (TN 43K). Notably, the phase transition exhibits hysteresis, with TN sensitive to whether the sample was cooled or heated prior to measurement. This suggests that the phase transition is weakly first order, as might be expected by a transition renormalized by phonons. The temperature dependence of the coherence length and the diffuse scattering, as well as the role played by Jahn-Teller phonons in the transition are discussed.

  12. Dimensional renormalization in {phi}{sup 3} theory: Ladders and rainbows

    Energy Technology Data Exchange (ETDEWEB)

    Delbourgo, R.; Elliott, D. [University of Tasmania, GPO Box 252-21, Hobart, Tasmania 7001 (Australia); McAnally, D.S. [University of Queensland, St Lucia, Brisbane, Queensland 4067 (Australia)


    The sum of all the ladder and rainbow diagrams in {phi}{sup 3} theory near six dimensions leads to self-consistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now succeeded in solving these equations, expressing the results in terms of generalized hypergeometric functions; the expansion and representation of these functions can then be used to prove the absence of renormalization factors which are transcendental for this theory and this topology to all orders in perturbation theory. The correct anomalous scaling dimensions of the Green functions are also obtained in the six-dimensional limit. {copyright} {ital 1997} {ital The American Physical Society}

  13. Analytic renormalized bipartite and tripartite quantum discords with quantum phase transition in XXZ spins chain (United States)

    Joya, Wajid; Khan, Salman; Khalid Khan, M.; Alam, Sher


    The behavior of bipartite quantum discord (BQD) and tripartite quantum discord (TQD) in the Heisenberg XXZ spins chain is investigated with the increasing size of the system using the approach of the quantum renormalization group method. Analytical relations for both BQD and TQD are obtained and the results are checked through numerical optimization. In the thermodynamics limit, both types of discord exhibit quantum phase transition (QPT). The boundary of QPT links the phases of saturated discord and zero discord. The first derivative of both discords becomes discontinuous at the critical point, which corresponds to the second-order phase transition. Qualitatively identical, the amount of saturated BQD strongly depends on the relative positions of spins inside a block. TQD can be a better candidate than BQD both for analyzing QPT and implementing quantum information tasks. The scaling behavior in the vicinity of the critical point is discussed.

  14. Low-energy electronic excitations and band-gap renormalization in CuO (United States)

    Rödl, Claudia; Ruotsalainen, Kari O.; Sottile, Francesco; Honkanen, Ari-Pekka; Ablett, James M.; Rueff, Jean-Pascal; Sirotti, Fausto; Verbeni, Roberto; Al-Zein, Ali; Reining, Lucia; Huotari, Simo


    Combining nonresonant inelastic x-ray scattering experiments with state-of-the-art ab initio many-body calculations, we investigate the electronic screening mechanisms in strongly correlated CuO in a large range of energy and momentum transfers. The excellent agreement between theory and experiment, including the low-energy charge excitations, allows us to use the calculated dynamical screening as a safe building block for many-body perturbation theory and to elucidate the crucial role played by d -d excitations in renormalizing the band gap of CuO. In this way we can dissect the contributions of different excitations to the electronic self-energy which is illuminating concerning both the general theory and this prototypical material.

  15. On the renormalization of topological Yang-Mills field theory in N=1 superspace

    Energy Technology Data Exchange (ETDEWEB)

    Oliveira, M.W. de; Penna Firme, A.B.


    We discuss the renormalization aspects of topological super-Yang-Mills field theory in N=1 superspace. Our approach makes use of the regularization independent BRS algebraic technique adapted to the case of a N=1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be BRS-coboundary, implying that the co-homological properties of the super topological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik {beta}-function of the model by employing a recently discovered supersymmetric antighost Ward identity. (author). 30 refs.

  16. Renormalization group equation analysis of a pseudoscalar portal dark matter model (United States)

    Ghorbani, Karim


    We investigate the vacuum stability and perturbativity of a pseudoscalar portal dark matter (DM) model with a Dirac DM candidate, through the renormalization group equation analysis at one-loop order. The model has a particular feature which can evade the direct detection upper bounds measured by XENON100 and even that from planned experiment XENON1T. We first find the viable regions in the parameter space which will give rise to correct DM relic density and comply with the constraints from Higgs physics. We show that for a given mass of the pseudoscalar, the mixing angle plays no significant role in the running of the couplings. Then we study the running of the couplings for various pseudoscalar masses at mixing angle θ =6^\\circ , and find the scale of validity in terms of the dark coupling, {λ }d. Depending on our choice of the cutoff scale, the resulting viable parameter space will be determined.

  17. Point-particle effective field theory I: classical renormalization and the inverse-square potential (United States)

    Burgess, C. P.; Hayman, Peter; Williams, M.; Zalavári, László


    Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original prob-lem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective point-particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction catalysis, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.

  18. Comparing finite elements and finite differences for developing diffusive models of glioma growth. (United States)

    Roniotis, Alexandros; Marias, Kostas; Sakkalis, Vangelis; Stamatakos, Georgios; Zervakis, Michalis


    Glioma is the most aggressive type of brain tumor. Several mathematical models have been developed during the last two decades, towards simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. The proposed diffusive models have mainly used finite differences (FDs) or finite elements (FEs) for the approximation of the solution of the partial differential DRE. This paper presents experimental results on the comparison of the FEs and FDs, especially focused on the glioma model case. It is studied how the different meshes of brain can affect computational consistency, simulation time and efficiency of the model. The experiments have been studied on a test case, for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the error that the different models yield.

  19. Solution of Finite Element Equations

    DEFF Research Database (Denmark)

    Krenk, Steen

    An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...

  20. Reduction of Couplings in Quantum Field Theories with applications in Finite Theories and the MSSM

    CERN Document Server

    Heinemeyer, S; Tracas, N; Zoupanos, G


    We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in perturbation theory. It has a remarkable predictive power since, at the unification scale, it leads to relations between gauge and Yukawa couplings in the dimensionless sectors and relations involving the trilinear terms and the Yukawa couplings, as well as a sum rule among the scalar masses and the unified gaugino mass in the soft breaking sector. In both the MSSM and the FUT model we predict the masses of the top and bottom quarks and the light Higgs in remarkable agreement with the experiment. Furthermore we also predict the masses of the other Higgses, as well as the supersymmetric spectrum, both being in very confortable agreement with the LHC bounds on Higgs and supersymmetric particles.

  1. Self-consistent calculations within the extended theory of finite Fermi systems (United States)

    Avdeenkov, A.; Grümmer, F.; Kamerdzhiev, S.; Krewald, S.; Lyutorovich, N.; Speth, J.


    The Extended Theory of Finite Fermi Systems (ETFFS) describes nuclear excitations considering phonons and pairing degrees of freedom, using the effective Landau-Migdal interaction and nuclear mean fields obtained from experimental data. Here we employ the nuclear mean field derived from Skyrme interactions and the corresponding particle-hole interaction. This allows to extend the range of applicability of the ETFFS to experimentally not yet investigated short-lived isotopes. We find that Skyrme interactions which reproduce at the mean field level both ground state properties and nuclear excitations are able to describe the spreading widths of the giant resonances in the new approach, but produce shifts of the centroid energies. A renormalization of the Skyrme interactions is required for approaches going beyond the mean field level.

  2. Self-consistent calculations within the extended theory of finite Fermi systems

    Energy Technology Data Exchange (ETDEWEB)

    Avdeenkov, A. [Institut fuer Kernphysik, Forschungszentrum Juelich, 52425 Juelich (Germany); Institute of Physics and Power Engineering, 249020 Obninsk (Russian Federation); Gruemmer, F. [Institut fuer Kernphysik, Forschungszentrum Juelich, 52425 Juelich (Germany); Kamerdzhiev, S. [Institute of Physics and Power Engineering, 249020 Obninsk (Russian Federation); Krewald, S. [Institut fuer Kernphysik, Forschungszentrum Juelich, 52425 Juelich (Germany); Lyutorovich, N. [Institut fuer Kernphysik, Forschungszentrum Juelich, 52425 Juelich (Germany); Institute of Physics, St. Petersburg University (Russian Federation); Speth, J. [Institut fuer Kernphysik, Forschungszentrum Juelich, 52425 Juelich (Germany); Institute of Nuclear Physics, PAN, PL-31-342 Cracow (Poland)], E-mail:


    The Extended Theory of Finite Fermi Systems (ETFFS) describes nuclear excitations considering phonons and pairing degrees of freedom, using the effective Landau-Migdal interaction and nuclear mean fields obtained from experimental data. Here we employ the nuclear mean field derived from Skyrme interactions and the corresponding particle-hole interaction. This allows to extend the range of applicability of the ETFFS to experimentally not yet investigated short-lived isotopes. We find that Skyrme interactions which reproduce at the mean field level both ground state properties and nuclear excitations are able to describe the spreading widths of the giant resonances in the new approach, but produce shifts of the centroid energies. A renormalization of the Skyrme interactions is required for approaches going beyond the mean field level.

  3. Massively Parallel Finite Element Programming

    KAUST Repository

    Heister, Timo


    Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

  4. The large-N Yang-Mills S matrix is ultraviolet finite, but the large-N QCD S matrix is only renormalizable (United States)

    Bochicchio, Marco


    Yang-Mills (YM) theory and QCD are known to be renormalizable, but not ultraviolet (UV) finite, order by order, in perturbation theory. It is a fundamental question whether YM theory or QCD is UV finite, or only renormalizable, order by order, in the large-N 't Hooft or Veneziano expansions. We demonstrate that the renormalization group (RG) and asymptotic freedom imply that in 't Hooft large-N expansion the S matrix in YM theory is UV finite, while in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massless QCD is renormalizable but not UV finite. By the same argument, the large-N N =1 supersymmetry (SUSY) YM S matrix is UV finite as well. Besides, we demonstrate that, in both 't Hooft and Veneziano large-N expansions, the correlators of local gauge-invariant operators, as opposed to the S matrix, are renormalizable but, in general, not UV finite, either in YM theory and N =1 SUSY YM theory or a fortiori in massless QCD. Moreover, we compute explicitly the counterterms that arise from renormalizing the 't Hooft and Veneziano expansions by deriving in confining massless QCD-like theories a low-energy theorem of the Novikov-Shifman-Vainshtein-Zakharov type that relates the log derivative with respect to the gauge coupling of a k -point correlator, or the log derivative with respect to the RG-invariant scale, to a (k +1 )-point correlator with the insertion of Tr F2 at zero momentum. Finally, we argue that similar results hold in the large-N limit of a vast class of confining massive QCD-like theories, provided a renormalization scheme exists—as, for example, MS ¯ —in which the beta function is not dependent on the masses. Specifically, in both 't Hooft and Veneziano large-N expansions, the S matrix in confining massive QCD and massive N =1 SUSY QCD is renormalizable but not UV finite.

  5. Finite element and finite difference methods in electromagnetic scattering

    CERN Document Server

    Morgan, MA


    This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca

  6. Lower Bound Limit Analysis Of Slabs With Nonlinear Yield Criteria

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars


    A finite element formulation of the limit analysis of perfectly plastic slabs is given. An element with linear moment fields for which equilibrium is satisfied exactly is used in connection with an optimization algorithm taking into account the full nonlinearity of the yield criteria. Both load...

  7. Yield stress independent column buckling curves

    DEFF Research Database (Denmark)

    Stan, Tudor‐Cristian; Jönsson, Jeppe


    in the definition of the normalised imperfection magnitudes. By introducing this factor it seems that the GMNIA analysis and knowledge of the independency of residual stress levels on the yield stress can be brought together and give results showing consistency between numerical modelling and a simple modified...... Ayrton‐Perry formulation. In this paper magnitudes of imperfections and residual stresses in relation to the Eurocode will be discussed. It will be shown that the use of equivalent imperfections may be very conservative if considered by finite element analysis as described in the current Eurocode code...

  8. Exact tensor hypercontraction: a universal technique for the resolution of matrix elements of local finite-range N-body potentials in many-body quantum problems. (United States)

    Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, Todd J


    Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the exact tensor hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchangelike" contractions.

  9. Fierz-complete NJL model study: Fixed points and phase structure at finite temperature and density (United States)

    Braun, Jens; Leonhardt, Marc; Pospiech, Martin


    Nambu-Jona-Lasinio-type models are frequently employed as low-energy models in various research fields. With respect to the theory of the strong interaction, this class of models is indeed often used to analyze the structure of the phase diagram at finite temperature and quark chemical potential. The predictions from such models for the phase structure at finite quark chemical potential are of particular interest as this regime is difficult to access with lattice Monte Carlo approaches. In this work, we consider a Fierz-complete version of a Nambu-Jona-Lasinio model. By studying its renormalization group flow, we analyze in detail how Fierz-incomplete approximations affect the predictive power of such model studies. In particular, we investigate the curvature of the phase boundary at small chemical potential, the critical value of the chemical potential above which no spontaneous symmetry breaking occurs, and the possible interpretation of the underlying dynamics in terms of difermion-type degrees of freedom. We find that the inclusion of four-fermion channels other than the conventional scalar-pseudoscalar channel is not only important at large chemical potential but also leaves a significant imprint on the dynamics at small chemical potential as measured by the curvature of the finite-temperature phase boundary.

  10. Extending Finite Memory Determinacy to Multiplayer Games

    National Research Council Canada - National Science Library

    Le Roux, Stéphane; Pauly, Arno


    We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite...

  11. Finite element computational fluid mechanics (United States)

    Baker, A. J.


    Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.

  12. quadratic spline finite element method

    Directory of Open Access Journals (Sweden)

    A. R. Bahadir


    Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.

  13. A finite amplitude necking model of rifting in brittle lithosphere (United States)

    Lin, Jian; Parmentier, E. M.


    We formulate a mechanical model describing the formation of rifts as finite amplitude necking of an elastic-plastic layer overlying a fluid substrate. A perfectly plastic rheology is a continuum description of faulting in rift zones. Two important aspects of rift evolution are illustrated by this model: the evolution of the rift width as extension proceeds and the finite strain that occurs. A region at yield initially develops with a width determined by the thickness of the brittle layer, and the internal deformation within this yield zone is proportional to the topographic slope. As extension proceeds, the surface within the rift subsides, and the width of the subsiding yield zone decreases. At any stage of rifting, material in regions just outside the yield zone is deformed but no longer deforming. The width of these deformed regions increases with increasing extension. Vertical forces due to the mass deficit of the rift depression will flex the elastic layer outside the yield zone, creating flanking uplifts. The external force required to maintain active rifting increases with the amount of lithospheric stretching, indicating that rifting is a quasi-static, stable process. Because the yield zone will revert to elastic behavior if the external force causing extension is removed, the model predicts that the rift depression and flanking uplifts will be preserved after extension stops. Our simple mechanical model demonstrates the inherent relationship among graben formation, lithospheric thinning, and rift shoulder uplift in rift zones.

  14. Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

    CERN Document Server

    Rodrigues, Davi C; de Almeida, Álefe O F


    General Relativity extensions based on Renormalization Group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post Newtonian limits of a realisation called Renormalization Group extended General Relativity (RGGR). Special attention is taken to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter $\\bar \

  15. Green's Functions and Finite Elements

    CERN Document Server

    Hartmann, Friedel


    This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions  and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

  16. Language dynamics in finite populations. (United States)

    Komarova, Natalia L; Nowak, Martin A


    Any mechanism of language acquisition can only learn a restricted set of grammars. The human brain contains a mechanism for language acquisition which can learn a restricted set of grammars. The theory of this restricted set is universal grammar (UG). UG has to be sufficiently specific to induce linguistic coherence in a population. This phenomenon is known as "coherence threshold". Previously, we have calculated the coherence threshold for deterministic dynamics and infinitely large populations. Here, we extend the framework to stochastic processes and finite populations. If there is selection for communicative function (selective language dynamics), then the analytic results for infinite populations are excellent approximations for finite populations; as expected, finite populations need a slightly higher accuracy of language acquisition to maintain coherence. If there is no selection for communicative function (neutral language dynamics), then linguistic coherence is only possible for finite populations. Copyright 2003 Elsevier Science Ltd.

  17. Domain Wall Fermion Study Of Scaling In Non-perturbative Renormalization Of Quark Bilinears And B(k)

    CERN Document Server

    Zhestkov, Y G


    We develop a non-perturbative scaling technique that connects the results of simulations at different values of coupling β to obtain the renormalization coefficients of scalar and pseudoscalar operators, local vector and axial currents, conserved vector and axial currents over the range of energy scales from 1 to 10 GeV. This technique is then applied to discuss the renormalization of the physically important operator ODS=2LL , central to our understanding of CP violation. We use the domain wall fermion formulation in the quenched approximation at a series of three values of β, 6.0, 6.45, and 7.05, corresponding to lattice spacing scaling by factors of two. The lattice volumes used in the series of simulations are 84 and 164 with the extent in the fifth dimension Ls = 14.

  18. Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven


    as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....

  19. Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven


    as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe...

  20. Finiteness and Computation in Toposes

    Directory of Open Access Journals (Sweden)

    Edward Hermann Haeusler


    Full Text Available Some notions in mathematics can be considered relative. Relative is a term used to denote when the variation in the position of an observer implies variation in properties or measures on the observed object. We know, from Skolem theorem, that there are first-order models where the set of real numbers is countable and some where it is not. This fact depends on the position of the observer and on the instrument/language the obserevr uses as well, i.e., it depends on whether he/she is inside the model or not and in this particular case the use of first-order logic. In this article, we assume that computation is based on finiteness rather than natural numbers and discuss Turing machines computable morphisms defined on top of the sole notion finiteness. We explore the relativity of finiteness in models provided by toposes where the Axiom of Choice (AC does not hold, since Tarski proved that if AC holds then all finiteness notions are equivalent. Our toposes do not have natural numbers object (NNO either, since in a topos with a NNO these finiteness notions are equivalent to Peano finiteness going back to computation on top of Natural Numbers. The main contribution of this article is to show that although from inside every topos, with the properties previously stated, the computation model is standard, from outside some of these toposes, unexpected properties on the computation arise, e.g., infinitely long programs, finite computations containing infinitely long ones, infinitely branching computations. We mainly consider Dedekind and Kuratowski notions of finiteness in this article.

  1. Programming the finite element method

    CERN Document Server

    Smith, I M; Margetts, L


    Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c

  2. Quantum field theory and phase transitions: universality and renormalization group; Theorie quantique des champs et transitions de phase: universalite et groupe de renormalisation

    Energy Technology Data Exchange (ETDEWEB)

    Zinn-Justin, J


    In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)

  3. Renormalization of modular invariant Coulomb gas and sine-Gordon theories, and the quantum Hall flow diagram

    Energy Technology Data Exchange (ETDEWEB)

    Carpentier, David [Laboratoire de Physique Theorique de l' Ecole Normale Superieure, Paris (France)


    Using the renormalization group (RG) we study two-dimensional electromagnetic Coulomb gas and extended sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following the proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram. (author)

  4. Effects of renormalization parameters on singularities and special soliton solutions of the modified complex Ginzburg-Landau equation

    Energy Technology Data Exchange (ETDEWEB)

    Kenfack-Jiotsa, A [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P 812 Yaounde (Cameroon); Fewo, S I [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P 812 Yaounde (Cameroon); Kofane, T C [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P 812 Yaounde (Cameroon)


    Considering a pulse-like ansatz, we derive different classes of exact soliton solutions of the modified complex Ginzburg-Landau equation. We then present the important variations which occur in the domain of stability of these solutions depending on the values of the renormalization coeffecients. This means that this term which can be considered for nonzero solutions and which does not generally occur in the literature could explain the lack of concordance between some theory and experiments.

  5. c-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow

    Directory of Open Access Journals (Sweden)

    V. Bacsó


    Full Text Available In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency β2, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (β2<8π to the infra-red limit is in good quantitative agreement with the expected Δc=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation is crucial to get sensible results even when a single frequency is used.

  6. Critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices. (United States)

    Monthus, Cécile; Garel, Thomas


    We study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices. These two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the partition function. (These exact renormalizations on diamond lattices can also be considered as approximate Migdal-Kadanoff renormalizations for hypercubic lattices.) In terms of the rescaled partition function z=Z/Z(typ) , we find that the critical point corresponds to a fixed point distribution with a power-law tail P(c)(z) ~ Phi(ln z)/z(1+mu) as z-->+infinity [up to some subleading logarithmic correction Phi(ln z)], so that all moments z(n) with n>mu diverge. For the wetting transition, the first moment diverges z=+infinity (case 0infinity (case 1fixed point distribution coincides with the transfer matrix describing a directed polymer on the Cayley tree, but the random weights determined by the fixed point distribution P(c)(z) are broadly distributed. This induces some changes in the traveling wave solutions with respect to the usual case of more narrow distributions.

  7. Friction welding; Magnesium; Finite element; Shear test.

    Directory of Open Access Journals (Sweden)

    Leonardo Contri Campanelli


    Full Text Available Friction spot welding (FSpW is one of the most recently developed solid state joining technologies. In this work, based on former publications, a computer aided draft and engineering resource is used to model a FSpW joint on AZ31 magnesium alloy sheets and subsequently submit the assembly to a typical shear test loading, using a linear elastic model, in order to conceive mechanical tests results. Finite element analysis shows that the plastic flow is concentrated on the welded zone periphery where yield strength is reached. It is supposed that “through the weld” and “circumferential pull-out” variants should be the main failure behaviors, although mechanical testing may provide other types of fracture due to metallurgical features.

  8. Driven interfaces in random media at finite temperature: existence of an anomalous zero-velocity phase at small external force. (United States)

    Monthus, Cécile; Garel, Thomas


    The motion of driven interfaces in random media at finite temperature T and small external force F is usually described by a linear displacement h{G}(t) approximately V(F,T)t at large times, where the velocity vanishes according to the creep formula as V(F,T) approximately e;{-K(T)F;{mu}} for F-->0 . In this paper, we question this picture on the specific example of the directed polymer in a two-dimensional random medium. We have recently shown [C. Monthus and T. Garel, J. Phys. A 41, 255002 (2008)] that its dynamics for F=0 can be analyzed in terms of a strong disorder renormalization procedure, where the distribution of renormalized barriers flows towards some "infinite disorder fixed point." In the present paper, we obtain that for small F , this "infinite disorder fixed point" becomes a "strong disorder fixed point" with an exponential distribution of renormalized barriers. The corresponding distribution of trapping times then only decays as a power law P(tau) approximately 1tau;{1+alpha} , where the exponent alpha(F,T) vanishes as alpha(F,T) proportional, variant F micro as F-->0 . Our conclusion is that in the small force region alpha(F,T)infinity induces strong non-self-averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value. We find instead that the motion is only sublinearly in time h{G}(t) approximately t;{alpha(F,T)} , i.e., the asymptotic velocity vanishes V=0 . This analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape. We moreover obtain that the roughness exponent, which is governed by the equilibrium value zeta{eq}=23 up to some large scale, becomes equal to zeta=1 at the largest scales.

  9. Renormalization group study of the minimal Majoronic dark radiation and dark matter model

    Energy Technology Data Exchange (ETDEWEB)

    Chang, We-Fu [Department of Physics, National Tsing Hua University,101, Sec. 2, KuangFu Rd., Hsinchu 300, Taiwan (China); Ng, John N. [Theory Group, TRIUMF,4004 Wesbrook Mall, Vancouver BC V6T 2A3 (Canada)


    We study the 1-loop renormalization group equation running in the simplest singlet Majoron model constructed by us earlier to accommodate the dark radiation and dark matter content in the universe. A comprehensive numerical study was performed to explore the whole model parameter space. A smaller effective number of neutrinos △N{sub eff}∼0.05, or a Majoron decoupling temperature higher than the charm quark mass, is preferred. We found that a heavy scalar dark matter, ρ, of mass 1.5–4 TeV is required by the stability of the scalar potential and an operational type-I see-saw mechanism for neutrino masses. A neutral scalar, S, of mass in the 10–100 GeV range and its mixing with the standard model Higgs as large as 0.1 is also predicted. The dominant decay modes are S into bb-bar and/or ωω. A sensitive search will come from rare Z decays via the chain Z→S+ff-bar, where f is a Standard Model fermion, followed by S into a pair of Majoron and/or b-quarks. The interesting consequences of dark matter bound state due to the sizable Sρρ-coupling are discussed as well. In particular, shower-like events with an apparent neutrino energy at M{sub ρ} could contribute to the observed effective neutrino flux in underground neutrino detectors such as IceCube.

  10. Renormalization Group Flows from Holography-Supersymmetry and a c-Theorem

    CERN Document Server

    Freedman, D.Z.; Pilch, K.; Warner, N.P.


    We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N=4 gauged supergravity theory holographically dual to a sector of N=2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function...

  11. Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams

    CERN Document Server

    Brodsky, Stanley J.; Gardi, Einan; Karliner, Marek; Samuel, Mark.A.; Brodsky, Stanley J.; Ellis, John; Gardi, Einan; Karliner, Marek; Samuel, Mark. A.


    We show that the Padé Approximant (PA) approach for resummation of perturbative series in QCD provides a systematic method for approximating the flow of momentum in Feynman diagrams. In the large-$\\beta_0$ limit, diagonal PA's generalize the Brodsky-Lepage-Mackenzie (BLM) scale-setting method to higher orders in a renormalization scale- and scheme-invariant manner, using multiple scales that represent Neubert's concept of the distribution of momentum flow through a virtual gluon. If the distribution is non-negative, the PA's have only real roots, and approximate the distribution function by a sum of delta-functions, whose locations and weights are identical to the optimal choice provided by the Gaussian quadrature method for numerical integration. We show how the first few coefficients in a perturbative series can set rigorous bounds on the all-order momentum distribution function, if it is positive. We illustrate the method with the vacuum polarization function and the Bjorken sum rule computed in the large...

  12. Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group (United States)

    Vian, F.


    The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.

  13. Many-body localization in one dimension as a dynamical renormalization group fixed poin (United States)

    Vosk, Ronen; Altman, Ehud


    We formulate a dynamical real space renormalization group approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. Lack of true thermalization in the long time limit is attributed to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble. Within the RG framework we show that long range resonances are irrelevant at strong randomness, and formulate a criterion for when they do become relevant and may cause a delocalization transition.

  14. Many-Body Localization in One Dimension as a Dynamical Renormalization Group Fixed Point (United States)

    Vosk, Ronen; Altman, Ehud


    We formulate a dynamical real space renormalization group (RG) approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular, we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. This is in striking contrast to the much slower entropy growth as log⁡log⁡t found for noninteracting fermions with bond disorder. Nonetheless, even the interacting system does not thermalize in the long time limit. We attribute this to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.

  15. Conductance Fano lineshapes for Kondo impurities on surfaces: A numerical renormalization group description. (United States)

    Sandler, Nancy; Dias da Silva, Luis; Ulloa, Sergio


    Scanning tunneling microscopy (STM) measurements of Kondo impurities on metallic surfaces has been an active field in recent years. For a flat density-of-states (DoS) near the Fermi energy in the host metal, the low-bias STM conductance acquires the characteristic Fano lineshape, with width proportional to the Kondo temperature TK. In this work, we study how this picture is modified when a structured DoS (non-flat) is considered. A variety of physical effects can introduce peak/dips in the DoS, including the presence of a second impurity, hybridization between surface and bulk conduction states, and a magnetic impurity embedded in a molecule. Using numerical renormalization group techniques, we calculate the low-temperature conductance for this system. The zero-bias dip in the Fano conductance is modified by the presence of resonances or anti-resonances in the DoS near EF. In particular, for DoS with pseudogaps and impurities in the mixed-valence regime, zero-bias Fano-like dips appear even when no Kondo state has developed, but governed by energy scales much larger than TK. We further show that measurements of the scattering phase could be used as an additional probe into the Kondo regime. Supported by NFS-NIRT.

  16. Density-matrix renormalization group studies on a magnetic impurity in graphene (United States)

    Shirakawa, Tomonori; Yunoki, Seiji


    Motivated by recent experiments on the emergence of magnetism in graphene induced by lattice defects or by magnetic adatoms, we have theoretically studied the ground state properties of single magnetic impurity in grapheme. First, we have developed a new numerical technique within the density-matrix renormalization group (DMRG) scheme for magnetic impurity model in general to study site-dependent quantities including local density of states even away from magnetic impurity site, Friedel density oscillations, and spin-spin correlation functions between the magnetic impurity and the surrounding conduction electrons. This new technique is applied to three different models: (i) a magnetic adatom on grapheme, (ii) a substitutional magnetic impurity in grapheme, and (iii) a model on defect in the graphene. Our systematic study of these models reveals that, in the presence of particle-hole symmetry, the ground state of model (i) exhibits the formation of local moments without Kondo-screening, whereas the others behave very similarly to the Kondo singlet states. We also discuss the real-space decay of spin-spin correlations between magnetic impurity and surrounding conduction electrons in these models.

  17. Versatile Method for Renormalized Stress-Energy Computation in Black-Hole Spacetimes. (United States)

    Levi, Adam; Ori, Amos


    We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a single symmetry. Thus far, we have developed three variants of the method, aimed for stationary, spherically symmetric, or axially symmetric BHs. We used this method to calculate the RSET of a minimally coupled massless scalar field in Schwarzschild and Reissner-Nordström backgrounds for several quantum states. We present here the results for the RSET in the Schwarzschild case in the Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at r≲2.78M. Then we use the RSET results to explore violation of the weak and null energy conditions. We find that both conditions are violated all the way from r≃4.9M to the horizon. We also find that the averaged weak energy condition is violated by a class of (unstable) circular timelike geodesics. Most remarkably, the circular null geodesic at r=3M violates the averaged null energy condition.

  18. Fast Quantum State Transfer and Entanglement Renormalization Using Long-Range Interactions (United States)

    Eldredge, Zachary; Gong, Zhe-Xuan; Young, Jeremy T.; Moosavian, Ali Hamed; Foss-Feig, Michael; Gorshkov, Alexey V.


    In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speedup possible is an open question. In this Letter, we present a protocol capable of transferring a quantum state across a distance L in d dimensions using long-range interactions with a strength bounded by 1 /rα. If α renormalization ansatz (MERA) tensor network and show that if the linear size of the MERA state is L , then it can be created in a time that scales with L identically to the state transfer up to logarithmic corrections. This protocol realizes an exponential speedup in cases of α =d , which could be useful in creating large entangled states for dipole-dipole (1 /r3) interactions in three dimensions.

  19. Large counterions boost the solubility and renormalized charge of suspended nanoparticles. (United States)

    Guerrero-García, Guillermo Iván; González-Mozuelos, Pedro; Olvera de la Cruz, Monica


    Colloidal particles are ubiquitous in biology and in everyday products such as milk, cosmetics, lubricants, paints, or drugs. The stability and aggregation of colloidal suspensions are of paramount importance in nature and in diverse nanotechnological applications, including the fabrication of photonic materials and scaffolds for biological assemblies, gene therapy, diagnostics, targeted drug delivery, and molecular labeling. Electrolyte solutions have been extensively used to stabilize and direct the assembly of colloidal particles. In electrolytes, the effective electrostatic interactions among the suspended colloids can be changed over various length scales by tuning the ionic concentration. However, a major limitation is gelation or flocculation at high salt concentrations. This is explained by classical theories, which show that the electrostatic repulsion among charged colloids is significantly reduced at high electrolyte concentrations. As a result, these screened colloidal particles are expected to aggregate due to short-range attractive interactions or dispersion forces as the salt concentration increases. We discuss here a robust, tunable mechanism for colloidal stability by which large counterions prevent highly charged nanoparticles from aggregating in salt solutions with concentrations up to 1 M. Large counterions are shown to generate a thicker ionic cloud in the proximity of each charged colloid, which strengthens short-range repulsions among colloidal particles and also increases the corresponding renormalized colloidal charge perceived at larger separation distances. These effects thus provide a reliable stabilization mechanism in a broad range of biological and synthetic colloidal suspensions.

  20. Renormalization group theory outperforms other approaches in statistical comparison between upscaling techniques for porous media (United States)

    Hanasoge, Shravan; Agarwal, Umang; Tandon, Kunj; Koelman, J. M. Vianney A.


    Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.

  1. Field induced spontaneous quasiparticle decay and renormalization of quasiparticle dispersion in a quantum antiferromagnet (United States)

    Hong, Tao; Qiu, Y.; Matsumoto, M.; Tennant, D. A.; Coester, K.; Schmidt, K. P.; Awwadi, F. F.; Turnbull, M. M.; Agrawal, H.; Chernyshev, A. L.


    The notion of a quasiparticle, such as a phonon, a roton or a magnon, is used in modern condensed matter physics to describe an elementary collective excitation. The intrinsic zero-temperature magnon damping in quantum spin systems can be driven by the interaction of the one-magnon states and multi-magnon continuum. However, detailed experimental studies on this quantum many-body effect induced by an applied magnetic field are rare. Here we present a high-resolution neutron scattering study in high fields on an S=1/2 antiferromagnet C9H18N2CuBr4. Compared with the non-interacting linear spin–wave theory, our results demonstrate a variety of phenomena including field-induced renormalization of one-magnon dispersion, spontaneous magnon decay observed via intrinsic linewidth broadening, unusual non-Lorentzian two-peak structure in the excitation spectra and a dramatic shift of spectral weight from one-magnon state to the two-magnon continuum. PMID:28474679

  2. Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction

    Energy Technology Data Exchange (ETDEWEB)

    Song, Xue-ke [School of Physics and Material Science, Anhui University, Hefei, 230039 (China); Wu, Tao [School of Physics and Electronics Science, Fuyang Normal College, Fuyang, 236037 (China); Xu, Shuai; He, Juan [School of Physics and Material Science, Anhui University, Hefei, 230039 (China); Ye, Liu, E-mail: [School of Physics and Material Science, Anhui University, Hefei, 230039 (China)


    In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.

  3. Study of two dimensional anisotropic Ising models via a renormalization group approach (United States)

    Taherkhani, Farid; Akbarzadeh, Hamed; Abroshan, Hadi; Ranjbar, Shahram; Fortunelli, Alessandro; Parsafar, Gholamabbas


    A method is developed to calculate the critical line of two dimensional (2D) anisotropic Ising model including nearest-neighbor interactions. The method is based on the real-space renormalization group (RG) theory with increasing block sizes. The reduced temperatures, Ks (where K={J}/{kBT} and J, kB, and T are the spin coupling interaction, the Boltzmann constant, and the absolute temperature, respectively), are calculated for different block sizes. By increasing the block size, the critical line for three types of lattice, namely: triangular, square, and honeycomb, is obtained and found to compare well with corresponding results reported by Onsager in the thermodynamic limit. Our results also show that, for the investigated lattices, there exist asymptotic limits for the critical line. Finally the critical exponents are obtained, again in good agreement with Onsager’s results. We show that the magnitude of the spin coupling interaction with anisotropic ferromagnetic characteristics does not change the values of the critical exponents, which stay constant along the direction of the critical line.

  4. An efficient density matrix renormalization group algorithm for chains with periodic boundary condition

    Directory of Open Access Journals (Sweden)

    Dayasindhu Dey


    Full Text Available The Density Matrix Renormalization Group (DMRG is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC from the conventional DMRG has been a challenging job from the inception of DMRG. The recent development of the Matrix Product State (MPS algorithm gives a new approach to find accurate results for the one dimensional PBC system. The most efficient implementation of the MPS algorithm can scale as O(p x m^3, where p can vary from 4 to m^2. In this paper, we propose a new DMRG algorithm, which is very similar to the conventional DMRG and gives comparable accuracy to that of MPS. The computation effort of the new algorithm goes as O(m^3 and the conventional DMRG code can be easily modified for the new algorithm. Received: 2 August 2016, Accepted: 12 October 2016; Edited by: K. Hallberg; DOI: Cite as: D Dey, D Maiti, M Kumar, Papers in Physics 8, 080006 (2016

  5. Backward renormalization-group inference of cortical dipole sources and neural connectivity efficacy (United States)

    Amaral, Selene da Rocha; Baccalá, Luiz A.; Barbosa, Leonardo S.; Caticha, Nestor


    Proper neural connectivity inference has become essential for understanding cognitive processes associated with human brain function. Its efficacy is often hampered by the curse of dimensionality. In the electroencephalogram case, which is a noninvasive electrophysiological monitoring technique to record electrical activity of the brain, a possible way around this is to replace multichannel electrode information with dipole reconstructed data. We use a method based on maximum entropy and the renormalization group to infer the position of the sources, whose success hinges on transmitting information from low- to high-resolution representations of the cortex. The performance of this method compares favorably to other available source inference algorithms, which are ranked here in terms of their performance with respect to directed connectivity inference by using artificially generated dynamic data. We examine some representative scenarios comprising different numbers of dynamically connected dipoles over distinct cortical surface positions and under different sensor noise impairment levels. The overall conclusion is that inverse problem solutions do not affect the correct inference of the direction of the flow of information as long as the equivalent dipole sources are correctly found.

  6. Scaling symmetry, renormalization, and time series modeling: the case of financial assets dynamics. (United States)

    Zamparo, Marco; Baldovin, Fulvio; Caraglio, Michele; Stella, Attilio L


    We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

  7. In-medium similarity renormalization group for closed and open-shell nuclei (United States)

    Hergert, H.


    We present a pedagogical introduction to the in-medium similarity renormalization group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band- or block-diagonal form. Exploiting this flexibility, we describe two complementary approaches for the description of closed- and open-shell nuclei: the first is the multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of non-empirical valence-space interactions that can be used as input for nuclear shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+shell model approach provides immediate access to excitation spectra, transitions, etc, but is limited in applicability by the factorial cost of the CI calculations. We review applications of the MR-IMSRG and IMSRG+shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground- and excited state properties of neon isotopes.

  8. Griffiths singularities in the random quantum Ising antiferromagnet: A tree tensor network renormalization group study (United States)

    Lin, Yu-Ping; Kao, Ying-Jer; Chen, Pochung; Lin, Yu-Cheng


    The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent z >1 , which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing z <1 , when the dynamics of the rare regions is hampered by the longitudinal field.

  9. Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity (United States)

    Toniato, Júnior D.; Rodrigues, Davi C.; de Almeida, Álefe O. F.; Bertini, Nicolas


    We apply the full Will-Nordtvedt version of the parametrized post-Newtonian (PPN) formalism to a class of general relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant G is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the external potential effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales; for any of them the Solar System bounds need to be considered.

  10. Renormalization-group theory for cooling first-order phase transitions in Potts models. (United States)

    Liang, Ning; Zhong, Fan


    We develop a dynamic field-theoretic renormalization-group (RG) theory for cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the q-state Potts model for q>10/3 in the RG theory are the origin of the dynamic scaling found recently from numerical simulations, apart from logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on q only slightly, consistent with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first-order phase transition of the Potts model.

  11. Ab initio excited states from the in-medium similarity renormalization group (United States)

    Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.


    We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

  12. Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches

    Energy Technology Data Exchange (ETDEWEB)

    Katanin, A, E-mail: [Institute of Metal Physics, 620041, Ekaterinburg (Russian Federation); Ural Federal University, 620002, Ekaterinburg (Russian Federation)


    I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider the Polchinski or Wick-ordered scheme with amputation of full (instead of bare) Green functions, as well as more general schemes, and establish their relation to the 'dynamical adjustment propagator' scheme by Salmhofer (2007 Ann. Phys., Lpz. 16 171). While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is also not evident how the mean-field solution of these problems is recovered in this scheme. For the Wick-ordered scheme, fully or partly excluding tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize the usefulness of the schemes, which are local in the cutoff parameter, and compare them to the one-particle irreducible approach. (paper)

  13. Deformation of Honeycomb with Finite Boundary Subjected to Uniaxial Compression

    Directory of Open Access Journals (Sweden)

    Dai-Heng Chen


    Full Text Available In this paper, the crushing behavior of hexagonal honeycomb structures with finite boundaries (finite width and height subjected to in-plane uniaxial compressive loading is studied based on the nonlinear finite element analysis. It is found that stress-strain responses for the honeycombs with finite boundaries can be classified into two types: Type I and Type II. Such a characteristic is affected by the wall thickness, the work-hardening coefficient and the yield stress for the honeycombs. Furthermore, a transition from the symmetric to asymmetric deformation mode can be observed in Type I, and these deformed cells were localized in a horizontal layer. However, for the case of Type II response, the symmetric and asymmetric deformation modes can be observed simultaneously, and the region of the asymmetric mode was formed by the cell layer along the diagonal direction. As a result, the shear deformation behavior was developed along that direction. Moreover, the effect of work-hardening on the deformation behavior for the honeycombs with finite boundaries can be explained from that for infinite honeycombs.

  14. A Finite Speed Curzon-Ahlborn Engine (United States)

    Agrawal, D. C.


    Curzon and Ahlborn achieved finite power output by introducing the concept of finite rate of heat transfer in a Carnot engine. The finite power can also be achieved through a finite speed of the piston on the four branches of the Carnot cycle. The present paper combines these two approaches to study the behaviour of output power in terms of…

  15. Solid finite elements through three decades


    Venkatesh, DN; Shrinivasa, U


    conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elemen...

  16. On characters of finite groups

    CERN Document Server

    Broué, Michel


    This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students, it is now better suited for graduate courses, and provides broader coverage than books that focus almost exclusively on groups. The book presents the basic tools, notions and theorems of character theory (including a new treatment of the control of fusion and isometries), and introduces readers to the categorical language at several levels. It includes and proves the major results on characteristic zero representations without any assumptions about the base field. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).

  17. Finite and profinite quantum systems

    CERN Document Server

    Vourdas, Apostolos


    This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and ...

  18. Sound radiation from finite surfaces

    DEFF Research Database (Denmark)

    Brunskog, Jonas


    A method to account for the effect of finite size in acoustic power radiation problem of planar surfaces using spatial windowing is developed. Cremer and Heckl presents a very useful formula for the power radiating from a structure using the spatially Fourier transformed velocity, which combined...... with spatially windowing of a plane waves can be used to take into account the finite size. In the present paper, this is developed by means of a radiation impedance for finite surfaces, that is used instead of the radiation impedance for infinite surfaces. In this way, the spatial windowing is included...... in the radiation formula directly, and no pre-windowing is needed. Examples are given for the radiation efficiency, and the results are compared with results found in the literature....

  19. Finite element methods for engineers

    CERN Document Server

    Fenner, Roger T


    This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...


    Directory of Open Access Journals (Sweden)



    Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.

  1. Finite elements of nonlinear continua

    CERN Document Server

    Oden, John Tinsley


    Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

  2. Variational collocation on finite intervals

    Energy Technology Data Exchange (ETDEWEB)

    Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); Cervantes, Mayra [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)


    In this paper, we study a set of functions, defined on an interval of finite width, which are orthogonal and which reduce to the sinc functions when the appropriate limit is taken. We show that these functions can be used within a variational approach to obtain accurate results for a variety of problems. We have applied them to the interpolation of functions on finite domains and to the solution of the Schroedinger equation, and we have compared the performance of the present approach with others.

  3. Origin of apparent viscosity in yield stress fluids below yielding

    NARCIS (Netherlands)

    Møller, P.C.F.; Fall, A.; Bonn, D.


    For more than 20 years it has been debated if yield stress fluids are solid below the yield stress or actually flow; whether true yield stress fluids exist or not. Advocates of the true yield stress picture have demonstrated that the effective viscosity increases very rapidly as the stress is

  4. Renormalization group theory for temperature-driven first-order phase transitions in scalar models (United States)

    Liang, Ning; Zhong, Fan


    We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of ϕ 3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found: a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from ϕ 3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two-loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as ϕ 3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.

  5. Mass renormalization and unconventional pairing in multi-band Fe-based superconductors- a phenomenological approach

    Energy Technology Data Exchange (ETDEWEB)

    Drechsler, S.L.; Efremov, D.; Grinenko, V. [IFW-Dresden (Germany); Johnston, S. [Inst. of Quantum Matter, University of British Coulumbia, Vancouver (Canada); Rosner, H. [MPI-cPfS, Dresden, (Germany); Kikoin, K. [Tel Aviv University (Israel)


    Combining DFT calculations of the density of states and plasma frequencies with experimental thermodynamic, optical, ARPES, and dHvA data taken from the literature, we estimate both the high-energy (Coulomb, Hund's rule coupling) and the low-energy (el-boson coupling) electronic mass renormalization [H(L)EMR] for typical Fe-pnictides with T{sub c}<40 K, focusing on (K,Rb,Cs)Fe{sub 2}As{sub 2}, (Ca,Na)122, (Ba,K)122, LiFeAs, and LaFeO{sub 1-x}F{sub x}As with and without As-vacancies. Using Eliashberg theory we show that these systems can NOT be described by a very strong el-boson coupling constant λ ≥ ∝ 2, being in conflict with the HEMR as seen by DMFT, ARPES and optics. Instead, an intermediate s{sub ±} coupling regime is realized, mainly based on interband spin fluctuations from one predominant pair of bands. For (Ca,Na)122, there is also a non-negligible intraband el-phonon/orbital fluctuation intraband contribution. The coexistence of magnetic As-vacancies and high-T{sub c}=28 K for LaFeO{sub 1-x}F{sub x}As{sub 1-δ} excludes an orbital fluctuation dominated s{sub ++} scenario at least for that system. In contrast, the line nodal BaFe{sub 2}(As,P){sub 2} near the quantum critical point is found as a superstrongly coupled system. The role of a pseudo-gap is briefly discussed for some of these systems.

  6. Renormalization group evolution of neutrino parameters in presence of seesaw threshold effects and Majorana phases

    Directory of Open Access Journals (Sweden)

    Shivani Gupta


    Full Text Available We examine the renormalization group evolution (RGE for different mixing scenarios in the presence of seesaw threshold effects from high energy scale (GUT to the low electroweak (EW scale in the Standard Model (SM and Minimal Supersymmetric Standard Model (MSSM. We consider four mixing scenarios namely Tri–Bimaximal Mixing, Bimaximal Mixing, Hexagonal Mixing and Golden Ratio Mixing which come from different flavor symmetries at the GUT scale. We find that the Majorana phases play an important role in the RGE running of these mixing patterns along with the seesaw threshold corrections. We present a comparative study of the RGE of all these mixing scenarios both with and without Majorana CP phases when seesaw threshold corrections are taken into consideration. We find that in the absence of these Majorana phases both the RGE running and seesaw effects may lead to θ13<5° at low energies both in the SM and MSSM. However, if the Majorana phases are incorporated into the mixing matrix the running can be enhanced both in the SM and MSSM. Even by incorporating non-zero Majorana CP phases in the SM, we do not get θ13 in its present 3σ range. The current values of the two mass squared differences and mixing angles including θ13 can be produced in the MSSM case with tan⁡β=10 and non-zero Majorana CP phases at low energy. We also calculate the order of effective Majorana mass and Jarlskog Invariant for each scenario under consideration.

  7. The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Hergert, H., E-mail: [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics, The Ohio State University, Columbus, OH 43210 (United States); Bogner, S.K., E-mail: [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Morris, T.D., E-mail: [Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Schwenk, A., E-mail: [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Tsukiyama, K., E-mail: [Center for Nuclear Study, Graduate School of Science, University of Tokyo, Hongo, Tokyo, 113-0033 (Japan)


    We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.

  8. Numerical Renormalization Group computation of temperature dependent specific heat for a two-channel Anderson model

    Energy Technology Data Exchange (ETDEWEB)

    Ferreira, J.V.B., E-mail: [Fundacao Universidade Federal de Mato Grosso do Sul (Brazil); Ferreira, A.I.I.; Leite, A.H. [Fundacao Universidade Federal de Mato Grosso do Sul (Brazil); Libero, V.L. [Instituto de Fisica de Sao Carlos, SP, Universidade Estadual de Sao Paulo (Brazil)


    The Numerical Renormalization Group (NRG) is applied to diagonalize a two-channel Anderson model describing a local magnetic impurity embedded in a fermionic bath. In spite of the difficulty in computing the specific heat using NRG, the interleaving discretization and multi-step iterative transformation virtually eliminate the numerical oscillations introduced by the logarithmic discretization of the conduction band. These allow to cover uniformly a large range of temperature, from the top of the band to a very small fraction of the bandwidth. This is relevant in describing, for instance, the presence of a low temperature Kondo resonance together with a high temperature Schottky peak, as well to cover Fermi and non-Fermi liquid regimes, like in the recent studied Ce{sub 1-x}La{sub x}Ni{sub 9}Ge{sub 4} family. We highlight the importance in describing the Schottky peak to define the number of degrees of freedom of the local levels, in order to correctly define the model to describe a given compound. - Highlights: Black-Right-Pointing-Pointer The two-channel Anderson model exhibits FL and nFL regimes. Black-Right-Pointing-Pointer NRG, with interleaving and the multi-step procedures, solve Hamiltonian. Black-Right-Pointing-Pointer Large temperature in the specific heat curves, from Kondo to Schottky peak. Black-Right-Pointing-Pointer Analysis of Ce{sub 1-x}La{sub x}Ni{sub 9}Ge{sub 4} compound. Black-Right-Pointing-Pointer Schottky-like peak in this compound suggests J=9/2 multiplet at the impurity level.

  9. Strong-coupling phases of 3D Dirac and Weyl semimetals. A renormalization group approach

    Energy Technology Data Exchange (ETDEWEB)

    González, J. [Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas,Serrano 123, Madrid, 28006 (Spain)


    We investigate the strong-coupling phases that may arise in 3D Dirac and Weyl semimetals under the effect of the long-range Coulomb interaction, considering the many-body theory of these electron systems as a variant of the conventional fully relativistic Quantum Electrodynamics (QED). For this purpose, we apply two different nonperturbative approaches, consisting in the sum of ladder diagrams and taking the limit of a large number N of fermion flavors. We benefit from the renormalizability that the theory shows in both cases to compute the anomalous scaling dimensions of different operators exclusively in terms of the renormalized coupling constant, allowing us to determine the precise location of the singularities signaling the onset of the strong-coupling phases. We show then that the QED of 3D Dirac semimetals has two competing effects at strong coupling. One of them is the tendency to chiral symmetry breaking and dynamical mass generation, which are analogous to the same phenomena arising in the conventional QED at strong coupling. This trend is however outweighed by the strong suppression of electron quasiparticles that takes place at large N, leading to a different type of critical point at sufficiently large interaction strength, shared also by the 3D Weyl semimetals. Overall, the phase diagram of the 3D Dirac semimetals turns out to be richer than that of their 2D counterparts, displaying a transition to a phase with non-Fermi liquid behavior which may be observed in materials hosting a sufficiently large number of Dirac or Weyl points.

  10. Finite-width effects in unstable-particle production at hadron colliders

    Energy Technology Data Exchange (ETDEWEB)

    Falgari, P. [Utrecht Univ. (Netherlands). Inst. for Theoretical Physics; Utrecht Univ. (Netherlands). Spinoza Inst.; Papanastasiou, A.S. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Signer, A. [Paul Scherrer Institut, Villigen (Switzerland); Zuerich Univ. (Switzerland). Inst. for Theoretical Physics


    We present a general formalism for the calculation of finite-width contributions to the differential production cross sections of unstable particles at hadron colliders. In this formalism, which employs an effective-theory description of unstable-particle production and decay, the matrix element computation is organized as a gauge-invariant expansion in powers of {Gamma}{sub X}/m{sub X}, with {Gamma}{sub X} and m{sub X} the width and mass of the unstable particle. This framework allows for a systematic inclusion of off-shell and non-factorizable effects whilst at the same time keeping the computational effort minimal compared to a full calculation in the complex-mass scheme. As a proof-of-concept example, we give results for an NLO calculation of top-antitop production in the q anti q partonic channel. As already found in a similar calculation of single-top production, the finite-width effects are small for the total cross section, as expected from the naive counting {proportional_to}{Gamma}{sub t}/m{sub t}{proportional_to}1%. However, they can be sizeable, in excess of 10%, close to edges of certain kinematical distributions. The dependence of the results on the mass renormalization scheme, and its implication for a precise extraction of the top-quark mass, is also discussed.

  11. Gluon propagator at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Mandula, J.E.; Ogilvie, M.


    The Landau gauge gluon propagator at finite temperature above and below the deconfinement transition is measured using lattice Monte Carlo simulation. The color electric and magnetic masses are determined. The most striking result of the calculation is that the time component of the gluon field appears to acquire a vacuum expected value in the deconfined region.

  12. A Typology for Finite Groups (United States)

    Tou, Erik R


    This project classifies groups of small order using a group's center as the key feature. Groups of a given order "n" are typed based on the order of each group's center. Students are led through a sequence of exercises that combine proof-writing, independent research, and an analysis of specific classes of finite groups…

  13. Linguistics, Logic, and Finite Trees

    NARCIS (Netherlands)

    Blackburn, P.; Meyer-Viol, W.


    A modal logic is developed to deal with finite ordered binary trees as they are used in (computational) linguistics. A modal language is introduced with operators for the 'mother of', 'first daughter of' and 'second daughter of' relations together with their transitive reflexive closures.

  14. Triaxial testing beyond yielding

    DEFF Research Database (Denmark)

    Sabaliauskas, Tomas; Ibsen, Lars Bo


    This paper is continuation of work published at ISOPE 2015, where capabilities of undrained triaxial testing were presented. Now, drained loading is emphasized, recovery of disturbed sand properties is observed. After liquefying or yielding, sand becomes disturbed: stiffness and resistance...... to liquefaction become compromised. However, sand can "heal" itself. It can recover during drained deformation cycles. The recovery mechanism can be observed using a triaxial apparatus. Such tests are relevant for offshore, seismic, and other fields of engineering, where disturbed soil states are encountered....

  15. Effects of simulation parameters on residual stresses for laser shock peening finite element analysis

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Ju Hee [Korea Military Academy, Seoul (Korea, Republic of); Kim, Yun Jae [Korea University, Seoul (Korea, Republic of); Kim, Joung Soo [KAERI, Daejeon (Korea, Republic of)


    By using finite element analysis, we proposed an applicable finite element method of laser shock peening (LSP) and discussed various parameters, such as solution time, stability limit, dynamic yield stress, peak pressure, pressure pulse duration, laser spot size, and multiple LSP. The effects of parameters related to the finite element simulation of the LSP process on the residual stresses of 35CD4 30HRC steel alloy are discussed. Parametric sensitivity analyses were performed to establish the optimum processing variables of the LSP process. In addition, we evaluated the effects of initial residual stress, such as welding-induced residual stress field.

  16. Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS.. (United States)

    Siegel, J.; Siegel, Edward Carl-Ludwig


    Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

  17. Grand canonical finite-size numerical approaches: A route to measuring bulk properties in an applied field (United States)

    Hotta, Chisa; Shibata, Naokazu


    We exploit a prescription to observe directly the physical properties of the thermodynamic limit in a continuously applied field in one-dimensional quantum finite lattice systems. By systematically scaling down the energy of the Hamiltonian of the open system from center toward both ends, one could adopt the edge sites with a negligibly small energy scale as the grand canonical small particle bath, and equilibrium states with noninteger arbitrary conserved numbers, e.g., electron numbers or sz, are realized in the main part of the system. This will enable the evaluation of response functions under a continuously varying external field in a small lattice without any fine-tuning or scaling of parameters while keeping the standard numerical accuracy. Demonstrations are given on quantum spin systems and on a Hubbard model by the density-matrix renormalization group.

  18. Magnetic Signatures of Quantum Critical Points of the Ferrimagnetic Mixed Spin-(1/2, S) Heisenberg Chains at Finite Temperatures (United States)

    Strečka, Jozef; Verkholyak, Taras


    Magnetic properties of the ferrimagnetic mixed spin-(1/2, S) Heisenberg chains are examined using quantum Monte Carlo simulations for two different quantum spin numbers S=1 and 3/2. The calculated magnetization curves at finite temperatures are confronted with zero-temperature magnetization data obtained within the density matrix renormalization group method, which imply an existence of two quantum critical points determining a breakdown of the gapped Lieb-Mattis ferrimagnetic phase and Tomonaga-Luttinger spin-liquid phase, respectively. While a square root behavior of the magnetization accompanying each quantum critical point is gradually smoothed upon rising temperature, the susceptibility and isothermal entropy change data at low temperatures provide a stronger evidence of the zero-temperature quantum critical points through marked local maxima and minima, respectively.

  19. Deconfinement and universality in the 3DU(1) lattice gauge theory at finite temperature: study in the dual formulation

    Energy Technology Data Exchange (ETDEWEB)

    Borisenko, O.; Chelnokov, V. [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine,UA-03680 Kiev (Ukraine); Gravina, M.; Papa, A. [Dipartimento di Fisica, Università della Calabria, and INFN - Gruppo collegato di Cosenza,I-87036 Arcavacata di Rende, Cosenza (Italy)


    We study analytically and numerically the three-dimensional U(1) lattice gauge theory at finite temperature in the dual formulation. For an appropriate disorder operator, we obtain the renormalization group equations describing the critical behavior of the model in the vicinity of the deconfinement phase transition. These equations are used to check the validity of the Svetitsky-Yaffe conjecture regarding the critical behavior of the lattice U(1) model. Furthermore, we perform numerical simulations of the model for N{sub t}=1,2,4,8 and compute, by a cluster algorithm, the dual correlation functions and the corresponding second moment correlation length. In this way we locate the position of the critical point and calculate critical indices.

  20. Modelos de dimensão finita para a estimação de parâmetros genéticos para a produção de leite de primeiras lactações de vacas da raça Holandesa Finite dimension models to estimate genetic parameters for first lactation milk yields of Holstein cows

    Directory of Open Access Journals (Sweden)

    Annaiza Braga Bignardi


    Full Text Available Foram estimados parâmetros genéticos para produção de leite acumulada até 305 dias (P305 e produção de leite no dia do controle (PLDC de 50.171 controles mensais de 9.281 primeiras lactações de vacas da raça Holandesa. A P305 e as PLDC foram analisadas por meio de modelo animal uni e bicaracterísticas. Para a P305 o modelo incluiu como aleatório, o efeito genético e como efeitos fixos o grupo de contemporâneos e a covariável idade da vaca ao parto. Para as PLDC foi usado o mesmo modelo descrito para a P305, incluindo como covariável o número de dias em lactação. Os componentes de variância foram estimados pelo Método da Máxima Verossimilhança Restrita. As estimativas de herdabilidade (h² para as PLDC oscilaram entre 0,07 e 0,19 em análises unicaracterísticas e, de 0,12 a 0,22 nas bicaracterísticas. Para a P305, as h² resultantes das análises uni-característica e bicaracterística foram 0,26 e 0,27, respectivamente. As correlações genéticas das PLDC com a P305 foram todas positivas e elevadas, variando de 0,63 a 1,00. As correlações genéticas entre as PLDC variaram de 0,30 a 1,00. A seleção para a P305 parece ser o melhor critério de seleção a ser adotado, uma vez que proporciona maiores ganhos genéticos para as produções de leite em, praticamente, todos os controles da lactação.Genetic parameters for 50,171 first lactation test-day milk yields and 305 day milk yield (Y305 of 9,281 Holstein cows were estimated, applying uni and bi-trait animal models. The model for Y305 included the additive genetic effect as random and the fixed effects of contemporary group and age of cow at calving as covariable. For TDMY the same animal model described for Y305 was used, including days in milk as covariable. Variance components were estimated by Restricted Maximum Likelihood. Heritability estimates obtained for TDMY ranged from 0.07 to 0.19 and from 0.12 to 0.22 by uni-trait and bi-trait analysis, respectively