Non-Perturbative Theory of Dispersion Interactions
Boström, M; Persson, C; Parsons, D F; Buhmann, S Y; Brevik, I; Sernelius, Bo E
2015-01-01
Some open questions exist with fluctuation-induced forces between extended dipoles. Conventional intuition derives from large-separation perturbative approximations to dispersion force theory. Here we present a full non-perturbative theory. In addition we discuss how one can take into account finite dipole size corrections. It is of fundamental value to investigate the limits of validity of the perturbative dispersion force theory.
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert;
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays...
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays...
Non-perturbative Nekrasov partition function from string theory
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, I., E-mail: ignatios.antoniadis@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Florakis, I., E-mail: florakis@mppmu.mpg.de [Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München (Germany); Hohenegger, S., E-mail: stefan.hohenegger@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Narain, K.S., E-mail: narain@ictp.trieste.it [High Energy Section, The Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11-34014 Trieste (Italy); Zein Assi, A., E-mail: zeinassi@cern.ch [Department of Physics, CERN – Theory Division, CH-1211 Geneva 23 (Switzerland); Centre de Physique Théorique (UMR CNRS 7644), Ecole Polytechnique, 91128 Palaiseau (France)
2014-03-15
We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3×T{sup 2} and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general Ω-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of [1] and provides further evidence for our proposal of a string theory realisation of the Ω-background.
Non perturbative methods in two dimensional quantum field theory
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
Alien calculus and non perturbative effects in Quantum Field Theory
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
A non-perturbative study of massive gauge theories
DEFF Research Database (Denmark)
Della Morte, Michele; Hernandez, Pilar
2013-01-01
We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists and the ...
Non-perturbative String Theory from Water Waves
Energy Technology Data Exchange (ETDEWEB)
Iyer, Ramakrishnan; Johnson, Clifford V.; /Southern California U.; Pennington, Jeffrey S.; /SLAC
2012-06-14
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.
Introduction to non-perturbative heavy quark effective theory
Energy Technology Data Exchange (ETDEWEB)
Sommer, R. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2010-08-15
My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti {lambda} and {lambda}{sub 1} lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m){sup n+1} if the theory was treated including (1/m){sup n} terms. Clearly, the weakest point of HQET is that it
Non-perturbative Thermodynamics in Matrix String Theory
Peñalba, J P
1999-01-01
A study of the thermodynamics in IIA Matrix String Theory is presented. The free string limit is calculated and seen to exactly reproduce the usual result. When energies are enough to excite non-perturbative objects like D-particles and specially membranes, the situation changes because they add a large number of degrees of freedom that do not appear at low energies. There seems to be a negative specific heat (even in the Microcanonical Ensemble) that moves the asymptotic temperature to zero. Besides, the mechanism of interaction and attachment of open strings to D-particles and D-membranes is analyzed. A first approach to type IIB Matrix String is carried out: its spectrum is found in the (2+1)-SYM and used to calculate an SL(2,Z) invariant partition function.
Topological string theory, modularity and non-perturbative physics
Energy Technology Data Exchange (ETDEWEB)
Rauch, Marco
2011-09-15
In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques of direct integration known from topological string theory can be used to solve the closed amplitudes of Hermitian multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, explicit expressions for the ring of non-holomorphic modular forms that are needed to express all closed matrix model amplitudes are given. This allows to integrate the holomorphic anomaly equation up to holomorphic modular terms that are fixed by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the non-holomorphic modular ring of the group {gamma}(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. Using these results it is possible to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, it is argued that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model. In the second part a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi-Yau manifold is derived using wall-crossing formulae and the theory of mock modular forms. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4- D2-D0 brane systems. The compatibility of this equation with anomaly equations previously observed in the context of N=4 topological Yang-Mills theory on P{sup 2} and E-strings obtained from wrapping M5-branes on a del Pezzo surface which in
Probing black holes in non-perturbative gauge theory
Iizuka, N; Lifschytz, G; Lowe, D A; Iizuka, Norihiro; Kabat, Daniel; Lifschytz, Gilad; Lowe, David A.
2002-01-01
We use a 0-brane to probe a ten-dimensional near-extremal black hole with N units of 0-brane charge. We work directly in the dual strongly-coupled quantum mechanics, using mean-field methods to describe the black hole background non-perturbatively. We obtain the distribution of W boson masses, and find a clear separation between light and heavy degrees of freedom. To localize the probe we introduce a resolving time and integrate out the heavy modes. After a non-trivial change of coordinates, the effective potential for the probe agrees with supergravity expectations. We compute the entropy of the probe, and find that the stretched horizon of the black hole arises dynamically in the quantum mechanics, as thermal restoration of unbroken U(N+1) gauge symmetry. Our analysis of the quantum mechanics predicts a correct relation between the horizon radius and entropy of a black hole.
Complex curves and non-perturbative effects in c=1 string theory
Alexandrov, S
2004-01-01
We investigate a complex curve in the $c=1$ string theory which provides a geometric interpretation for different kinds of D-branes. The curve is constructed for a theory perturbed by a tachyon potential using its matrix model formulation. The perturbation removes the degeneracy of the non-perturbed curve and allows to identify its singularities with ZZ branes. Also, using the constructed curve, we find non-perturbative corrections to the free energy and elucidate their CFT origin.
Kovtun, Pavel; Ünsal, Mithat; Yaffe, Laurence G.
2003-12-01
We prove an equivalence, in the large N limit, between certain U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. Lattice regularization is used to provide a non-perturbative definition of these theories; our proof applies in the strong coupling, large mass phase of the theories. Equivalence is demonstrated by constructing and comparing the loop equations for a parent theory and its orbifold projections. Loop equations for both expectation values of single-trace observables, and for connected correlators of such observables, are considered; hence the demonstrated non-perturbative equivalence applies to the large N limits of both string tensions and particle spectra.
Non-perturbative selection rules in F-theory
Energy Technology Data Exchange (ETDEWEB)
Martucci, Luca [Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova, and I.N.F.N. Sezione di Padova, via Marzolo 8, Padova, I-35131 (Italy); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität, Philosophenweg 19, Heidelberg, 69120 (Germany)
2015-09-29
We discuss the structure of charged matter couplings in 4-dimensional F-theory compactifications. Charged matter is known to arise from M2-branes wrapping fibral curves on an elliptic or genus-one fibration Y. If a set of fibral curves satisfies a homological relation in the fibre homology, a coupling involving the states can arise without exponential volume suppression due to a splitting and joining of the M2-branes. If the fibral curves only sum to zero in the integral homology of the full fibration, no such coupling is possible. In this case an M2-instanton wrapping a 3-chain bounded by the fibral matter curves can induce a D-term which is volume suppressed. We elucidate the consequences of this pattern for the appearance of massive U(1) symmetries in F-theory and analyse the structure of discrete selection rules in the coupling sector. The weakly coupled analogue of said M2-instantons is worked out to be given by D1-F1 instantons. The generation of an exponentially suppressed F-term requires the formation of half-BPS bound states of M2 and M5-instantons. This effect and its description in terms of fluxed M5-instantons is discussed in a companion paper.
Non-Perturbative Effects in 2-D String Theory or Beyond the Liouville Wall
Brustein, Ram
1997-01-01
We discuss continuous and discrete sectors in the collective field theory of $d=1$ matrix models. A canonical Lorentz invariant field theory extension of collective field theory is presented and its classical solutions in Euclidean and Minkowski space are found. We show that the discrete, low density, sector of collective field theory includes single eigenvalue Euclidean instantons which tunnel between different vacua of the extended theory. We further show that these ``stringy" instantons induce non-perturbative effective operators of strength $e^{-{1\\over g}}$ in the extended theory. The relationship of the world sheet description of string theory and Liouville theory to the effective space-time theory is explained. We also comment on the role of the discrete, low density, sector of collective field theory in that framework.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Energy Technology Data Exchange (ETDEWEB)
Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
The b-quark mass from non-perturbative $N_f=2$ Heavy Quark Effective Theory at $O(1/m_h)$
DEFF Research Database (Denmark)
Bernardoni, F.; Blossier, B.; Bulava, J.
2014-01-01
We report our final estimate of the b-quark mass from $N_f=2$ lattice QCD simulations using Heavy Quark Effective Theory non-perturbatively matched to QCD at $O(1/m_h)$. Treating systematic and statistical errors in a conservative manner, we obtain $\\overline{m}_{\\rm b}^{\\overline{\\rm MS}}(2 {\\rm...
Time-dependent backgrounds of 2D string theory: Non-perturbative effects
Alexandrov, S Yu; Alexandrov, Sergei Yu.; Kostov, Ivan K.
2005-01-01
We study the non-perturbative corrections (NPC) to the partition function of a compactified 2D string theory in a time-dependent background generated by a tachyon source. The sine-Liouville deformation of the theory is a particular case of such a background. We calculate the leading as well as the subleading NPC using the dual description of the string theory as matrix quantum mechanics. As in the minimal string theories, the NPC are classified by the double points of a complex curve. We calculate them by two different methods: by solving Toda equation and by evaluating the quasiclassical fermion wave functions. We show that the result can be expressed in terms of correlation functions of the bosonic field associated with the tachyon source and identify the leading and the subleading corrections as the contributions from the one-point (disk) and two-point (annulus) correlation functions.
Non-perturbative studies of N = 2 conformal quiver gauge theories
Energy Technology Data Exchange (ETDEWEB)
Ashok, S.K.; Dell' Aquila, E.; John, R.R. [Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai (India); Billo, M.; Frau, M.; Lerda, A. [Universita di Torino, Dipartimento di Fisica (Italy); I.N.F.N., Sezione di Torino (Italy)
2015-05-01
We study N = 2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n = 1, 2, also in the presence of an Ω-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotential a la Nekrasov using localization methods. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Musso, Daniele
2012-01-01
The non-perturbative dynamics of quantum field theories is studied using theoretical tools inspired by string formalism. Two main lines are developed: the analysis of stringy instantons in a class of four-dimensional N=2 gauge theories and the holographic study of the minimal model for a strongly coupled unbalanced superconductor. The field theory instanton calculus admits a natural and efficient description in terms of D-brane models. In addition, the string viewpoint offers the possibility of generalizing the ordinary instanton configurations. Even though such generalized, or stringy, instantons would be absent in a purely field-theoretical, low-energy treatment, we demonstrate that they do alter the IR effective description of the brane dynamics by introducing contributions related to the string scale. In the first part of this thesis we compute explicitly the stringy instanton corrections to the effective prepotential in a class of quiver gauge theories. In the second part of the thesis, we present a deta...
Non-perturbative QCD: renormalization, O(a)-improvement and matching to Heavy Quark Effective Theory
Sommer, R
2006-01-01
We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed directly to an overview of the literature and our personal assessment of what has been achieved and what is missing. II. The computation of the running coupling, running quark masses and the extraction of the renormalization group invariants. We focus on the basic strategy and on the large effort that has been invested in understanding the continuum limit. We point out what remains to be done. III. Non-perturbative Heavy Quark Effective Theory. Since the literature on this subject is still rather sparse, we go beyond the basic ideas and discuss in some detail how the theory works in principle and in practice.
3rd UK-QFT Meeting: Non-Perturbative Quantum Field Theory and Quantum Gravity
2014-01-01
The meeting aims to bringing together Students, Postdoctoral Researchers and Senior Scientists to discuss recent trends in advanced Quantum Field Theory and Quantum Gravity. The format of the meeting is a series of informal talks to allow for discussion and the exchange of ideas amongst participants. We plan for up to 8 slots for short presentations depending on demand and one final longer seminar given by Frank Saueressig (Mainz). This is the third meeting of its kind and details on the previous two can be found on the following: 1st UK-QFT Meeting: Non-perturbative aspects in field theory (KCL) 2nd UK-QFT Meeting: Advances in quantum field theory and gravity (Sussex)
Non-perturbative QCD. Renormalization, O(a)-improvement and matching to heavy quark effective theory
Energy Technology Data Exchange (ETDEWEB)
Sommer, R.
2006-11-15
We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed directly to an overview of the literature and our personal assessment of what has been achieved and what is missing. II. The computation of the running coupling, running quark masses and the extraction of the renormalization group invariants. We focus on the basic strategy and on the large effort that has been invested in understanding the continuum limit. We point out what remains to be done. III. Non-perturbative Heavy Quark Effective Theory. Since the literature on this subject is still rather sparse, we go beyond the basic ideas and discuss in some detail how the theory works in principle and in practice. (orig.)
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
Directory of Open Access Journals (Sweden)
Samuel Friot
2010-10-01
Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.
Chishtie, F A
2002-01-01
Pade approximants (PA) have been widely applied in practically all areas of physics. This thesis focuses on developing PA as tools for both perturbative and non- perturbative quantum field theory (QFT). In perturbative QFT, we systematically estimate higher (unknown) loop terms via the asymptotic formula devised by Samuel et al. This algorithm, generally denoted as the asymptotic Pade approximation procedure (APAP), has greatly enhanced scope when it is applied to renormalization-group-(RG-) invariant quantities. A presently-unknown higher-loop quantity can then be matched with the approximant over the entire momentum region of phenomenological interest. Furthermore, the predicted value of the RG coefficients can be compared with the RG-accessible coefficients (at the higher-loop order), allowing a clearer indication of the accuracy of the predicted RG-inaccessible term. This methodology is applied to hadronic Higgs decay rates (H → bb¯ and H → gg, both within the Standard Model and...
Anagnostopoulos, Konstantinos N; Nishimura, Jun
2012-01-01
The IKKT or IIB matrix model has been postulated to be a non perturbative definition of superstring theory. It has the attractive feature that spacetime is dynamically generated, which makes possible the scenario of dynamical compactification of extra dimensions, which in the Euclidean model manifests by spontaneously breaking the SO(10) rotational invariance (SSB). In this work we study using Monte Carlo simulations the 6 dimensional version of the Euclidean IIB matrix model. Simulations are found to be plagued by a strong complex action problem and the factorization method is used for effective sampling and computing expectation values of the extent of spacetime in various dimensions. Our results are consistent with calculations using the Gaussian Expansion method which predict SSB to SO(3) symmetric vacua, a finite universal extent of the compactified dimensions and finite spacetime volume.
Non-Perturbative Self-Consistent Model in SU(N Gauge Field Theory
Directory of Open Access Journals (Sweden)
Koshelkin A.V.
2012-06-01
Full Text Available Non-perturbative quasi-classical model in a gauge theory with the Yang-Mills (YM field is developed. The self-consistent solutions of the Dirac equation in the SU(N gauge field, which is in the eikonal approximation, and the Yang-Mills (YM equations containing the external fermion current are solved. It shown that the developed model has the self-consistent solutions of the Dirac and Yang-Mills equations at N ≥ 3. In this way, the solutions take place provided that the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to self-interaction of it.
Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity
Energy Technology Data Exchange (ETDEWEB)
Eichhorn, Astrid
2011-09-06
In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F{sub {mu}}{sub {nu}}F{sup {mu}}{sup {nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the {beta} function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension
Tellgren, E I; Teale, A M; Furness, J W; Lange, K K; Ekström, U; Helgaker, T
2014-01-21
We present a novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.
Energy Technology Data Exchange (ETDEWEB)
Tellgren, E. I., E-mail: erik.tellgren@kjemi.uio.no; Lange, K. K.; Ekström, U.; Helgaker, T. [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway); Teale, A. M., E-mail: andrew.teale@nottingham.ac.uk [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway); School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom); Furness, J. W. [School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2014-01-21
We present a novel implementation of Kohn–Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals—the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.
Non-perturbative black holes in Type-IIA String Theory vs. the No-Hair conjecture
Bueno, Pablo
2013-01-01
We obtain the first black hole solution to Type-IIA String Theory compactified on an arbitrary self-mirror Calabi Yau manifold in the presence of non-perturbative quantum corrections. Remarkably enough, the solution involves multivalued functions, which could lead to a violation of the No-Hair conjecture. We discuss how String Theory forbids such secenario. However the possibility still remains open in the context of four-dimensional ungauged Supergravity.
Non-perturbative Heavy Quark Effective Theory: An application to semi-leptonic B-decays
Della Morte, Michele; Simma, Hubert; Sommer, Rainer
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays at the leading order in 1/m_h.
Non-perturbative renormalization of the energy-momentum tensor in SU(3) Yang-Mills theory
Giusti, Leonardo
2014-01-01
We present a strategy for a non-perturbative determination of the finite renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. The computation is performed by imposing on the lattice suitable Ward Identites at finite temperature in presence of shifted boundary conditions. We show accurate preliminary numerical data for values of the bare coupling g_0^2 ranging for 0 to 1.
A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2001-05-11
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.
A non-perturbative formulation of N=4 super Yang-Mills theory based on the large-N reduction
Ishiki, Goro; Tsuchiya, Asato
2011-01-01
We study a non-perturbative formulation of N=4 super Yang-Mills theory (SYM) on RxS^3 proposed in arXiv:0807.2352. This formulation is based on the large-N reduction, and the theory can be described as a particular large-N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S^3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
Non-perturbative Solutions to N=2 Supersymmetric Yang-Mills Theories Progress and Perspective
Ohta, Y
1999-01-01
This note reviews the progress on the low energy dynamics of N=2 supersymmetric Yang-Mills theories after the works of Seiberg and Witten. Specifically, the theory of prepotential for non-specialists is reviewed.
Instantons and large N an introduction to non-perturbative methods in quantum field theory
Marino, Marcos
2015-01-01
This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang-Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behaviour of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.
A non-perturbative study of non-commutative U(1) gauge theory
Energy Technology Data Exchange (ETDEWEB)
Nishimura, J. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Graduate Univ. for Advanced Studies (SOKENDAI), Tsukuba (Japan). Dept. of Particle and Nuclear Physics; Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Susaki, Y. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Tsukuba Univ. (Japan). Graduate School of Pure and Applied Science; Volkholz, J. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2007-06-15
We study U(1) gauge theory on a 4d non-commutative torus, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non- commutativity parameter {theta}, which provides evidence for a possible continuum theory. In the weak coupling symmetric phase, the dispersion relation involves a negative IR-singular term, which is responsible for the observed phase transition. (orig.)
Non-perturbative renormalization of the static quark theory in a large volume
Korcyl, Piotr; Ishikawa, Tomomi
2015-01-01
We report on progress to renormalize non-pertubatively the static heavy quark theory on the lattice. In particular, we present first results for position-space renormalization scheme for heavy-light bilinears. We test our approach on RBC's 16^3 x 32 lattice ensemble with m_pi = 420 MeV, Iwasaki gauge action and domain wall light fermions.
Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory
Giusti, Leonardo
2015-01-01
We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare` invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang--Mills theory discretized with the standard Wilson action in presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0<= g^2_0<=1.
Non-Perturbative Calculation of the Scalar Yukawa Theory in Four-Body Truncation
Li, Yang; Maris, P; Vary, James P
2014-01-01
The scalar Yukawa theory is solved in the light-front Tamm-Dancoff approach including up to four constituents (one scalar nucleon, three scalar pions). The Fock sector dependent renormalization is implemented. By studying the Fock sector norms, we find that the lowest two Fock sectors dominate the state even in the large-coupling region. The one-body sector shows convergence with respect to the Fock sector truncation. However, the four-body norm exceeds the three-body norm at the coupling $\\alpha \\approx 1.7$.
Buchert, Thomas
2012-01-01
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate consequences by functionally evaluating relevant variables. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to address non-perturbatively, e.g. problems of structu...
Guazzini, Damiano; Meyer, Harvey B
2007-01-01
We carry out the non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B mesons. We obtain its two-loop anomalous dimension in a Schr"odinger functional scheme by successive one-loop conversions to the lattice MS scheme and the MS-bar scheme. We then compute the scale evolution of the operator non-perturbatively in the N_f=0 theory between $\\mu \\approx 0.3$ GeV and $\\mu \\approx 100$ GeV, where contact is made with perturbation theory. The overall renormalization factor that converts the bare lattice operator to its renormalization group invariant form is given for the Wilson gauge action and two standard discretizations of the heavy-quark action. As an application, we find that this factor brings the previous quenched predictions of the B* - B mass splitting closer to the experimental value than found with a perturbative renormalization. The same ren...
Non-perturbative description of quantum systems
Feranchuk, Ilya; Le, Van-Hoang; Ulyanenkov, Alexander
2015-01-01
This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
New Methods in Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)
2017-01-31
In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.
A non-perturbative study of the correlation functions of three-dimensional Yang-Mills theory
Huber, Markus Q
2016-01-01
Yang-Mills theory is studied in three dimensions using the equations of motion of the $1$PI and $3$PI effective actions. The employed self-contained truncation includes the propagators, the three-point functions and the four-gluon vertex dynamically. In the gluon propagator also two-loop diagrams are taken into account. The higher gluonic correlation functions show sizable deviations from the tree-level only at low momenta. Also the couplings derived from the vertices agree well down to a few GeV. In addition, different methods to subtract spurious divergences are explored.
Capri, M A L; Pereira, A D; Fiorentini, D; Guimaraes, M S; Mintz, B W; Palhares, L F; Sorella, S P
2016-01-01
In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST invariant meaning to the possible positivity violation of ...
Non-perturbative quantum geometry III
Krefl, Daniel
2016-08-01
The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stokes phenomena over the combined string coupling and quantized Kähler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local ℙ1 + ℙ1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stokes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local ℙ2 near the conifold point in moduli space is also provided.
Non-Perturbative Quantum Geometry III
Krefl, Daniel
2016-01-01
The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.
Non-perturbative renormalization in kaon decays
Donini, Andrea; Martinelli, G; Rossi, G C; Talevi, M; Testa, M; Vladikas, A
1996-01-01
We discuss the application of the MPSTV non-perturbative method \\cite{NPM} to the operators relevant to kaon decays. This enables us to reappraise the long-standing question of the $\\Delta I=1/2$ rule, which involves power-divergent subtractions that cannot be evaluated in perturbation theory. We also study the mixing with dimension-six operators and discuss its implications to the chiral behaviour of the $B_K$ parameter.
Non-perturbative quark mass renormalization
Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.
1998-01-01
We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.
Non-Perturbative Flat Direction Decay
Basboll, A; Riva, F; West, S M; Basboll, Anders; Maybury, David; Riva, Francesco; West, Stephen M.
2007-01-01
We argue that supersymmetric flat direction vevs can decay non-perturbatively via preheating. Considering the case of a single flat direction, we explicitly calculate the scalar potential in the unitary gauge for a U(1) theory and show that the mass matrix for excitations around the flat direction has non-diagonal entries which vary with the phase of the flat direction vev. Furthermore, this mass matrix has 2 zero eigenvalues (associated with the excitations along the flat direction) whose eigenstates change with time. We show that these 2 light degrees of freedom are produced copiously in the non-perturbative decay of the flat direction vev. We also comment on the application of these results to the MSSM flat direction H_uL.
Statistical theory and inference
Olive, David J
2014-01-01
This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.
Scheck, Florian
2016-01-01
Scheck’s textbook starts with a concise introduction to classical thermodynamics, including geometrical aspects. Then a short introduction to probabilities and statistics lays the basis for the statistical interpretation of thermodynamics. Phase transitions, discrete models and the stability of matter are explained in great detail. Thermodynamics has a special role in theoretical physics. Due to the general approach of thermodynamics the field has a bridging function between several areas like the theory of condensed matter, elementary particle physics, astrophysics and cosmology. The classical thermodynamics describes predominantly averaged properties of matter, reaching from few particle systems and state of matter to stellar objects. Statistical Thermodynamics covers the same fields, but explores them in greater depth and unifies classical statistical mechanics with quantum theory of multiple particle systems. The content is presented as two tracks: the fast track for master students, providing the essen...
Non-perturbative monodromies in N=2 heterotic string vacua
Lópes-Cardoso, G; Mohaupt, T; Cardoso, Gabriel Lopes; Lust, Dieter; Mohaupt, Thomas
1995-01-01
We address non-perturbative effects and duality symmetries in N=2 heterotic string theories in four dimensions. Specifically, we consider how each of the four lines of enhanced gauge symmetries in the perturbative moduli space of N=2 T_2 compactifications is split into 2 lines where monopoles and dyons become massless. This amounts to considering non-perturbative effects originating from enhanced gauge symmetries at the microscopic string level. We show that the perturbative and non-perturbative monodromies consistently lead to the results of Seiberg-Witten upon identication of a consistent truncation procedure from local to rigid N=2 supersymmetry.
Dynamic statistical information theory
Institute of Scientific and Technical Information of China (English)
XING; Xiusan
2006-01-01
In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy production rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel
Non-perturbative study of QCD correlators
Lokhov, A Y
2006-01-01
This PhD dissertation is devoted to a non-perturbative study of QCD correlators. The main tool that we use is lattice QCD. We concentrated our efforts on the study of the main correlators of the pure Yang - Mills theory in the Landau gauge, namely the ghost and the gluon propagators. We are particularly interested in determining the $\\Lqcd$ parameter. It is extracted by means of perturbative predictions available up to NNNLO. The related topic is the influence of non-perturbative effects that show up as appearance of power-corrections to the low-momentum behaviour of the Green functions. A new method of removing these power corrections allows a better estimate of $\\Lqcd$. Our result is $\\Lambda^{n_f=0}_{\\ms} = 269(5)^{+12}_{-9}$ MeV. Another question that we address is the infrared behaviour of Green functions, at momenta of order and below $\\Lqcd$. At low energy the momentum dependence of the propagators changes considerably, and this is probably related to confinement. The lattice approach allows to check t...
Non-perturbative effects and the refined topological string
Hatsuda, Yasuyuki; Moriyama, Sanefumi; Okuyama, Kazumi
2013-01-01
The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P1xP1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.
Non-perturbative effects and the refined topological string
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematiques; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P{sup 1} x P{sup 1}, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.
Non-perturbative match of ultraviolet renormalon
Zakharov, V I
2003-01-01
The paper is motivated by observation of a kind of branes in the vacuum state of the lattice SU(2) gluodynamics. The branes represent two-dimensional vortices whose total area scales in physical units while the non-Abelian action diverges in the ultraviolet. We consider the question whether effects of the branes can be accommodated into the continuum theory. We demonstrate that at least in case of the gluon condensate (plaquette action) and of the heavy quark potential the contribution of the branes corresponds to the ultraviolet renormalon. Thus, the vortices might represent a non-perturbative match of the ultraviolet renormalon. Such an identification constrains, in turn, properties of the branes.
Non-perturbative lorentzian quantum gravity, causality and topology change
Ambjørn, J.; Loll, R.
1998-01-01
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum limit coincides with the theory obtained by quantizing 2d conti
Nakatsukasa, Takashi
2012-01-01
We present the basic concepts and our recent developments in the density functional approaches with the Skyrme functionals for describing nuclear dynamics at low energy. The time-dependent density-functional theory (TDDFT) is utilized for the exact linear response with an external perturbation. For description of collective dynamics beyond the perturbative regime, we present a theory of a decoupled collective submanifold to describe for a slow motion based on the TDDFT. Selected applications are shown to demonstrate the quality of their performance and feasibility. Advantages and disadvantages in the numerical aspects are also discussed.
Information theory and statistics
Kullback, Solomon
1997-01-01
Highly useful text studies logarithmic measures of information and their application to testing statistical hypotheses. Includes numerous worked examples and problems. References. Glossary. Appendix. 1968 2nd, revised edition.
Statistical theory of signal detection
Helstrom, Carl Wilhelm; Costrell, L; Kandiah, K
1968-01-01
Statistical Theory of Signal Detection, Second Edition provides an elementary introduction to the theory of statistical testing of hypotheses that is related to the detection of signals in radar and communications technology. This book presents a comprehensive survey of digital communication systems. Organized into 11 chapters, this edition begins with an overview of the theory of signal detection and the typical detection problem. This text then examines the goals of the detection system, which are defined through an analogy with the testing of statistical hypotheses. Other chapters consider
Measure theory of statistical convergence
Institute of Scientific and Technical Information of China (English)
CHENG LiXin; LIN GuoChen; LAN YongYi; LIU Hui
2008-01-01
The question of establishing measure theory for statistical convergence has been moving closer to center stage, since a kind of reasonable theory is not only fundamental for unifying various kinds of statistical convergence, but also a bridge linking the studies of statistical convergence across measure theory, integration theory, probability and statistics. For this reason, this paper, in terms of subdifferential, first shows a representation theorem for all finitely additive probability measures defined on the σ-algebra of all subsets of N, and proves that every such measure can be uniquely decomposed into a convex combination of a countably additive probability measure and a statistical measure (i.e. a finitely additive probability measure μ with μ(k) = 0 for all singletons {k}). This paper also shows that classical statistical measures have many nice properties, such as: The set of all such measures endowed with the topology of point-wise convergence on forms a compact convex Hausdorff space; every classical statistical measure is of continuity type (hence, atomless), and every specific class of statistical measures fits a complementation minimax rule for every subset in N. Finally, this paper shows that every kind of statistical convergence can be unified in convergence of statistical measures.
Measure theory of statistical convergence
Institute of Scientific and Technical Information of China (English)
2008-01-01
The question of establishing measure theory for statistical convergence has been moving closer to center stage, since a kind of reasonable theory is not only fundamental for unifying various kinds of statistical convergence, but also a bridge linking the studies of statistical convergence across measure theory, integration theory, probability and statistics. For this reason, this paper, in terms of subdifferential, first shows a representation theorem for all finitely additive probability measures defined on the σ-algebra A of all subsets of N, and proves that every such measure can be uniquely decomposed into a convex combination of a countably additive probability measure and a statistical measure (i.e. a finitely additive probability measure μ with μ(k) = 0 for all singletons {k}). This paper also shows that classical statistical measures have many nice properties, such as: The set S of all such measures endowed with the topology of point-wise convergence on A forms a compact convex Hausdorff space; every classical statistical measure is of continuity type (hence, atomless), and every specific class of statistical measures fits a complementation minimax rule for every subset in N. Finally, this paper shows that every kind of statistical convergence can be unified in convergence of statistical measures.
Statistical theory of breakup reactions
Energy Technology Data Exchange (ETDEWEB)
Bertulani, Carlos A., E-mail: carlos.bertulani@tamuc.edu [Department of Physics and Astronomy, Texas A and M University-Commerce, Commerce, TX (United States); Descouvemont, Pierre, E-mail: pdesc@ulb.ac.be [Physique Nucleaire Theorique et Physique Mathematique, Universite Libre de Bruxelles (ULB), Brussels (Belgium); Hussein, Mahir S., E-mail: hussein@if.usp.br [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Estudos Avancados
2014-07-01
We propose an alternative for Coupled-Channels calculations with loosely bound exotic nuclei (CDCC), based on the the Random Matrix Model of the statistical theory of nuclear reactions. The coupled channels equations are divided into two sets. The first set, described by the CDCC, and the other set treated with RMT. The resulting theory is a Statistical CDCC (CDCC{sub s}), able in principle to take into account many pseudo channels. (author)
Statistical Theory of Breakup Reactions
Directory of Open Access Journals (Sweden)
Bertulani Carlos A.
2014-04-01
Full Text Available We propose an alternative for Coupled-Channels calculations with looselybound exotic nuclei(CDCC, based on the the Random Matrix Model of the statistical theory of nuclear reactions. The coupled channels equations are divided into two sets. The first set, described by the CDCC, and the other set treated with RMT. The resulting theory is a Statistical CDCC (CDCCs, able in principle to take into account many pseudo channels.
Statistical Theory of Breakup Reactions
Bertulani, Carlos A; Hussein, Mahir S
2014-01-01
We propose alternatives to coupled-channels calculations with loosely-bound exotic nuclei (CDCC), based on the the random matrix (RMT) and the optical background (OPM) models for the statistical theory of nuclear reactions. The coupled channels equations are divided into two sets. The first set, described by the CDCC, and the other set treated with RMT. The resulting theory is a Statistical CDCC (CDCC$_S$), able in principle to take into account many pseudo channels.
Statistical Theory of Breakup Reactions
Bertulani, Carlos A.; Descouvemont, Pierre; Hussein, Mahir S.
2014-04-01
We propose an alternative for Coupled-Channels calculations with looselybound exotic nuclei(CDCC), based on the the Random Matrix Model of the statistical theory of nuclear reactions. The coupled channels equations are divided into two sets. The first set, described by the CDCC, and the other set treated with RMT. The resulting theory is a Statistical CDCC (CDCCs), able in principle to take into account many pseudo channels.
Importance of Non-Perturbative QCD Parameters for Bottom Mesons
Upadhyay, A
2015-01-01
The importance of non-perturbative Quantum Chromodynamics [QCD] parameters is discussed in context to the predicting power for bottom meson masses and isospin splitting. In the framework of heavy quark effective theory, the work presented here focuses on the different allowed values of the two non perturbative QCD parameters used in heavy quark effective theory formula and using the best fitted parameter, masses of the excited bottom meson states in JP=(1/2)+ doublet in strange as well as non-strange sector are calculated here. The calculated masses are found to be matching well with experiments and other phenomenological models. The mass and hyperfine splitting has also been analyzed for both strange and non-strange heavy mesons with respect to spin and flavor symmetries.
Non-perturbative QCD and hadron physics
Cobos-Martínez, J. J.
2016-10-01
A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented.
Probability, statistics, and queueing theory
Allen, Arnold O
1990-01-01
This is a textbook on applied probability and statistics with computer science applications for students at the upper undergraduate level. It may also be used as a self study book for the practicing computer science professional. The successful first edition of this book proved extremely useful to students who need to use probability, statistics and queueing theory to solve problems in other fields, such as engineering, physics, operations research, and management science. The book has also been successfully used for courses in queueing theory for operations research students. This second edit
Elliptic CY3folds and non-perturbative modular transformation
Energy Technology Data Exchange (ETDEWEB)
Iqbal, Amer [Government College University, Abdus Salam School of Mathematical Sciences, Lahore (Pakistan); Shabbir, Khurram [Government College University, Department of Mathematics, Lahore (Pakistan)
2016-03-15
We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections. (orig.)
Fractional statistics and quantum theory
Khare, Avinash
1997-01-01
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
Estimation Theory and Statistical Physics.
1985-12-01
Guerra, F., L. Rosen and B. Simon (1975): The P(0) 2 Euclidean Quantum Field Theory as Classical Statistical Mechanics, Annals of Mathematics , 101, pp. 111...Scientia Sinica, XXIV, pp. 483-496. 19. Segal, I. (1970): Construction of Nonlinear Local Quantum Processes 1, Annals of Mathematics 92, pp. 462-481. - 20
Statistical Inference and String Theory
Heckman, Jonathan J
2013-01-01
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a d-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a non-linear sigma model in d dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring com...
Statistical mechanics of vortices from field theory
Kajantie, Keijo; Neuhaus, T; Rajantie, A; Rummukainen, K
1999-01-01
We study with lattice Monte Carlo simulations the interactions and macroscopic behaviour of a large number of vortices in the 3-dimensional U(1) gauge+Higgs field theory, in an external magnetic field. We determine non-perturbatively the (attractive or repelling) interaction energy between two or more vortices, as well as the critical field strength H_c, the thermodynamical discontinuities, and the surface tension related to the boundary between the Meissner phase and the Coulomb phase in the type I region. We also investigate the emergence of vortex lattice and vortex liquid phases in the type II region. For the type I region the results obtained are in qualitative agreement with mean field theory, except for small values of H_c, while in the type II region there are significant discrepancies. These findings are relevant for superconductors and some models of cosmic strings, as well as for the electroweak phase transition in a magnetic field.
Building a non-perturbative quark-gluon vertex from a perturbative one
Bermudez, Rocio
2016-10-01
The quark-gluon vertex describes the electromagnetic and the strong interaction among these particles. The description of this interaction at high precision in both regimes, perturbative and non-perturbative, continues being a matter of interest in the context of QCD and Hadron Physics. There exist very helpful models in the literature that explain perturbative aspects of the theory but they fail describing non-perturbative phenomena, as confinement and dynamic chiral symmetry breaking. In this work we study the structure of the quark-gluon vertex in a non-perturbative regime examining QCD, checking results with QED, and working in the Schwinger-Dyson formalism.
Theory of games and statistical decisions
Blackwell, David A
1979-01-01
Evaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory.The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games
Non-Perturbative Topological Strings And Conformal Blocks
Cheng, Miranda C N; Vafa, Cumrun
2010-01-01
We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.
Non-perturbative topological strings and conformal blocks
Cheng, Miranda C. N.; Dijkgraaf, Robbert; Vafa, Cumrun
2011-09-01
We give a non-perturbative completion of a class of closed topological string theories in terms of building blocks of dual open strings. In the specific case where the open string is given by a matrix model these blocks correspond to a choice of integration contour. We then apply this definition to the AGT setup where the dual matrix model has logarithmic potential and is conjecturally equivalent to Liouville conformal field theory. By studying the natural contours of these matrix integrals and their monodromy properties, we propose a precise map between topological string blocks and Liouville conformal blocks. Remarkably, this description makes use of the light-cone diagrams of closed string field theory, where the critical points of the matrix potential correspond to string interaction points.
Bayes linear statistics, theory & methods
Goldstein, Michael
2007-01-01
Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...
Statistical dynamo theory: Mode excitation.
Hoyng, P
2009-04-01
We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B= summation operator_{k}a;{k}(t)b;{k}(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a;{k} is governed by a stochastic differential equation from which we infer their averages a;{k} , autocorrelation functions a;{k}(t)a;{k *}(t+tau) , and an equation for the cross correlations a;{k}a;{l *} . The eigenfunctions of the dynamo equation (with eigenvalues lambda_{k} ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Ilambda_{k} and -1/Rlambda_{k} , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for |a;{k}|;{2}/|a;{0}|;{2} in case the fundamental mode b;{0} has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that |a;{k}|;{2}/|a;{0}|;{2} approximately 1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rlambda_{k}<0 .
Statistical Decision Theory Estimation, Testing, and Selection
Liese, Friedrich
2008-01-01
Suitable for advanced graduate students and researchers in mathematical statistics and decision theory, this title presents an account of the concepts and a treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory
Testing QCD in the non-perturbative regime
Energy Technology Data Exchange (ETDEWEB)
A.W. Thomas
2007-01-01
This is an exciting time for strong interaction physics. We have a candidate for a fundamental theory, namely QCD, which has passed all the tests thrown at it in the perturbative regime. In the non-perturbative regime it has also produced some promising results and recently a few triumphs but the next decade will see enormous progress in our ability to unambiguously calculate the consequences of non-perturbative QCD and to test those predictions experimentally. Amongst the new experimental facilities being constructed, the hadronic machines at JPARC and GSI-FAIR and the 12 GeV Upgrade at Jefferson Lab, the major new electromagnetic facility worldwide, present a beautifully complementary network aimed at producing precise new measurements which will advance our knowledge of nuclear systems and push our ability to calculate the consequences of QCD to the limit. We will first outline the plans at Jefferson Lab for doubling the energy of CEBAF. The new facility presents some wonderful opportunities for discovery in strong interaction physics, as well as beyond the standard model. Then we turn to the theoretical developments aimed at extracting precise results for physical hadron properties from lattice QCD simulations. This discussion will begin with classical examples, such as the mass of the nucleon and ?, before dealing with a very recent and spectacular success involving information extracted from modern parity violating electron scattering.
Non-Perturbative Quantum Dynamics of a New Inflation Model
Boyanovsky, D; De Vega, H J; Holman, R; Kumar, S P
1998-01-01
We consider an O(N) model coupled self-consistently to gravity in the semiclassical approximation, where the field is subject to `new inflation' type initial conditions. We study the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. We find that a very specific combination of these large fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. We show how this reinterpretation saves the standard picture of how metric perturbations are generated during inflation and that the spinodal growth of fluctuations dominates the time dependence of the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensor perturb...
Casimir operator dependences of non-perturbative fermionic QCD amplitudes
Fried, H M; Hofmann, R
2015-01-01
In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes, when based on the newly discovered effective locality property, depart from a sole dependence on the SUc(3) quadratic Casimir operator, evaluated over the fundamental gauge group representation.Though noticed in non-relativistic Quark Models, an additional dependence on the cubic Casimir operator is in contradistinction with perturbation theory, and also with a number of non-perturbative approaches such as the MIT Bag, the Stochastic Vacuum Models and lattice simulations. It accounts for the full algebraic content of the rank-2 Lie algebra of SUc(3). We briefly discuss the orders of magnitude of quadratic and cubic Casimir operator contributions.
A Perturbative Window into Non-Perturbative Physics
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2002-01-01
We argue that for a large class of N=1 supersymmetric gauge theories the effective superpotential as a function of the glueball chiral superfield is exactly given by a summation of planar diagrams of the same gauge theory. This perturbative computation reduces to a matrix model whose action is the tree-level superpotential. For all models that can be embedded in string theory we give a proof of this result, and we sketch an argument how to derive this more generally directly in field theory. These results are obtained without assuming any conjectured dualities and can be used as a systematic method to compute instanton effects: the perturbative corrections up to n-th loop can be used to compute up to n-instanton corrections. These techniques allow us to see many non-perturbative effects, such as the Seiberg-Witten solutions of N=2 theories, the consequences of Montonen-Olive S-duality in N=1* and Seiberg-like dualities for N=1 theories from a completely perturbative planar point of view in the same gauge theo...
An Elementary Introduction to Statistical Learning Theory
Kulkarni, Sanjeev
2011-01-01
A thought-provoking look at statistical learning theory and its role in understanding human learning and inductive reasoning A joint endeavor from leading researchers in the fields of philosophy and electrical engineering, An Elementary Introduction to Statistical Learning Theory is a comprehensive and accessible primer on the rapidly evolving fields of statistical pattern recognition and statistical learning theory. Explaining these areas at a level and in a way that is not often found in other books on the topic, the authors present the basic theory behind contemporary machine learning and
Controlling quark mass determinations non-perturbatively in three-flavour QCD
Directory of Open Access Journals (Sweden)
Campos Isabel
2017-01-01
Full Text Available The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS¯$\\overline {{\\rm{MS}}} $ scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf = 3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Controlling quark mass determinations non-perturbatively in three-flavour QCD
Campos, Isabel; Pena, Carlos; Preti, David; Ramos, Alberto; Vladikas, Anastassios
2016-01-01
The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2007-06-15
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)
Pire, B
2009-01-01
QCD is the theory of strong interactions and non-perturbative methods have been developed to address the confinement property of QCD. Many experimental measurements probe the confining dynamics, and it is well-known that hard scattering processes allow the extraction of non perturbative hadronic matrix elements. To study exclusive hard processes, such as electromagnetic form factors and reactions like gamma* N -> gamma N', gamma* N -> pi N', gamma* gamma -> pi pi, antiproton proton ->gamma* pi in particular kinematics (named as generalized Bjorken regime), one introduces specific non-perturbative objects, namely generalized parton distributions (GPDs), distribution amplitudes (DA) and transition distribution amplitudes (TDA), which are Fourier transformed non-diagonal matrix elements of non-local operators on the light-cone. We review here a selected sample of exclusive amplitudes in which the quark and gluon content of hadrons is probed, and emphasize that much remains to be done to successfully compute thei...
Integrable matrix theory: Level statistics.
Scaramazza, Jasen A; Shastry, B Sriram; Yuzbashyan, Emil A
2016-09-01
We study level statistics in ensembles of integrable N×N matrices linear in a real parameter x. The matrix H(x) is considered integrable if it has a prescribed number n>1 of linearly independent commuting partners H^{i}(x) (integrals of motion) [H(x),H^{i}(x)]=0, [H^{i}(x),H^{j}(x)]=0, for all x. In a recent work [Phys. Rev. E 93, 052114 (2016)2470-004510.1103/PhysRevE.93.052114], we developed a basis-independent construction of H(x) for any n from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the N→∞ limit provided n scales at least as logN; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values x=x_{0} or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at O(N^{-0.5}) deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest-neighbor level statistics.
Integrable matrix theory: Level statistics
Scaramazza, Jasen A.; Shastry, B. Sriram; Yuzbashyan, Emil A.
2016-09-01
We study level statistics in ensembles of integrable N ×N matrices linear in a real parameter x . The matrix H (x ) is considered integrable if it has a prescribed number n >1 of linearly independent commuting partners Hi(x ) (integrals of motion) "]Hi(x ) ,Hj(x ) ]">H (x ) ,Hi(x ) =0 , for all x . In a recent work [Phys. Rev. E 93, 052114 (2016), 10.1103/PhysRevE.93.052114], we developed a basis-independent construction of H (x ) for any n from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the N →∞ limit provided n scales at least as logN ; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values x =x0 or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at O (N-0.5) deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest-neighbor level statistics.
Statistical Topics Concerning Radiometer Theory
Hunter, Todd R
2015-01-01
We present a derivation of the radiometer equation based on the original references and fundamental statistical concepts. We then perform numerical simulations of white noise to illustrate the radiometer equation in action. Finally, we generate 1/f and 1/f^2 noise, demonstrate that it is non-stationary, and use it to simulate the effect of gain fluctuations on radiometer performance.
Non-Perturbative Two-Dimensional Dilaton Gravity
Mikovic, A
1993-01-01
We present a review of the canonical quantization approach to the problem of non-perturbative 2d dilaton gravity. In the case of chiral matter we describe a method for solving the constraints by constructing a Kac-Moody current algebra. For the models of interest, the relevant Kac-Moody algebras are based on SL(2,R) X U(1) group and on an extended 2d Poincare group. As a consequence, the constraints become free-field Virasoro generators with background charges. We argue that the same happens in the non-chiral case. The problem of the corresponding BRST cohomology is discussed as well as the unitarity of the theory. One can show that the theory is unitary by chosing a physical gauge, and hence the problem of transitions from pure into mixed sates is absent. Implications for the physics of black holes are discussed. (Based on the talks presented at Trieste conference on Gauge Theories, Applied Supersymmetry and Quantum Gravity, May 1993 and at Danube '93 Workshop, Belgrade, Yugoslavia, June 1993)
Integrable matrix theory: Level statistics
2016-01-01
We study level statistics in ensembles of integrable $N\\times N$ matrices linear in a real parameter $x$. The matrix $H(x)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i(x)$ (integrals of motion) $\\left[H(x),H^i(x)\\right] = 0$, $\\left[H^i(x), H^j(x)\\right]$ = 0, for all $x$. In a recent work, we developed a basis-independent construction of $H(x)$ for any $n$ from which we derived the probability density function, thereby determin...
Aspects of multivariate statistical theory
Muirhead, Robb J
2009-01-01
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to pen
Probability theory and mathematical statistics for engineers
Pugachev, V S
1984-01-01
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
Hatsuda, Yasuyuki
2015-11-01
The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of "non-perturbative" poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.
Random matrix theory and multivariate statistics
Diaz-Garcia, Jose A.; Jáimez, Ramon Gutiérrez
2009-01-01
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases the classical random matrix ensembles, are proposed. Some properties of these classes of ensemble are analysed. In addition, the random matrix ensemble approach is extended and a unified theory proposed for the study of distributions for real normed divisio...
Holomorphic couplings in non-perturbative string compactifications
Energy Technology Data Exchange (ETDEWEB)
Klevers, Denis Marco
2011-06-15
In this thesis we present an analysis of several aspects of four-dimensional, non-perturbative N = 1 compactifications of string theory. Our focus is on the study of brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N=1 effective action, most prominently the superpotential W. The thesis is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we demonstrate exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefold Z{sub 3}, that is canonically constructed from the original five-brane and Calabi-Yau threefold Z{sub 3} via a blow-up. We exploit the use of the blow-up threefold Z{sub 3} as a tool to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpret Z{sub 3} as a flux compactification dual to the original five-brane by defining an SU(3)-structure on Z{sub 3}, that is generated dynamically by the five-brane backreaction. (orig.)
Non-perturbative Euler-Heisenberg Lagrangian and paraelectricity in magnetized massless QED
Energy Technology Data Exchange (ETDEWEB)
Ferrer, Efrain J. [Department of Physics, University of Texas at El Paso, 500 W. University Ave., El Paso, TX 79968 (United States); Incera, Vivian de la, E-mail: vincera@utep.edu [Department of Physics, University of Texas at El Paso, 500 W. University Ave., El Paso, TX 79968 (United States); Sanchez, Angel [Department of Physics, University of Texas at El Paso, 500 W. University Ave., El Paso, TX 79968 (United States)
2012-11-21
In this paper we calculate the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field H, where the breaking of the chiral symmetry is dynamically catalyzed by the external magnetic field via the formation of an electro-positron condensate. This chiral condensate leads to the generation of dynamical parameters that have to be found as solutions of non-perturbative Schwinger-Dyson equations. Since the electron-positron pairing mechanism leading to the breaking of the chiral symmetry is mainly dominated by the contributions from the infrared region of momenta much smaller than {radical}(eH), the magnetic field introduces a dynamical ultraviolet cutoff in the theory that also enters in the non-perturbative Euler-Heisenberg action. Using this action, we show that the system exhibits a significant paraelectricity in the direction parallel to the magnetic field. The non-perturbative nature of this effect is reflected in the non-analytic dependence of the obtained electric susceptibility on the fine-structure constant. The strong paraelectricity in the field direction is linked to the orientation of the electric dipole moments of the pairs that form the chiral condensate. The large electric susceptibility can be used to detect the realization of the magnetic catalysis of chiral symmetry breaking in physical systems.
Information Theory and Statistical Physics - Lecture Notes
Merhav, Neri
2010-01-01
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information Theory, as well as to graduate students in Physics who have basic background in Information Theory. Strong emphasis is given to the analogy and parallelism between Information Theory and Statistical Physics, as well as to the insights, the analysis tools and techniques that can be borrowed from Statistical Physics and `imported' to certain problem areas in Information Theory. This is a research trend that has been very active in the last few decades, and the hope is that by exposing the student to the meeting points between these two disciplines, we will enhance his/her background and perspective to carry out research in the field. A short outline of the course is as follows: Introduction; Elementary Statistical Physics and its Relation to Information Theory; Analysis Tools in ...
Perturbative tests of non-perturbative counting
Dabholkar, Atish; Gomes, João
2010-03-01
We observe that a class of quarter-BPS dyons in mathcal{N} = 4 theories with charge vector ( Q, P) and with nontrivial values of the arithmetic duality invariant I := gcd( Q∧ P) are nonperturbative in one frame but perturbative in another frame. This observation suggests a test of the recently computed nonperturbative partition functions for dyons with nontrivial values of the arithmetic invariant. For all values of I, we show that the nonperturbative counting yields vanishing indexed degeneracy for this class of states everywhere in the moduli space in precise agreement with the perturbative result.
Statistical test theory for the behavioral sciences
de Gruijter, Dato N M
2007-01-01
Since the development of the first intelligence test in the early 20th century, educational and psychological tests have become important measurement techniques to quantify human behavior. Focusing on this ubiquitous yet fruitful area of research, Statistical Test Theory for the Behavioral Sciences provides both a broad overview and a critical survey of assorted testing theories and models used in psychology, education, and other behavioral science fields. Following a logical progression from basic concepts to more advanced topics, the book first explains classical test theory, covering true score, measurement error, and reliability. It then presents generalizability theory, which provides a framework to deal with various aspects of test scores. In addition, the authors discuss the concept of validity in testing, offering a strategy for evidence-based validity. In the two chapters devoted to item response theory (IRT), the book explores item response models, such as the Rasch model, and applications, incl...
Further generalization of the Borel transform for the non-perturbative regime
Energy Technology Data Exchange (ETDEWEB)
Epele, L.N.; Fanchiotti, H.; Garcia Canal, C.A.; Marucho, M. E-mail: afa@venus.fisica.unlp.edu.ar
2000-09-04
A new generalization of the Borel transform improving the Duncan-Pernice proposal, and designed for obtaining any non perturbative contributions is presented. This new transform leads to a non-ambiguous reconstruction of the original theory. This generalized transform is applied to the analysis of a one-dimensional spin chain and the two-dimensional non-linear sigma model on the lattice. In both models the singularity structure related to renormalons is obtained.
Geometric transition in Non-perturbative Topological string
Sugimoto, Yuji
2016-01-01
We study a geometric transition in non-perturbative topological string. We consider two cases. One is the geometric transition from the closed topological string on the local $\\mathcal{B}_{3}$ to the closed topological string on the resolved conifold. The other is the geometric transition from the closed topological string on the local $\\mathcal{B}_{3}$ to the open topological string on the resolved conifold with a toric A-brane. We find that, in both cases, the geometric transition can be applied for the non-perturbative topological string. We also find the corrections of the value of K\\"ahler parameters at which the geometric transition occurs.
Statistical turbulence theory and turbulence phenomenology
Herring, J. R.
1973-01-01
The application of deductive turbulence theory for validity determination of turbulence phenomenology at the level of second-order, single-point moments is considered. Particular emphasis is placed on the phenomenological formula relating the dissipation to the turbulence energy and the Rotta-type formula for the return to isotropy. Methods which deal directly with most or all the scales of motion explicitly are reviewed briefly. The statistical theory of turbulence is presented as an expansion about randomness. Two concepts are involved: (1) a modeling of the turbulence as nearly multipoint Gaussian, and (2) a simultaneous introduction of a generalized eddy viscosity operator.
Insights on non-perturbative aspects of TMDs from models
Energy Technology Data Exchange (ETDEWEB)
H. Avakian, A. Efremov, P. Schweitzer, O. Teryaev, F. Yuan, P. Zavada
2009-12-01
Transverse momentum dependent parton distribution functions are a key ingredient in the description of spin and azimuthal asymmetries in deep-inelastic scattering processes. Recent results from non-perturbative calculations in effective approaches are reviewed, with focus on relations among different parton distribution functions in QCD and models.
Statistics of extremes theory and applications
Beirlant, Jan; Segers, Johan; Teugels, Jozef; De Waal, Daniel; Ferro, Chris
2006-01-01
Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.
Quantum information theory and quantum statistics
Energy Technology Data Exchange (ETDEWEB)
Petz, D. [Alfred Renyi Institute of Mathematics, Budapest (Hungary)
2008-07-01
Based on lectures given by the author, this book focuses on providing reliable introductory explanations of key concepts of quantum information theory and quantum statistics - rather than on results. The mathematically rigorous presentation is supported by numerous examples and exercises and by an appendix summarizing the relevant aspects of linear analysis. Assuming that the reader is familiar with the content of standard undergraduate courses in quantum mechanics, probability theory, linear algebra and functional analysis, the book addresses graduate students of mathematics and physics as well as theoretical and mathematical physicists. Conceived as a primer to bridge the gap between statistical physics and quantum information, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions to prepare the reader for deeper studies, not least through the selection of well chosen exercises. (orig.)
Studies in Statistical Optics - Theory & Application
2015-07-29
page 9. 15. SUBJECT TERMS Coherence and statistical optics; scattering; propagation; reflection and refraction . 16. SECURITY CLASSIFICATION OF: 17...Scattering from Quasi-Homogeneous Media”, Opt. Commun., 294, 43-48 (2013). 7. M. Lahiri and E. Wolf, “Theory of Refraction and Reflection with Partially... Refraction and on Reflection ”, JOSA A, 30, 1107-1112 (2013). 9. S. B. Raghunathan, T. D. Visser, and E. Wolf, “Far-zone Properties of Electromagnetic
Ergodic theorem, ergodic theory, and statistical mechanics.
Moore, Calvin C
2015-02-17
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject--namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Black hole entropy from non-perturbative gauge theory
Kabat, D; Lowe, D A; Kabat, Daniel; Lifschytz, Gilad; Lowe, David A.
2001-01-01
We present the details of a mean-field approximation scheme for the quantum mechanics of N D0-branes at finite temperature. The approximation can be applied at strong 't Hooft coupling. We find that the resulting entropy is in good agreement with the Bekenstein-Hawking entropy of a ten-dimensional non-extremal black hole with 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. We discuss ways of resolving the black hole horizon, and also study the spectrum of single-string excitations within the quantum mechanics.
Statistical mechanical theory of fluid mixtures
Zhao, Yueqiang; Wu, Zhengming; Liu, Weiwei
2014-01-01
A general statistical mechanical theory of fluid mixtures (liquid mixtures and gas mixtures) is developed based on the statistical mechanical expression of chemical potential of components in the grand canonical ensemble, which gives some new relationships between thermodynamic quantities (equilibrium ratio Ki, separation factor α and activity coefficient γi) and ensemble average potential energy u for one molecule. The statistical mechanical expressions of separation factor α and activity coefficient γi derived in this work make the fluid phase equilibrium calculations can be performed by molecular simulation simply and efficiently, or by the statistical thermodynamic approach (based on the saturated-vapor pressure of pure substance) that does not need microscopic intermolecular pair potential functions. The physical meaning of activity coefficient γi in the liquid phase is discussed in detail from a viewpoint of molecular thermodynamics. The calculated Vapor-Liquid Equilibrium (VLE) properties of argon-methane, methanol-water and n-hexane-benzene systems by this model fit well with experimental data in references, which indicates that this model is accurate and reliable in the prediction of VLE properties for small, large and strongly associating molecules; furthermore the statistical mechanical expressions of separation factor α and activity coefficient γi have good compatibility with classical thermodynamic equations and quantum mechanical COSMO-SAC approach.
Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
Hatsuda, Yasuyuki
2015-01-01
The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of "non-perturbative" poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example as...
Applications of measure theory to statistics
Pantsulaia, Gogi
2016-01-01
This book aims to put strong reasonable mathematical senses in notions of objectivity and subjectivity for consistent estimations in a Polish group by using the concept of Haar null sets in the corresponding group. This new approach – naturally dividing the class of all consistent estimates of an unknown parameter in a Polish group into disjoint classes of subjective and objective estimates – helps the reader to clarify some conjectures arising in the criticism of null hypothesis significance testing. The book also acquaints readers with the theory of infinite-dimensional Monte Carlo integration recently developed for estimation of the value of infinite-dimensional Riemann integrals over infinite-dimensional rectangles. The book is addressed both to graduate students and to researchers active in the fields of analysis, measure theory, and mathematical statistics.
Statistical mechanics approach to lattice field theory
Amador, Arturo; Olaussen, Kåre
2016-01-01
The mean spherical approximation (MSA) is a closure relation for pair correlation functions (two-point functions) in statistical physics. It can be applied to a wide range of systems, is computationally fairly inexpensive, and when properly applied and interpreted lead to rather good results. In this paper we promote its applicability to euclidean quantum field theories formulated on a lattice, by demonstrating how it can be used to locate the critical lines of a class of multi-component bosonic models. The MSA has the potential to handle models lacking a positive definite integration measure, which therefore are difficult to investigate by Monte-Carlo simulations.
Non-Gaussian Statistical Communication Theory
Middleton, David
2012-01-01
The book is based on the observation that communication is the central operation of discovery in all the sciences. In its "active mode" we use it to "interrogate" the physical world, sending appropriate "signals" and receiving nature's "reply". In the "passive mode" we receive nature's signals directly. Since we never know a prioriwhat particular return signal will be forthcoming, we must necessarily adopt a probabilistic model of communication. This has developed over the approximately seventy years since it's beginning, into a Statistical Communication Theory (or SCT). Here it is the set or
Jet Extinction from Non-Perturbative Quantum Gravity Effects
Kilic, Can; Lath, Amitabh; Rose, Keith; Thomas, Scott
2012-01-01
The infrared-ultraviolet properties of quantum gravity suggest on very general grounds that hard short distance scattering processes are highly suppressed for center of mass scattering energies beyond the fundamental Planck scale. If this scale is not too far above the electroweak scale, these non-perturbative quantum gravity effects could be manifest as an extinction of high transverse momentum jets at the LHC. To model these effects we implement an Extinction Monte Carlo modification of the...
M{sub b} and f{sub B} from non-perturbatively renormalized HQET with N{sub f} = 2 light quarks
Energy Technology Data Exchange (ETDEWEB)
Blossier, Benoit [CNRS et Univ. Paris-Sud XI, Orsay (France). Lab. de Physique Theorique; Bulava, John [CERN, Geneva (Switzerland). Physics Dept.; Della Morte, Michele; Hippel, Georg von [Mainz Univ. (Germany). Inst. fuer Kernphysik; Donnellan, Michael; Simma, Hubert; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). NIC; Fritzsch, Patrick [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Garron, Nicolas [Edinburgh Univ. (United Kingdom). Tait Inst.; Heitger, Jochen [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1
2011-12-15
We present an updated analysis of the non-perturbatively renormalized b-quark mass and B meson decay constant based on CLS lattices with two dynamical non-perturbatively improved Wilson quarks. This update incorporates additional light quark masses and lattice spacings in large physical volume to improve chiral extrapolations and to reach the continuum limit. We use Heavy Quark Effective Theory (HQET) including 1/m{sub b} terms with non-perturbative coefficients based on the matching of QCD and HQET developed by the ALPHA collaboration during the past years. (orig.)
Non-perturbative inputs for gluon distributions in the hadrons
Ermolaev, B. I.; Troyan, S. I.
2017-03-01
Description of hadronic reactions at high energies is conventionally done in the framework of QCD factorization. All factorization convolutions comprise non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct inputs for the gluon-hadron scattering amplitudes in the forward kinematics and, using the optical theorem, convert them into inputs for gluon distributions in the hadrons, embracing the cases of polarized and unpolarized hadrons. In the first place, we formulate mathematical criteria which any model for the inputs should obey and then suggest a model satisfying those criteria. This model is based on a simple reasoning: after emitting an active parton off the hadron, the remaining set of spectators becomes unstable and therefore it can be described through factors of the resonance type, so we call it the resonance model. We use it to obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available types of QCD factorization: basic, K_T-and collinear factorizations.
Statistical Tests of Galactic Dynamo Theory
Chamandy, Luke; Shukurov, Anvar; Taylor, A. Russ
2016-12-01
Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare predictions of mean-field dynamo models to observational data on magnetic pitch angle and the strength of the mean magnetic field. We demonstrate that a standard {α }2{{Ω }} dynamo model produces pitch angles of the regular magnetic fields of nearby galaxies that are reasonably consistent with available data. The dynamo estimates of the magnetic field strength are generally within a factor of a few of the observational values. Reasonable agreement between theoretical and observed pitch angles generally requires the turbulent correlation time τ to be in the range of 10-20 {Myr}, in agreement with standard estimates. Moreover, good agreement also requires that the ratio of the ionized gas scale height to root-mean-square turbulent velocity increases with radius. Our results thus widen the possibilities to constrain interstellar medium parameters using observations of magnetic fields. This work is a step toward systematic statistical tests of galactic dynamo theory. Such studies are becoming more and more feasible as larger data sets are acquired using current and up-and-coming instruments.
Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks
DEFF Research Database (Denmark)
Bernardoni, F.; Blossier, B.; Bulava, J.;
2014-01-01
We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on Nf=2 gauge field ensembles, covering three...... limits. Our final results read fB=186(13)MeV, fBs=224(14)MeV and fBs/fB=1.203(65). A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible....
Do fragmentation functions in factorization theorems correctly treat non-perturbative effects?
Collins, John
2016-01-01
Current all-orders proofs of factorization of hard processes are made by extracting the leading power behavior of Feynman graphs, i.e., by extracting asymptotics strictly order-by-order in perturbation theory. The resulting parton densities and fragmentation functions include non-perturbative effects. I show how there are missing elements in the proofs; these are related to and exemplified by string and cluster models of hadronization. The proofs rely on large rapidity differences between different parts of graphs for the process; but in reality large rapidity gaps are filled in
B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCD
Bernardoni, Fabio; Bulava, John; Della Morte, Michele; Fritzsch, Patrick; Garron, Nicolas; Gerardin, Antoine; Heitger, Jochen; von Hippel, Georg M; Simma, Hubert
2013-01-01
We report on the ALPHA Collaboration's lattice B-physics programme based on N_f=2 O(a) improved Wilson fermions and HQET, including all NLO effects in the inverse heavy quark mass, as well as non-perturbative renormalization and matching, to fix the parameters of the effective theory. Our simulations in large physical volume cover 3 lattice spacings a ~ (0.08-0.05) fm and pion masses down to 190 MeV to control continuum and chiral extrapolations. We present the status of results for the b-quark mass and the B_(s)-meson decay constants, f_B and f_{B_s}.
A statistical mechanics approach to Granovetter theory
Barra, Adriano
2010-01-01
In this paper we try to bridge breakthroughs in quantitative sociology/econometrics pioneered during the last decades by Mac Fadden, Brock-Durlauf, Granovetter and Watts-Strogats through introducing a minimal model able to reproduce essentially all the features of social behavior highlighted by these authors. Our model relies on a pairwise Hamiltonian for decision maker interactions which naturally extends the multi-populations approaches by shifting and biasing the pattern definitions of an Hopfield model of neural networks. Once introduced, the model is investigated trough graph theory (to recover Granovetter and Watts-Strogats results) and statistical mechanics (to recover Mac-Fadden and Brock-Durlauf results). Due to internal symmetries of our model, the latter is obtained as the relaxation of a proper Markov process, allowing even to study its out of equilibrium properties. The method used to solve its equilibrium is an adaptation of the Hamilton-Jacobi technique recently introduced by Guerra in the spin...
Non-perturbative QCD Modeling and Meson Physics
Nguyen, T; Tandy, P C
2009-01-01
Using a ladder-rainbow kernel previously established for light quark hadron physics, we explore the extension to masses and electroweak decay constants of ground state pseudoscalar and vector quarkonia and heavy-light mesons in the c- and b-quark regions. We make a systematic study of the effectiveness of a constituent mass concept as a replacement for a heavy quark dressed propagator for such states. The difference between vector and axial vector current correlators is explored within the same model to provide an estimate of the four quark chiral condensate and the leading distance scale for the onset of non-perturbative phenomena in QCD.
Non-perturbative QCD amplitudes in quenched and eikonal approximations
Fried, H. M.; Grandou, T.; Sheu, Y.-M.
2014-05-01
Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.
Statistical Theory of the Ideal MHD Geodynamo
Shebalin, J. V.
2012-01-01
A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the
Non-perturbative closure calculation for fluids and plasmas
Tang, Xianzhu; McDevitt, Chris; Guo, Zehua
2015-11-01
Closure calculation of the Chapman-Enskog type is based on a perturbative expansion in the small parameter of Knudsen number, which is defined as the ratio of the thermal particle mean-free-path and the system gradient length scale. The error in the analysis can be locally measured in phase space using the local Knudsen number, which for the energy squared dependence of the mean-free-path, is much larger for high energy particles. Such breakdown, if occurs at sufficiently high energy, has small impact on closure results, but in cases of strong spatial gradients, can have large effect and invalidate the perturbative calculation. Here we show a non-perturbative closure formulation and its application in calculating standard closure quantitities such as heat flux. This approach applies as long as the thermal bulk is close to a Maxwellian, where a perturbative analysis can be matched onto a non-perturbative treatment of the tail population. Work supported by DOE via LANL-LDRD.
Classical statistical computation of the Schwinger mechanism
Gelis, F
2013-01-01
In this paper, we show how classical statistical field theory techniques can be used to efficiently perform the numerical evaluation of the non-perturbative Schwinger mechanism of particle production by quantum tunneling. In some approximation, we also consider the back-reaction of the produced particles on the external field, as well as the self-interactions of the produced particles.
Towards a non-perturbative construction of the operator product expansion
Energy Technology Data Exchange (ETDEWEB)
Holland, Jan [Universitaet Leipzig (Germany)
2016-07-01
Our current understanding of Quantum Field Theory (QFT) is based to a large extent on perturbative - i.e. approximate - methods. Exact constructions in QFT are not only of fundamental conceptual interest, but they offer insights into physical phenomena that are intractable by perturbative means. In this talk, I present progress on a novel approach towards the non-perturbative construction of the Operator Product Expansion (OPE). The OPE is a structure encoding the complete algebraic skeleton as well as the short distance properties of a Quantum Field Theory. Our construction method is based on a recently found recursion formula for the OPE, which is discussed along with recent results on mathematical properties of the OPE in perturbation theory.
A statistical mechanics approach to Granovetter theory
Barra, Adriano; Agliari, Elena
2012-05-01
In this paper we try to bridge breakthroughs in quantitative sociology/econometrics, pioneered during the last decades by Mac Fadden, Brock-Durlauf, Granovetter and Watts-Strogatz, by introducing a minimal model able to reproduce essentially all the features of social behavior highlighted by these authors. Our model relies on a pairwise Hamiltonian for decision-maker interactions which naturally extends the multi-populations approaches by shifting and biasing the pattern definitions of a Hopfield model of neural networks. Once introduced, the model is investigated through graph theory (to recover Granovetter and Watts-Strogatz results) and statistical mechanics (to recover Mac-Fadden and Brock-Durlauf results). Due to the internal symmetries of our model, the latter is obtained as the relaxation of a proper Markov process, allowing even to study its out-of-equilibrium properties. The method used to solve its equilibrium is an adaptation of the Hamilton-Jacobi technique recently introduced by Guerra in the spin-glass scenario and the picture obtained is the following: shifting the patterns from [-1,+1]→[0.+1] implies that the larger the amount of similarities among decision makers, the stronger their relative influence, and this is enough to explain both the different role of strong and weak ties in the social network as well as its small-world properties. As a result, imitative interaction strengths seem essentially a robust request (enough to break the gauge symmetry in the couplings), furthermore, this naturally leads to a discrete choice modelization when dealing with the external influences and to imitative behavior à la Curie-Weiss as the one introduced by Brock and Durlauf.
Statistical theory of turbulent incompressible multimaterial flow
Energy Technology Data Exchange (ETDEWEB)
Kashiwa, B.
1987-10-01
Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of kappa-epsilon modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy kappa, and the rate of fluctuational energy dissipation epsilon, for each material. Hence a set of kappa and epsilon equations must be solved, together with mean mass and momentum conservation equations, for each material. Both kappa and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a
Non-perturbative QCD effects in jets at hadron colliders
Dasgupta, Mrinal; Salam, Gavin P
2008-01-01
We discuss non-perturbative QCD contributions to jet observables, computing their dependence on the jet radius R, and on the colour and transverse momentum of the parton initiating the jet. We show, using analytic QCD models of power corrections as well as Monte Carlo simulations, that hadronisation corrections grow at small values of R, behaving as 1/R, while underlying event contributions grow with the jet area as R^2. We highlight the connection between hadronisation corrections to jets and those for event shapes in e^+e^- and DIS; we note the limited dependence of our results on the choice of jet algorithm; finally, we propose several measurements in the context of which to test or implement our predictions. The results presented here reinforce the motivation for the use of a range of R values, as well as a plurality of infrared-safe jet algorithms, in precision jet studies at hadron colliders.
Non-perturbative quantization of the electroweak model's electrodynamic sector
Fry, M P
2015-01-01
Consider the Euclidean functional integral representation of any physical process in the electroweak model. Integrating out the fermion degrees of freedom introduces twenty-four fermion determinants. These multiply the Gaussian functional measures of the Maxwell, $Z$, $W$ and Higgs fields to give an effective functional measure. Suppose the functional integral over the Maxwell field is attempted first. This paper is concerned with the large amplitude behavior of the Maxwell effective measure. It is assumed that the large amplitude variation of this measure is insensitive to the presence of the $Z$, $W$ and $H$ fields; they are assumed to be a subdominant perturbation of the large amplitude Maxwell sector. Accordingly, we need only examine the large amplitude variation of a single QED fermion determinant. To facilitate this the Schwinger proper time representation of this determinant is decomposed into a sum of three terms. The advantage of this is that the separate terms can be non-perturbatively estimated fo...
Non-perturbative renormalization of three-quark operators
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Kaltenbrunner, Thomas [Regensburg Univ. (DE). Inst. fuer Theoretische Physik] (and others)
2008-10-15
High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wavefunction and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS scheme at {mu}=2 GeV. (orig.)
World-Line Formalism: Non-Perturbative Applications
Directory of Open Access Journals (Sweden)
Dmitry Antonov
2016-11-01
Full Text Available This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields.
Non-perturbative QCD amplitudes in quenched and eikonal approximations
Energy Technology Data Exchange (ETDEWEB)
Fried, H.M. [Physics Department, Brown University, Providence, RI 02912 (United States); Grandou, T., E-mail: Thierry.Grandou@inln.cnrs.fr [Université de Nice-Sophia Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS 7335, 1361 routes des Lucioles, 06560 Valbonne (France); Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu [Université de Nice-Sophia Antipolis, Institut Non Linéaire de Nice, UMR 6618 CNRS 7335, 1361 routes des Lucioles, 06560 Valbonne (France)
2014-05-15
Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality. The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD. - Highlights: • We discuss the physical insight of effective locality to QCD fermionic amplitudes. • We show that an unavoidable delta function goes along with the effective locality property. • The generic structure of QCD fermion amplitudes is obtained through Random Matrix calculus.
A non-perturbative approach to relativistic quantum communication channels
Landulfo, Andre G S
2016-01-01
We investigate the transmission of both classical and quantum information between two arbitrary observers in globally hyperbolic spacetimes using a quantum field as a communication channel. The field is supposed to be in some arbitrary quasifree state and no choice of representation of its canonical commutation relations is made. Both sender and receiver posses some localized two-level quantum system with which they can interact with the quantum field to prepare the input and receive the output of the channel, respectively. The interaction between the two-level systems and the quantum field is such that one can trace out the field degrees of freedom exactly and thus obtain the quantum channel in a non-perturbative way. We end the paper determining the unassisted as well as the entanglement-assisted classical and quantum channel capacities.
Kar, Supriya
2016-01-01
We show that the massless form fields, in $(4+1)$-dimensional non-perturbation theory of emergent gravity, become massive in a perturbative phase without Higgs mechanism. In particular an axionic scalar sourced by a non-perturbative dynamical correction is absorbed by the form fields to describe a massive NS field theory on an emergent gravitational pair of $(3{\\bar 3})$-brane. Arguably the novel idea of Higgs mechanism is naturally invoked in an emergent gravity underlying a ${\\rm CFT}_6$. Analysis reveals "gravito-weak" and "electro-weak" phases respectively on a vacuum pair in $(4+1)$ and $(3+1)$-dimensions. It is argued that the massive NS field quanta may govern an emergent graviton on a gravitational $3$-brane.
PREFACE: Loops 11: Non-Perturbative / Background Independent Quantum Gravity
Mena Marugán, Guillermo A.; Barbero G, J. Fernando; Garay, Luis J.; Villaseñor, Eduardo J. S.; Olmedo, Javier
2012-05-01
Loops 11 The international conference LOOPS'11 took place in Madrid from the 23-28 May 2011. It was hosted by the Instituto de Estructura de la Materia (IEM), which belongs to the Consejo Superior de Investigaciones Cientĺficas (CSIC). Like previous editions of the LOOPS meetings, it dealt with a wealth of state-of-the-art topics on Quantum Gravity, with special emphasis on non-perturbative background-independent approaches to spacetime quantization. The main topics addressed at the conference ranged from the foundations of Quantum Gravity to its phenomenological aspects. They encompassed different approaches to Loop Quantum Gravity and Cosmology, Polymer Quantization, Quantum Field Theory, Black Holes, and discrete approaches such as Dynamical Triangulations, amongst others. In addition, this edition celebrated the 25th anniversary of the introduction of the now well-known Ashtekar variables and the Wednesday morning session was devoted to this silver jubilee. The structure of the conference was designed to reflect the current state and future prospects of research on the different topics mentioned above. Plenary lectures that provided general background and the 'big picture' took place during the mornings, and the more specialised talks were distributed in parallel sessions during the evenings. To be more specific, Monday evening was devoted to Shape Dynamics and Phenomenology Derived from Quantum Gravity in Parallel Session A, and to Covariant Loop Quantum Gravity and Spin foams in Parallel Session B. Tuesday's three Parallel Sessions dealt with Black Hole Physics and Dynamical Triangulations (Session A), the continuation of Monday's session on Covariant Loop Quantum Gravity and Spin foams (Session B) and Foundations of Quantum Gravity (Session C). Finally, Thursday and Friday evenings were devoted to Loop Quantum Cosmology (Session A) and to Hamiltonian Loop Quantum Gravity (Session B). The result of the conference was very satisfactory and enlightening. Not
ER= EPR and Non-Perturbative Action Integrals for Quantum Gravity
Alasfar, L A
2016-01-01
In this paper, we summarise a conjuncture for constructing and calculating path integrals (in non perturbative fashion ) by summing over homotopy classes of paths in a multiply-connected spacetime. The topology of the spacetime is defined by Einstein-Rosen bridges (ERB) forming from the entanglement of Wheeler's quantum foam described by S.W Hawking paper 'Virtual Blackholes' (Phys.Rev. D53 (1996) 3099-3107). Because these 'bubbles' are entangled, they are connected by Plankian ERB's by the ER=EPR conjecture of L. Susskind Hence the spacetime will possess a large first Betti number $ B_1$. For any compact 2-surface in the spacetime, the topology ( in particular the homotopy ) of that surface is not trivial, due to the large number of Plankian ERB's that define homotopy though this surface. The quantisation of spacetime with this topology - along with the proper choice of the 2-surfaces- is conjectured to allow a non perturbative path integrals of quantum gravity theory over the spacetime manifold. The task is...
Non-perturbative effects of vacuum energy on the recent expansion of the universe
Parker, L; Parker, Leonard; Raval, Alpan
1999-01-01
We show that the vacuum energy of a free quantized field of very low mass can significantly alter the recent expansion of the universe. The effective action of the theory is obtained from a non-perturbative sum of scalar curvature terms in the propagator. We numerically investigate the semiclassical Einstein equations derived from it. As a result of non-perturbative quantum effects, the scalar curvature of the matter-dominated universe stops decreasing and approaches a constant value. The universe in our model evolves from an open matter-dominated epoch to a mildly inflating de Sitter expansion. The Hubble constant during the present de Sitter epoch, as well as the time at which the transition occurs from matter-dominated to de Sitter expansion, are determined by the mass of the field and by the present matter density. The model provides a theoretical explanation of the observed recent acceleration of the universe, and gives a good fit to data from high-redshift Type Ia supernovae, with a mass of about 10^{-3...
Non-perturbative renormalization of the static axial current in two-flavour QCD
Della Morte, M; Heitger, J; Fritzsch, Patrick; Heitger, Jochen; Morte, Michele Della
2007-01-01
We perform the non-perturbative renormalization of matrix elements of the static-light axial current by a computation of its scale dependence in lattice QCD with two flavours of massless O(a) improved Wilson quarks. The regularization independent factor that relates any running renormalized matrix element of the axial current in the static effective theory to the renormalization group invariant one is evaluated in the Schroedinger functional scheme, where in this case we find a significant deviation of the non-perturbative running from the perturbative prediction. An important technical ingredient to improve the precision of the results consists in the use of modified discretizations of the static quark action introduced earlier by our collaboration. As an illustration how to apply the renormalization of the static axial current presented here, we connect the bare matrix element of the current to the B_s-meson decay constant in the static approximation for one value of the lattice spacing, a ~ 0.08 fm, employ...
Statistics of polarization speckle: theory versus experiment
DEFF Research Database (Denmark)
Wang, Wei; Hanson, Steen Grüner; Takeda, Mitsuo
2010-01-01
In this paper, we reviewed our recent work on the statistical properties of polarization speckle, described by stochastic Stokes parameters fluctuating in space. Based on the Gaussian assumption for the random electric field components and polar-interferometer, we investigated theoretically...... and experimentally the statistics of Stokes parameters of polarization speckle, including probability density function of Stokes parameters with the spatial degree of polarization, autocorrelation of Stokes vector and statistics of spatial derivatives for Stokes parameters....
Statistical Ensemble Theory of Gompertz Growth Model
Directory of Open Access Journals (Sweden)
Takuya Yamano
2009-11-01
Full Text Available An ensemble formulation for the Gompertz growth function within the framework of statistical mechanics is presented, where the two growth parameters are assumed to be statistically distributed. The growth can be viewed as a self-referential process, which enables us to use the Bose-Einstein statistics picture. The analytical entropy expression pertain to the law can be obtained in terms of the growth velocity distribution as well as the Gompertz function itself for the whole process.
Information Theory and Statistical Mechanics Revisited
Zhou, Jian
2016-01-01
We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with special cases of modified Naudts' $\\phi$-entropy.
Parametric statistical inference basic theory and modern approaches
Zacks, Shelemyahu; Tsokos, C P
1981-01-01
Parametric Statistical Inference: Basic Theory and Modern Approaches presents the developments and modern trends in statistical inference to students who do not have advanced mathematical and statistical preparation. The topics discussed in the book are basic and common to many fields of statistical inference and thus serve as a jumping board for in-depth study. The book is organized into eight chapters. Chapter 1 provides an overview of how the theory of statistical inference is presented in subsequent chapters. Chapter 2 briefly discusses statistical distributions and their properties. Chapt
Probability, statistics and queueing theory, with computer science applications
Allen, Arnold O
1978-01-01
Probability, Statistics, and Queueing Theory: With Computer Science Applications focuses on the use of statistics and queueing theory for the design and analysis of data communication systems, emphasizing how the theorems and theory can be used to solve practical computer science problems. This book is divided into three parts. The first part discusses the basic concept of probability, probability distributions commonly used in applied probability, and important concept of a stochastic process. Part II covers the discipline of queueing theory, while Part III deals with statistical inference. T
Nucleon resonance electrocouplings in the non-perturbative regime
Energy Technology Data Exchange (ETDEWEB)
Philip L. Cole, Viktor Mokeev, Ralf Gothe
2012-09-01
There is an extensive search for baryon resonances using the CLAS detector in Hall B of JLab. Extracting the transition helicity amplitudes (or the {gamma}{sub v}NN* photo- and electrocouplings) sheds light on nature of the non-perturbative strong interaction. We have extended the data on differential cross sections to Q{sup 2} = 6.0 GeV{sup 2} for the {pi}N electroproduction channel. Electroproduction data were also collected on the two-charged-pion channel off protons, which provides nine independent differential {pi}{sup +}{pi}{sup -}p cross sections at Q{sup 2} up to 1.5 GeV{sup 2}. The two-pion results, moreover, are consistent with those from independent {pi}N electroproduction analyses, where the background contributions in the two-pion channel are completely different from that of the single-pion one. A phenomenological approach developed at Jefferson Lab - Moscow State University is employed for separating the resonant and non-resonant contributions to the final state. The Q{sup 2}-dependent electrocouplings were then obtained for the P{sub 11}(1440) and D{sub 13}(1520) excited baryon states. The new data will be discussed in light of these new developments in systematically exploring the affects of meson-baryon dressing on the transition helicity amplitudes as a function of Q{sup 2}.
Palombi, Filippo; Peña, C; Wittig, H
2006-01-01
We discuss the renormalisation properties of the complete set of $\\Delta B = 2$ four-quark operators with the heavy quark treated in the static approximation. We elucidate the role of heavy quark symmetry and other symmetry transformations in constraining their mixing under renormalisation. By employing the Schroedinger functional, a set of non-perturbative renormalisation conditions can be defined in terms of suitable correlation functions. As a first step in a fully non-perturbative determination of the scale-dependent renormalisation factors, we evaluate these conditions in lattice perturbation theory at one loop. Thereby we verify the expected mixing patterns and determine the anomalous dimensions of the operators at NLO in the Schroedinger functional scheme. Finally, by employing twisted-mass QCD it is shown how finite subtractions arising from explicit chiral symmetry breaking can be avoided completely.
Energy Technology Data Exchange (ETDEWEB)
Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Papinutto, M. [Istituto Nazionale di Fisica Nucleare, Rome (Italy); Pena, C. [European Organization for Nuclear Research, Geneva (Switzerland). Theoretical Physics Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2006-04-15
We discuss the renormalisation properties of the complete set of {delta}B=2 four-quark operators with the heavy quark treated in the static approximation. We elucidate the role of heavy quark symmetry and other symmetry transformations in constraining their mixing under renormalisation. By employing the Schroedinger functional, a set of non-perturbative renormalisation conditions can be defined in terms of suitable correlation functions. As a first step in a fully non-perturbative determination of the scale-dependent renormalisation factors, we evaluate these conditions in lattice perturbation theory at one loop. Thereby we verify the expected mixing patterns and determine the anomalous dimensions of the operators at NLO in the Schroedinger functional scheme. Finally, by employing twisted-mass QCD it is shown how finite subtractions arising from explicit chiral symmetry breaking can be avoided completely. (Orig.)
Sciarappa, Antonio
2016-10-01
Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to incompleteness of Omega background regularization in odd dimension, may be solved if we consider gauge theory on compact S 5 and S 3 geometries. We will develop this idea further by giving a full Bethe/Gauge correspondence dictionary on S 5 and S 3 focussing mainly on the eigenfunctions of (open and closed) relativistic 2-particle Toda chain and its quantized spectral curve: these are most properly written in terms of non-perturbatively completed NS open topological strings. A key ingredient is Faddeev's modular double structure which is naturally implemented by the S 5 and S 3 geometries.
Sciarappa, Antonio
2016-01-01
Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to incompleteness of Omega background regularization in odd dimension, may be solved if we consider gauge theory on compact $S^5$ and $S^3$ geometries. We will develop this idea further by giving a full Bethe/Gauge correspondence dictionary on $S^5$ and $S^3$ focussing mainly on the eigenfunctions of (open and closed) relativistic 2-particle Toda chain and its quantized spectral curve: these are most properly written in terms of non-perturbatively completed NS open topological strings. A key ingredient is Faddeev's modular double structure which is naturally implemented by the $S^5$ and $S^3$ geometries.
Information and exponential families in statistical theory
Barndorff-Nielsen, O
2014-01-01
First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.
Constraining a fourth generation of quarks. Non-perturbative Higgs boson mass bounds
Energy Technology Data Exchange (ETDEWEB)
Bulava, J. [European Lab. for Particle Physics (CERN), Geneva (Switzerland); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Nagy, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2013-01-15
We present a non-perturbative determination of the upper and lower Higgs boson mass bounds with a heavy fourth generation of quarks from numerical lattice computations in a chirally symmetric Higgs-Yukawa model. We find that the upper bound only moderately rises with the quark mass while the lower bound increases significantly, providing additional constraints on the existence of a straight-forward fourth quark generation. We examine the stability of the lower bound under the addition of a higher dimensional operator to the scalar field potential using perturbation theory, demonstrating that it is not significantly altered for small values of the coupling of this operator. For a Higgs boson mass of {proportional_to}125 GeV we find that the maximum value of the fourth generation quark mass is {proportional_to}300 GeV, which is already in conflict with bounds from direct searches.
The B-meson mass splitting from non-perturbative quenched lattice QCD
Grozin, A G; Marquard, P; Meyer, H B; Piclum, J H; Sommer, R; Steinhauser, M
2007-01-01
We perform the non-perturbative (quenched) renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and its three-loop matching to QCD. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B-mesons. These new computed factors are affected by an uncertainty negligible in comparison to the known bare matrix element of the operator between B-states. Furthermore, they push the quenched determination of the spin splitting for the Bs-meson much closer to its experimental value than the previous perturbatively renormalized computations. The renormalization factor for three commonly used heavy quark actions and the Wilson gauge action and useful parametrizations of the matching coefficient are provided.
Inspecting non-perturbative contributions to the Entanglement Entropy via wavefunctions
Bhattacharyya, Arpan; Lau, P H C; Liu, Si-Nong
2016-01-01
In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true ground state after taking the tunnelling effects into account and find some simple patterns. Notably, in the case of multiple particle interactions, entanglement entropy generically decreases with increasing number of minima. The knowledge of the subsystem actually increases as the number of minima increases. The reduced density matrix can also be seen to have close connections with graph spectra. In a more careful study of the two-well tunnelling system, we also extract the exponentially suppressed tail contribution, the analogues of instantons. To understand the effects of multiple minima in a field theory, it inspir...
Integrability and non-perturbative effects in the AdS/CFT correspondence
Gómez, C; Gómez, César; Hernández, Rafael
2007-01-01
We present a non-perturbative resummation of the asymptotic strong-coupling expansion for the dressing phase factor of the AdS_5xS^5 string S-matrix. The non-perturbative resummation provides a general form for the coefficients in the weak-coupling expansion, in agreement with crossing symmetry and transcendentality. The ambiguities of the non-perturbative prescription are discussed together with the similarities with the non-perturbative definition of the c=1 matrix model.
Statistical theory of hierarchical avalanche ensemble
Olemskoi, Alexander I.
1999-01-01
The statistical ensemble of avalanche intensities is considered to investigate diffusion in ultrametric space of hierarchically subordinated avalanches. The stationary intensity distribution and the steady-state current are obtained. The critical avalanche intensity needed to initiate the global avalanche formation is calculated depending on noise intensity. The large time asymptotic for the probability of the global avalanche appearance is derived.
Statistical tests of galactic dynamo theory
Chamandy, Luke; Taylor, A Russ
2016-01-01
Mean-field galactic dynamo theory is the leading theory to explain the prevalence of regular magnetic fields in spiral galaxies, but its systematic comparison with observations is still incomplete and fragmentary. Here we compare predictions of mean-field dynamo models to observational data on magnetic pitch angle and the strength of the mean magnetic field. We demonstrate that a standard $\\alpha^2\\Omega$ dynamo model produces pitch angles of the regular magnetic fields of nearby galaxies that are reasonably consistent with available data. The dynamo estimates of the magnetic field strength are generally within a factor of a few of the observational values. Reasonable agreement between theoretical and observed pitch angles generally requires the turbulent correlation time $\\tau$ to be in the range 10-20 Myr, in agreement with standard estimates. Moreover, good agreement also requires that the ratio of the ionized gas scale height to root-mean-square turbulent velocity increases with radius. Our results thus w...
Statistic Ensemble Theory of Small Superconducting Grains
Institute of Scientific and Technical Information of China (English)
CHEN Zhi-Qian; ZHENG Ren-Rong
2001-01-01
We apply the random matrix theory to small metallic grains in different spin states of S = 0, 1/2, 1, 3/2, 2, 5/2, .., and find that there exist theoretical critical level spacings de at which the superconductivity would breakdown. We also find that the higher the spin state, the smaller the critical level spacing, and for the state of S = 0superconducting enhancement actually exists.
Statistical Theory of Hedonic Price Indices
Brachinger, Hans Wolfgang
2002-01-01
In the economic literature, essentially, hedonic techniques either are applied straightforwardly or the economic foundations of the hedonic hypothesis are discussed. In this paper, the statistical foundations of hedonic price indices are developed. After a short overview on well-known functional forms of hedonic equations, first, precise hedonic notions of a good and its price are specified. These specifications allow a clear-cut definition of true hedonic price indices. Then, the problem of ...
The theory of gambling and statistical logic
Epstein, Richard A
1995-01-01
Richard Epstein's classic book on gambling and its mathematical analysis covers the full range of games from penny matching, to blackjack and other casino games, to the stock market (including Black-Scholes analysis). He even considers what light statistical inference can shed on the study of paranormal phenomena. Epstein is witty and insightful, a pleasure to dip into and read and rewarding to study.
A course in mathematical statistics and large sample theory
Bhattacharya, Rabi; Patrangenaru, Victor
2016-01-01
This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics — parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods. Large Sample theory with many worked examples, numerical calculations, and simulations to illustrate theory Appendices provide ready access to a number of standard results, with many proofs Solutions given to a number of selected exercises from Part I Part II exercises with ...
Methods of quantum field theory in statistical physics
Abrikosov, A A; Gorkov, L P; Silverman, Richard A
1975-01-01
This comprehensive introduction to the many-body theory was written by three renowned physicists and acclaimed by American Scientist as ""a classic text on field theoretic methods in statistical physics."
Extensive Generalization of Statistical Mechanics Based on Incomplete Information Theory
Directory of Open Access Journals (Sweden)
Qiuping A. Wang
2003-06-01
Full Text Available Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization is used to obtain generalized entropy . The concomitant incomplete statistical mechanics is applied to some physical systems in order to show the effect of the incompleteness of information. It is shown that this extensive generalized statistics can be useful for the correlated electron systems in weak coupling regime.
Statistical approach to quantum field theory an introduction
Wipf, Andreas
2013-01-01
Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems w...
Perturbative versus non-perturbative decoupling of heavy quarks
Energy Technology Data Exchange (ETDEWEB)
Knechtli, Francesco [Wuppertal Univ. (Germany). Dept. of Physics; Bruno, Mattia [Brookhaven National Laboratory, Upton, NY (United States); Finkenrath, Jacob [CaSToRC, Cyl Athalassa Campus, Nicosia (Cyprus); Leder, Bjoern [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Collaboration: ALPHA Collaboration
2015-11-15
We simulate a theory with N{sub f}=2 heavy quarks of mass M. At energies much smaller than M the heavy quarks decouple and the theory can be described by an effective theory which is a pure gauge theory to leading order in 1/M. We present results for the mass dependence of ratios such as t{sub 0}(M)/t{sub 0}(0). We compute these ratios from simulations and compare them to the perturbative prediction. The latter relies on a factorisation formula for the ratios which is valid to leading order in 1/M.
Statistics of resonances and delay times in random media: beyond random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Kottos, Tsampikos [Department of Physics, Wesleyan University, Middletown, CT 06459-0155 (United States); Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Goettingen (Germany)
2005-12-09
We review recent developments in quantum scattering from mesoscopic systems. Various spatial geometries whose closed analogues show diffusive, localized or critical behaviour are considered. These are the features that cannot be described by the universal random matrix theory results. Instead, one has to go beyond this approximation and incorporate them in a non-perturbative way. Here, we pay particular attention to the traces of these non-universal characteristics, in the distribution of the Wigner delay times and resonance widths. The former quantity captures time-dependent aspects of quantum scattering while the latter is associated with the poles of the scattering matrix.
Bohá\\{v}cik, J; August\\'\\{i}n, P
2013-01-01
We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.
Energy Technology Data Exchange (ETDEWEB)
Broemmel, D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik; Horsley, R.; Zanotti, J. [Edinburgh Univ. (United Kingdom). School of Physics; Morozov, S.M. [Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Nakamura, Y.; Pleiter, D. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Stueben, H. [Konrad-Zuse-Zentrum fuer Informationstechnik Berlin (ZIB) (Germany)
2007-10-15
We present first results from the QCDSF collaboration for the kaon semileptonic decay form factors at zero momentum transfer, using two flavours of non-perturbatively O(a)-improved Wilson quarks. A lattice determination of these form factors is of particular interest to improve the accuracy on the CKM matrix element vertical stroke V{sub us} vertical stroke. Calculations are performed on lattices with lattice spacing of about 0.08 fm with different values of light and strange quark masses, which allows us to extrapolate to chiral limit. Employing double ratio techniques, we are able to get small statistical errors. (orig.)
Quantum statistical correlations in thermal field theories: boundary effective theory
Bessa, A; de Carvalho, C A A; Fraga, E S
2010-01-01
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $\\phi_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schr\\"{o}dinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $\\phi_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Check of a new non-perturbative mechanism for elementary fermion mass generation
Capitani, Stefano; Dimopoulos, Petros; Frezzotti, Roberto; Garofalo, M; Knippschild, Bastian; Kostrzewa, Bartosz; Ottnad, Konstantin; Rossi, Giancarlo; Schrröck, Mario; Urbach, Carsten
2016-01-01
We consider a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an irrelevant Wilson-like term. Despite the presence of these two chiral breaking operators in the Lagrangian, an exact symmetry acting on fermions and scalars prevents perturbative mass corrections. In the phase where fermions are massless (Wigner phase) the Yukawa coupling can be tuned to a critical value at which chiral transformations acting on fermions only become a symmetry of the theory (up to cutoff effects). In the Nambu-Goldstone phase of the critical theory a fermion mass term of dynamical origin is expected to arise in the Ward identities of the purely fermionic chiral transformations. Such a non-perturbative mechanism of dynamical mass generation can provide a "natural" (\\`a la 't Hooft) alternative to the Higgs mechanism adopted in the Standard Model. Here we lay down the theoretical framework necessary to demonstrate...
Perturbative and Non-Perturbative Partial Supersymmetry Breaking $N=4 \\to N=2 \\to N=1$
Kiritsis, Elias B
1997-01-01
We show the existence of a supersymmetry breaking mechanism in string theory, where N=4 supersymmetry is broken spontaneously to N=2 and N=1 with moduli dependent gravitino masses. The spectrum of the spontaneously broken theory with lower supersymmetry is in one-to-one correspondence with the spectrum of the heterotic N=4 string. The mass splitting of the N=4 spectrum depends on the compactification moduli as well as the three R-symmetry charges. In the large moduli limit a restoration of the N=4 supersymmetry is obtained. As expected the graviphotons and some of the gauge bosons become massive in N=1 vacua. At some special points of the moduli space some of the N=4 states with non-zero winding numbers and with spin 0 and {1/2} become massless chiral superfields of the unbroken N=1 supersymmetry. Such vaccua have a dual type II description, in which there are magnetically charged states with spin 0 and {1/2} that become massless. The heterotic-type II duality suggests some novel non-perturbative transitions ...
A Framework for Non-Equilibrium Statistical Ensemble Theory
Institute of Scientific and Technical Information of China (English)
BI Qiao; HE Zu-Tan; LIU Jie
2011-01-01
Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to non-equilibrium phenomena domain, however the status of the theory of nonequilibrium phenomena can not be said as firm as well established as the Gibbsian ensemble theory. In this work, we present a framework for the non-equilibrium statistical ensemble formalism based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.
Models for probability and statistical inference theory and applications
Stapleton, James H
2007-01-01
This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readersModels for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses mo...
Local Finite Density Theory, Statistical Blocking and Color Superconductivity
Ying, S
2000-01-01
The motivation for the development of a local finite density theory is discussed. One of the problems related to an instability in the baryon number fluctuation of the chiral symmetry breaking phase of the quark system in the local theory is shown to exist. Such an instability problem is removed by taking into account the statistical blocking effects for the quark propagator, which depends on a macroscopic {\\em statistical blocking parameter} $\\epsilon$. This new frame work is then applied to study color superconducting phase of the light quark system.
Statistical Gauge Theory for Relativistic Finite Density Problems
Institute of Scientific and Technical Information of China (English)
YING Shu-Qian
2001-01-01
A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.
Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
Becirevic, D; Lubicz, V; Martinelli, G; Papinutto, Mauro; Reyes, J
2004-01-01
We present the results of an extensive lattice calculation of the renormalization constants of bilinear and four-quark operators for the non-perturbatively O(a)-improved Wilson action. The results are obtained in the quenched approximation at four values of the lattice coupling by using the non-perturbative RI/MOM renormalization method. Several sources of systematic uncertainties, including discretization errors and final volume effects, are examined. The contribution of the Goldstone pole, which in some cases may affect the extrapolation of the renormalization constants to the chiral limit, is non-perturbatively subtracted. The scale independent renormalization constants of bilinear quark operators have been also computed by using the lattice chiral Ward identities approach and compared with those obtained with the RI-MOM method. For those renormalization constants the non-perturbative estimates of which have been already presented in the literature we find an agreement which is typically at the level of 1%...
Propagation of Gluons From a Non-Perturbative Evolution Equation in Axial Gauges
Kinder-Geiger, Klaus
1999-01-01
We derive a non-perturbative evolution equation for the gluon propagator in axial gauges based on the framework of Wetterich's formulation of the exact renormalization group. We obtain asymptotic solutions to this equation in the ultraviolet and infrared limits.
Exotic branes and non-perturbative seven branes
Eyras, E; Lozano, Y
2000-01-01
We construct the effective action of certain exotic branes in the Type Ii theories which are not predicted by their space-time supersymmetry algebras. We analyze in detail the case of the NS-7B brane, S-dual to the D7-brane, and connected by T-duality to other exotic branes in Type IIA: the KK-6A br
FOURIER SERIES AND CHEBYSHEV POLYNOMIALS IN STATISTICAL DISTRIBUTION THEORY.
After the elementary functions, the Fourier series are the most important functions in applied mathematics. Nevertheless, they have been somewhat...neglected in statistical distribution theory. In this paper, the reasons for this omission are investigated and certain modifications of the Fourier ... series proposed. These results are presented in the form of representation theorems. In addition to the basic theorems, computational algorithms and
Extreme value theory and statistics for heavy tail data
S. Caserta; C.G. de Vries (Casper)
2003-01-01
textabstractA scientific way of looking beyond the worst-case return is to employ statistical extreme value methods. Extreme Value Theory (EVT) shows that the probability on very large losses is eventually governed by a simple function, regardless the specific distribution that underlies the return
Statistical Perturbation Theory of Cosmic Fields; 1, Basic Formalism and Second-order Theory
Matsubara, T
2000-01-01
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields, which we call as ``Statistical Perturbation Theory''. The formalism is an extensive generalization of the method used by Matsubara (1994) who derived a weakly nonlinear formula of the genus statistic in a 3D density field. After describing the general method, we apply the formalism especially to analyses of more general genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clearly described. These examples are applied to some cosmic fields, including 3D density field, 3D velocity field, 2D projected density field, and 2D weak lensing field. The results are detailed for second order theory of the formalism. The reason why the genus curves etc. in CDM-like models exhibit smaller deviations from Gaussian predictions when t...
Tellgren, Erik I; Fliegl, Heike
2013-10-28
In the present study a non-perturbative approach to ab initio calculations of molecules in strong, linearly varying, magnetic fields is developed. The use of London atomic orbitals (LAOs) for non-uniform magnetic fields is discussed and the standard rationale of gauge-origin invariance is generalized to invariance under arbitrary constant shifts of the magnetic vector potential. Our approach is applied to study magnetically induced anapole moments (or toroidal moments) and the related anapole susceptibilities for a test set of chiral and nonchiral molecules. For the first time numerical anapole moments are accessible on an ab initio level of theory. Our results show that the use of London atomic orbitals dramatically improves the basis set convergence also for magnetic properties related to non-uniform magnetic fields, at the cost that the Hellmann-Feynman theorem does not apply for a finite LAO basis set. It is shown that the mixed anapole susceptibility can be related to chirality, since its trace vanishes for an achiral molecule.
Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string
Sun, Kaiwen; Wang, Xin; Huang, Min-xin
2017-01-01
We establish the precise relation between the Nekrasov-Shatashvili (NS) quantization scheme and Grassi-Hatsuda-Mariño conjecture for the mirror curve of arbitrary toric Calabi-Yau threefold. For a mirror curve of genus g, the NS quantization scheme leads to g quantization conditions for the corresponding integrable system. The exact NS quantization conditions enjoy a self S-duality with respect to Planck constant h and can be derived from the Lockhart-Vafa partition function of non-perturbative topological string. Based on a recent observation on the correspondence between spectral theory and topological string, another quantization scheme was proposed by Grassi-Hatsuda-Mariño, in which there is a single quantization condition and the spectra are encoded in the vanishing of a quantum Riemann theta function. We demonstrate that there actually exist at least g nonequivalent quantum Riemann theta functions and the intersections of their theta divisors coincide with the spectra determined by the exact NS quantization conditions. This highly nontrivial coincidence between the two quantization schemes requires infinite constraints among the refined Gopakumar-Vafa invariants. The equivalence for mirror curves of genus one has been verified for some local del Pezzo surfaces. In this paper, we generalize the correspondence to higher genus, and analyze in detail the resolved C^3/Z_5 orbifold and several SU( N ) geometries. We also give a proof for some models at ħ = 2π /k.
General framework of the non-perturbative renormalization group for non-equilibrium steady states
Energy Technology Data Exchange (ETDEWEB)
Canet, Leonie [Laboratoire de Physique et Modelisation des Milieux Condenses, Universite Joseph Fourier Grenoble I-CNRS, BP166, 38042 Grenoble Cedex (France); Chate, Hugues [Service de Physique de l' Etat Condense, CEA-Saclay, 91191 Gif-sur-Yvette Cedex (France); Delamotte, Bertrand, E-mail: leonie.canet@grenoble.cnrs.fr [Laboratoire de Physique Theorique de la Matiere Condensee, Universite Pierre et Marie Curie, Paris VI, CNRS UMR 7600, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2011-12-09
This paper is devoted to presenting in detail the non-perturbative renormalization group (NPRG) formalism to investigate out-of-equilibrium systems and critical dynamics in statistical physics. The general NPRG framework for studying non-equilibrium steady states in stochastic models is expounded and fundamental technicalities are stressed, mainly regarding the role of causality and of It o-bar 's discretization. We analyze the consequences of It o-bar 's prescription in the NPRG framework and eventually provide an adequate regularization to encode them automatically. Besides, we show how to build a supersymmetric NPRG formalism with emphasis on time-reversal symmetric problems, whose supersymmetric structure allows for a particularly simple implementation of NPRG in which causality issues are transparent. We illustrate the two approaches on the example of Model A within the derivative expansion approximation at order 2 and check that they yield identical results. We stress, though, that the framework presented here also applies to genuinely out-of-equilibrium problems. (paper)
Koopmans' theorem in statistical Hartree-Fock theory
Pain, Jean-Christophe
2011-01-01
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but that a restricted version of the theorem can be obtained, by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
Statistics and Probability Theory In Pursuit of Engineering Decision Support
Faber, Michael Havbro
2012-01-01
This book provides the reader with the basic skills and tools of statistics and probability in the context of engineering modeling and analysis. The emphasis is on the application and the reasoning behind the application of these skills and tools for the purpose of enhancing decision making in engineering. The purpose of the book is to ensure that the reader will acquire the required theoretical basis and technical skills such as to feel comfortable with the theory of basic statistics and probability. Moreover, in this book, as opposed to many standard books on the same subject, the perspective is to focus on the use of the theory for the purpose of engineering model building and decision making. This work is suitable for readers with little or no prior knowledge on the subject of statistics and probability.
Conformal bootstrap: non-perturbative QFT's under siege
CERN. Geneva
2016-01-01
[Exceptionally in Council Chamber] Originally formulated in the 70's, the conformal bootstrap is the ambitious idea that one can use internal consistency conditions to carve out, and eventually solve, the space of conformal field theories. In this talk I will review recent developments in the field which have boosted this program to a new level. I will present a method to extract quantitative informations in strongly-interacting theories, such as 3D Ising, O(N) vector model and even systems without a Lagrangian formulation. I will explain how these techniques have led to the world record determination of several critical exponents. Finally, I will review exact analytical results obtained using bootstrap techniques.
Statistical theory for the kinetics and dynamics of roaming reactions.
Klippenstein, Stephen J; Georgievskii, Yuri; Harding, Lawrence B
2011-12-22
We present a statistical theory for the effect of roaming pathways on product branching fractions in both unimolecular and bimolecular reactions. The analysis employs a separation into three distinct steps: (i) the formation of weakly interacting fragments in the long-range/van der Waals region of the potential via either partial decomposition (for unimolecular reactants) or partial association (for bimolecular reactants), (ii) the roaming step, which involves the reorientation of the fragments from one region of the long-range potential to another, and (iii) the abstraction, addition, and/or decomposition from the long-range region to yield final products. The branching between the roaming induced channel(s) and other channels is obtained from a steady-state kinetic analysis for the two (or more) intermediates in the long-range region of the potential. This statistical theory for the roaming-induced product branching is illustrated through explicit comparisons with reduced dimension trajectory simulations for the decompositions of H(2)CO, CH(3)CHO, CH(3)OOH, and CH(3)CCH. These calculations employ high-accuracy analytic potentials obtained from fits to wide-ranging CASPT2 ab initio electronic structure calculations. The transition-state fluxes for the statistical theory calculations are obtained from generalizations of the variable reaction coordinate transition state theory approach. In each instance, at low energy the statistical analysis accurately reproduces the branching obtained from the trajectory simulations. At higher energies, e.g., above 1 kcal/mol, increasingly large discrepancies arise, apparently due to a dynamical biasing toward continued decomposition of the incipient molecular fragments (for unimolecular reactions). Overall, the statistical theory based kinetic analysis is found to provide a useful framework for interpreting the factors that determine the significance of roaming pathways in varying chemical environments.
Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics
Wolpert, David H.
2005-01-01
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.
Non-perturbative studies of QCD at small quark masses
Energy Technology Data Exchange (ETDEWEB)
Wennekers, J.
2006-07-15
We investigate the quenched approximation of lattice QCD with numerical simulations of Ginsparg-Wilson fermions, which are a fermion discretisation with exact chiral symmetry. We compute the renormalisation constant of the scalar density, which allows to extrapolate the chiral condensate to the continuum limit. Furthermore we match lattice results of matrix elements describing hadronic kaon decays to Chiral Perturbation Theory in finite volume and at almost vanishing quark mass. The resulting low-energy constants in the considered SU(4)-flavour symmetric case indicate a substantial contribution of low scale QCD effects to the {delta}I = 1/2 rule. (Orig.)
Non-perturbative gravity at different length scales
Energy Technology Data Exchange (ETDEWEB)
Folkerts, Sarah
2013-12-18
In this thesis, we investigate different aspects of gravity as an effective field theory. Building on the arguments of self-completeness of Einstein gravity, we argue that any sensible theory, which does not propagate negative-norm states and reduces to General Relativity in the low energy limit is self-complete. Due to black hole formation in high energy scattering experiments, distances smaller than the Planck scale are shielded from any accessibility. Degrees of freedom with masses larger than the Planck mass are mapped to large classical black holes which are described by the already existing infrared theory. Since high energy (UV) modifications of gravity which are ghost-free can only produce stronger gravitational interactions than Einstein gravity, the black hole shielding is even more efficient in such theories. In this light, we argue that conventional attempts of a Wilsonian UV completion are severely constrained. Furthermore, we investigate the quantum picture for black holes which emerges in the low energy description put forward by Dvali and Gomez in which black holes are described as Bose-Einstein condensates of many weakly coupled gravitons. Specifically, we investigate a non-relativistic toy model which mimics certain aspects of the graviton condensate picture. This toy model describes the collapse of a condensate of attractive bosons which emits particles due to incoherent scattering. We show that it is possible that the evolution of the condensate follows the critical point which is accompanied by the appearance of a light mode. Another aspect of gravitational interactions concerns the question whether quantum gravity breaks global symmetries. Arguments relying on the no hair theorem and wormhole solutions suggest that global symmetries can be violated. In this thesis, we parametrize such effects in terms of an effective field theory description of three-form fields. We investigate the possible implications for the axion solution of the strong CP
1998-01-01
We systematically study the exclusion statistics for quasi-particles for Conformal Field Theory spectra by employing a method based on recursion relations for truncated spectra. Our examples include generalized fermions in c
An Entropy-Weighted Sum over Non-Perturbative Vacua
Gregori, Andrea
2007-01-01
We discuss how, in a Universe restricted to the causal region connected to the observer, General Relativity implies the quantum nature of physical phenomena and directly leads to a string theory scenario, whose dynamics is ruled by a functional that weights all configurations according to their entropy. The most favoured configurations are those of minimal entropy. Along this class of vacua a four-dimensional space-time is automatically selected; when, at large volume, a description of space-time in terms of classical geometry can be recovered, the entropy-weighted sum reduces to the ordinary Feynman's path integral. What arises is a highly predictive scenario, phenomenologically compatible with the experimental observations and measurements, in which everything is determined in terms of the fundamental constants and the age of the Universe, with no room for freely-adjustable parameters. We discuss how this leads to the known spectrum of particles and interactions. Besides the computation of masses and coupli...
Statistical field theory description of inhomogeneous polarizable soft matter
Martin, Jonathan M.; Li, Wei; Delaney, Kris T.; Fredrickson, Glenn H.
2016-10-01
We present a new molecularly informed statistical field theory model of inhomogeneous polarizable soft matter. The model is based on fluid elements, referred to as beads, that can carry a net monopole of charge at their center of mass and a fixed or induced dipole through a Drude-type distributed charge approach. The beads are thus polarizable and naturally manifest attractive van der Waals interactions. Beyond electrostatic interactions, beads can be given soft repulsions to sustain fluid phases at arbitrary densities. Beads of different types can be mixed or linked into polymers with arbitrary chain models and sequences of charged and uncharged beads. By such an approach, it is possible to construct models suitable for describing a vast range of soft-matter systems including electrolyte and polyelectrolyte solutions, ionic liquids, polymerized ionic liquids, polymer blends, ionomers, and block copolymers, among others. These bead models can be constructed in virtually any ensemble and converted to complex-valued statistical field theories by Hubbard-Stratonovich transforms. One of the fields entering the resulting theories is a fluctuating electrostatic potential; other fields are necessary to decouple non-electrostatic interactions. We elucidate the structure of these field theories, their consistency with macroscopic electrostatic theory in the absence and presence of external electric fields, and the way in which they embed van der Waals interactions and non-uniform dielectric properties. Their suitability as a framework for computational studies of heterogeneous soft matter systems using field-theoretic simulation techniques is discussed.
Casimir-Polder forces -- a non-perturbative approach
Buhmann, S Y; Knöll, L; Welsch, D G; Buhmann, Stefan Yoshi; Dung, Ho Trung; Kn\\"{o}ll, Ludwig; Welsch, Dirk-Gunnar
2004-01-01
Within the frame of macroscopic quantum electrodynamics in linear, causal media, the problem of radiation forces acting on excited atomic systems near dispersing and absorbing magnetodielectric bodies is studied. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the Casimir-Polder force. To go beyond perturbation theory, the exact Heisenberg equation of motion for the center-of-mass gross motion is used to derive a very general expression for the force. For a non-driven atomic system in the weak coupling regime the total force as a function of time is a superposition of force components that are related to the intra-atomic density matrix elements at chosen time. It is shown that even the force component associated with the atomic ground state is not exactly derivable from a potential, because of the position dependence of the atomic polarizability. Further, it is found that when the atomic system is initially prepared in a coherent superposition...
Quench echo and work statistics in integrable quantum field theories.
Pálmai, T; Sotiriadis, S
2014-11-01
We propose a boundary thermodynamic Bethe ansatz calculation technique to obtain the Loschmidt echo and the statistics of the work done when a global quantum quench is performed on an integrable quantum field theory. We derive an analytic expression for the lowest edge of the probability density function and find that it exhibits universal features, in the sense that its scaling form depends only on the statistics of excitations. We perform numerical calculations on the sinh-Gordon model, a deformation of the free boson theory, and we obtain that by turning on the interaction the density function develops fermionic properties. The calculations are facilitated by a previously unnoticed property of the thermodynamic Bethe ansatz construction.
The Statistical Theory of Relaxation and the Metastable Vapor.
Kellerman, Peter L.
A generalization to equilibrium statistical thermodynamics is proposed, capable of describing the relaxation of a system to its equilibrium state. This theory, referred to as the "statistical theory of relaxation" (STR), is centered around a macroscopic diffusion equation, which involves a fluctuating entropy, as well as certain "diffusion constants". Although STR is a phenomenological theory, an underlying microscopic picture is presented as well, which "enriches" STR by suggesting a microscopic prescription for the entropy and symmetry conditions on the diffusion constants. An H-theorem also is proved, which places additional "irreversibility conditions" on the diffusion constants, and which can be interpreted as a statistical generalization to the entropy-production theorem of non-equilibrium thermodynamics. STR is employed to describe the statistical collapse (through nucleation) of a metastable vapor. Two mechanisms are proposed: "nucleation through liquid growth" (NLG), whereby a liquid droplet fluctuates past a critical size, and "nucleation through vapor collapse" (NVC), whereby a quantity of vapor larger than the critical size, homogeneously fluctuates to its liquid state. Both mechanisms contribute to the collapse of the metastable vapor state. It is found that for shallow "quenches", NLG predominates, yielding results similar to classical nucleation theory, although with certain differences in the "prefactor terms". For deep quenches, it is found that NVC predominates, yielding the result that the lifetime of the metastable state goes to zero (exactly) at the spinodal point. This confirms the notion of the spinodal point being the absolute limit to the metastable state, and also is consistent with the results of other approaches that predict the appearance of "ramified" droplets in deep quenches. The nucleation rate (as a function of temperature and time) is calculated with the aid of a computer for water vapor, yielding results in excellent agreement
Statistical Decision Theory Applied to Radiation Therapy Treatment Decisions
Schultheiss, T. E.; El-Mahdi, Anas M.
1982-01-01
Statistical decision theory has been applied to the treatment planning decision of radiation therapy. The decision involves the choice of parameters which determine the radiation dose distribution. To choose among dose distributions requires a decision rule which reflects the uncertainty of possible outcomes for any specific dose distribution and the various risks associated with each outcome. A relative gravity or morbidity is assigned to each possible complication of treatment. In this stud...
The Application of Statistical Turbulence Theory to Convective Instabilities.
1986-11-01
1985]. Here, we shall discuss the applications of statistical turbulence theory to determine the quasi-steady-state spectral density function (SDF...follow Sudan’s prescription for deriving the form of one- dimensional spectral - density function . The main difference is that we have attempted to relax...the conservation property of the basic equations is ’V preserved in the DIA or WCA equations for the spectral density function itself. This property is
A Statistical Theory for Hydrogen Bonding Networks: One Component Case
Institute of Scientific and Technical Information of China (English)
WANG Hai-Jun; BA Xin-Wu; ZHAO Min; LI Ze-Sheng
2000-01-01
The theory of reversible gelation is shown to be applicable to the hydrogen bonding system by analyzing their similarities in statistical viewpoint. The size distribution of hydrogen bonding clusters, the gelation condition and the generalized scaling law can be obtained directly. These results show that such a system can undergo phase transition process. Furthermore, a relationship between Gibbs free energy of forming hydrogen bond and conversions of groups is given. As an example, the chemical shift of OH groups is considered.
Korcyl, Piotr
2016-01-01
We determine quark mass dependent order $a$ improvement terms of the form $b_Jam$ for non-singlet scalar, pseudoscalar, vector and axialvector currents using correlators in coordinate space on a set of CLS ensembles. These have been generated employing non-perturbatively improved Wilson Fermions and the tree-level L\\"uscher-Weisz gauge action at $\\beta = 3.4, 3.46, 3.55$ and $3.7$, corresponding to lattice spacings ranging from $a \\approx 0.085$ fm down to $0.05$ fm. In the $N_f=2+1$ flavour theory two types of improvement coefficients exist: $b_J$, proportional to non-singlet quark mass combinations, and $\\bar{b}_J$ (or $\\tilde{b}_J$), proportional to the trace of the quark mass matrix. Combining our non-perturbative determinations with perturbative results, we quote Pad\\'e approximants parameterizing the $b_J$ improvement coefficients within the above window of lattice spacings. We also give preliminary results for $\\tilde{b}_J$ at $\\beta=3.4$.
Light-Front Holography and Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; de Teramond, Guy F.; /Costa Rica U.
2009-12-09
The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M{sup 2} = 4{kappa}{sup 2}(n + L + S = 2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable {zeta}. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time {tau}. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.
Jain, Shekhar; Dominik, Aleksandra; Chapman, Walter G
2007-12-28
A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.
The Mathematical Statistics Theory Application on the Price Fluctuation Analysis
Directory of Open Access Journals (Sweden)
Jintao Meng
2013-01-01
Full Text Available Grain price and output fluctuation are the normal state of market economy. It is one of the most important economic researches to understand grain price and output fluctuation law, which provides theory basis for the macroeconomic regulation and control. According to the cobweb model theory, the relationship between citrus production and price is accord with the divergence type of cobweb model .This means that simply relying on market regulation can make fluctuation between production and price bigger, go against citrus production and cultivation, thus, affecting the interests of farmers. It is well-known most farmers are concerned about the future price trend and the probability of price fluctuation. This paper uses mathematical statistics theory to study the citrus price changes, and the corresponding change trend, providing a theoretical basis for majority of farmers to better estimate citrus price change trend.
Statistical Theory of Selectivity and Conductivity in Biological Channels
Luchinsky, D G; Kaufman, I; Timucin, D A; Eisenberg, R S; McClintock, P V E
2016-01-01
We present an equilibrium statistical-mechanical theory of selectivity in biological ion channels. In doing so, we introduce a grand canonical ensemble for ions in a channel's selectivity filter coupled to internal and external bath solutions for a mixture of ions at arbitrary concentrations, we use linear response theory to find the current through the filter for small gradients of electrochemical potential, and we show that the conductivity of the filter is given by the generalized Einstein relation. We apply the theory to the permeation of ions through the potassium selectivity filter, and are thereby able to resolve the long-standing paradox of why the high selectivity of the filter brings no associated delay in permeation. We show that the Eisenman selectivity relation follows directly from the condition of diffusion-limited conductivity through the filter. We also discuss the effect of wall fluctuations on the filter conductivity.
A New Approach to Analytic, Non-Perturbative and Gauge-Invariant QCD
Fried, H M; Sheu, Y -M
2012-01-01
Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional "idealistic" description of QCD and a more "realistic" description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of the Green's functional and the vacuum functional. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called "Effective Locality", in which the interact...
More on the non-perturbative Gribov-Zwanziger quantization of linear covariant gauges
Capri, M A L; Fiorentini, D; Guimaraes, M S; Justo, I F; Mintz, B W; Palhares, L F; Pereira, A D; Sobreiro, R F; Sorella, S P
2015-01-01
In this paper, we discuss the gluon propagator in the linear covariant gauges in $D=2,3,4$ Euclidean dimensions. Non-perturbative effects are taken into account via the so-called Refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for $D=3,4$, the gluon propagator displays a massive (decoupling) behaviour, while for $D=2$, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced non-perturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our non-perturbative definition of the linear covariant gauge.
Non-perturbative gluon-hadron inputs for all available forms of QCD factorization
Ermolaev, B I
2016-01-01
Description of hadronic reactions at high energies is conventionally done on basis of QCD factoriza- tion so that factorization convolutions involve non-perturbative inputs mimicking non-perturbative contributions and perturbative evolution of those inputs. We construct the inputs for the gluon- hadron scattering amplitudes in the forward kinematics and, using the Optical theorem, convert them into inputs for gluon distributions in the both polarized and unpolarized hadrons. Firstly, we derive general mathematical criteria which any model for the inputs should obey and then suggest a Resonance Model satisfying those criteria. This model is inspired by a simple observation: after emitting an active parton off the hadron, the remaining ensemble of spectators becomes unstable and therefore it can be described through factors of the resonance type. Exploiting Resonance Model, we obtain non-perturbative inputs for gluon distributions in unpolarized and polarized hadrons for all available forms of QCD factorization...
Collider searches for non-perturbative low-scale gravity states
Gingrich, Douglas M
2015-01-01
The possibility of producing non-perturbative low-scale gravity states in collider experiments was first discussed in about 1998. The ATLAS and CMS experiments have searched for non-perturbative low-scale gravity states using the Large Hadron Collider (LHC) with a proton--proton centre of mass energy of 8 TeV. These experiments have now seriously confronted the possibility of producing non-perturbative low-scale gravity states which were proposed over 17 years ago. I will summarise the results of the searches, give a personal view of what they mean, and make some predictions for 13 TeV centre of mass energy. I will also discuss early ATLAS 13 TeV centre of mass energy results.
Resonance model for non-perturbative inputs to gluon distributions in the hadrons
Ermolaev, B I; Troyan, S I
2015-01-01
We construct non-perturbative inputs for the elastic gluon-hadron scattering amplitudes in the forward kinematic region for both polarized and non-polarized hadrons. We use the optical theorem to relate invariant scattering amplitudes to the gluon distributions in the hadrons. By analyzing the structure of the UV and IR divergences, we can determine theoretical conditions on the non-perturbative inputs, and use these to construct the results in a generalized Basic Factorization framework using a simple Resonance Model. These results can then be related to the K_T and Collinear Factorization expressions, and the corresponding constrains can be extracted.
Scalar coupling evolution in a non-perturbative QCD resummation scheme
Energy Technology Data Exchange (ETDEWEB)
Gomez, J.D., E-mail: jgomez@ufabc.edu.br [Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, SP (Brazil); Natale, A.A., E-mail: natale@ift.unesp.br [Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, SP (Brazil); Instituto de Física Teórica, UNESP, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070, São Paulo, SP (Brazil)
2015-07-30
We compute the Standard Model scalar coupling (λ) evolution in a particular QCD resummation scheme, where the QCD coupling becomes infrared finite due to the presence of a dynamically generated gluon mass, leading to the existence of a non-perturbative infrared fixed point. We discuss how this scheme can be fixed taking recourse to phenomenological considerations in the infrared region. The QCD β function associated to this non-perturbative coupling when introduced into the SM renormalization group equations increases the λ values at high energies.
Finite-frequency counting statistics of electron transport: Markovian theory
Energy Technology Data Exchange (ETDEWEB)
Marcos, D; Aguado, R [Departamento de Teoria y Simulacion de Materiales, Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco 28049, Madrid (Spain); Emary, C; Brandes, T, E-mail: david.marcos@icmm.csic.es [Institut fuer Theoretische Physik, Hardenbergstrasse 36, TU Berlin, D-10623 Berlin (Germany)
2010-12-15
We present a theory of frequency-dependent counting statistics of electron transport through nanostructures within the framework of Markovian quantum master equations. Our method allows the calculation of finite-frequency current cumulants of arbitrary order, as we explicitly show for the second- and third-order cumulants. Our formulae generalize previous zero-frequency expressions in the literature and can be viewed as an extension of MacDonald's formula beyond shot noise. When combined with an appropriate treatment of tunneling using, e.g., the Liouvillian perturbation theory in Laplace space, our method can deal with arbitrary bias voltages and frequencies, as we illustrate with the paradigmatic example of transport through a single resonant level model. We discuss various interesting limits, including the recovery of the fluctuation-dissipation theorem near linear response, as well as some drawbacks inherent to the Markovian description arising from the neglect of quantum fluctuations.
Statistical Analysis of Designed Experiments Theory and Applications
Tamhane, Ajit C
2012-01-01
A indispensable guide to understanding and designing modern experiments The tools and techniques of Design of Experiments (DOE) allow researchers to successfully collect, analyze, and interpret data across a wide array of disciplines. Statistical Analysis of Designed Experiments provides a modern and balanced treatment of DOE methodology with thorough coverage of the underlying theory and standard designs of experiments, guiding the reader through applications to research in various fields such as engineering, medicine, business, and the social sciences. The book supplies a foundation for the
Computational Information Geometry in Statistics: Theory and Practice
Directory of Open Access Journals (Sweden)
Frank Critchley
2014-05-01
Full Text Available A broad view of the nature and potential of computational information geometry in statistics is offered. This new area suitably extends the manifold-based approach of classical information geometry to a simplicial setting, in order to obtain an operational universal model space. Additional underlying theory and illustrative real examples are presented. In the inﬁnite-dimensional case, challenges inherent in this ambitious overall agenda are highlighted and promising new methodologies indicated.
Mature students learning statistics: The activity theory perspective
Gordon, Sue
1993-09-01
The concept of approach "stresses relationships between intention, process and outcome within a specified context as described by an individual" (Schmeck, 1988, p. 10). This paper explores the approaches to learning of a group of mature students from the theoretical perspective of activity theory in order to gain an insight into some of the ways statistics is learned. In this framework, learning, regarded as goal-directed behaviour, is analysed by exploring the socio-historical factors relating to students' self regulation of their cognitive activities. The material is derived from questionnaires and interviews with five students, and focuses on the students' own interpretations of the contexts affecting their approaches.
Stochastical modeling for Viral Disease: Statistical Mechanics and Network Theory
Zhou, Hao; Deem, Michael
2007-04-01
Theoretical methods of statistical mechanics are developed and applied to study the immunological response against viral disease, such as dengue. We use this theory to show how the immune response to four different dengue serotypes may be sculpted. It is the ability of avian influenza, to change and to mix, that has given rise to the fear of a new human flu pandemic. Here we propose to utilize a scale free network based stochastic model to investigate the mitigation strategies and analyze the risk.
Decision making, movement planning and statistical decision theory.
Trommershäuser, Julia; Maloney, Laurence T; Landy, Michael S
2008-08-01
We discuss behavioral studies directed at understanding how probability information is represented in motor and economic tasks. By formulating the behavioral tasks in the language of statistical decision theory, we can compare performance in equivalent tasks in different domains. Subjects in traditional economic decision-making tasks often misrepresent the probability of rare events and typically fail to maximize expected gain. By contrast, subjects in mathematically equivalent movement tasks often choose movement strategies that come close to maximizing expected gain. We discuss the implications of these different outcomes, noting the evident differences between the source of uncertainty and how information about uncertainty is acquired in motor and economic tasks.
SOLVING PROBLEMS OF STATISTICS WITH THE METHODS OF INFORMATION THEORY
Directory of Open Access Journals (Sweden)
Lutsenko Y. V.
2015-02-01
Full Text Available The article presents a theoretical substantiation, methods of numerical calculations and software implementation of the decision of problems of statistics, in particular the study of statistical distributions, methods of information theory. On the basis of empirical data by calculation we have determined the number of observations used for the analysis of statistical distributions. The proposed method of calculating the amount of information is not based on assumptions about the independence of observations and the normal distribution, i.e., is non-parametric and ensures the correct modeling of nonlinear systems, and also allows comparable to process heterogeneous (measured in scales of different types data numeric and non-numeric nature that are measured in different units. Thus, ASC-analysis and "Eidos" system is a modern innovation (ready for implementation technology solving problems of statistical methods of information theory. This article can be used as a description of the laboratory work in the disciplines of: intelligent systems; knowledge engineering and intelligent systems; intelligent technologies and knowledge representation; knowledge representation in intelligent systems; foundations of intelligent systems; introduction to neuromaturation and methods neural networks; fundamentals of artificial intelligence; intelligent technologies in science and education; knowledge management; automated system-cognitive analysis and "Eidos" intelligent system which the author is developing currently, but also in other disciplines associated with the transformation of data into information, and its transformation into knowledge and application of this knowledge to solve problems of identification, forecasting, decision making and research of the simulated subject area (which is virtually all subjects in all fields of science
Physical consequences of black holes in non-perturbative quantum gravity and inflationary cosmology
Reska, P.M.
2011-01-01
In this thesis the consequences of the presence of a Schwarzschild black hole in de Sitter space are studied in the setting of non-perturbative quantum gravity and in inflationary cosmology. We first review the formalism of Causal Dynamical Triangulations (CDT) which implements a lattice regularizat
Constraining the Higgs boson mass: A non-perturbative lattice study
Jansen, Karl; Nagy, Attila
2012-01-01
We present non-perturbatively obtained results for upper and lower Higgs boson mass bounds using a chiral invariant lattice formulation of the Higgs-Yukawa sector of the standard model. We determine the mass bounds both, for a standard model top quark mass and for a possible fourth quark generation with masses up to 700GeV.
Statistical rate theory and kinetic energy-resolved ion chemistry: theory and applications.
Armentrout, P B; Ervin, Kent M; Rodgers, M T
2008-10-16
Ion chemistry, first discovered 100 years ago, has profitably been coupled with statistical rate theories, developed about 80 years ago and refined since. In this overview, the application of statistical rate theory to the analysis of kinetic-energy-dependent collision-induced dissociation (CID) reactions is reviewed. This procedure accounts for and quantifies the kinetic shifts that are observed as systems increase in size. The statistical approach developed allows straightforward extension to systems undergoing competitive or sequential dissociations. Such methods can also be applied to the reverse of the CID process, association reactions, as well as to quantitative analysis of ligand exchange processes. Examples of each of these types of reactions are provided and the literature surveyed for successful applications of this statistical approach to provide quantitative thermochemical information. Such applications include metal-ligand complexes, metal clusters, proton-bound complexes, organic intermediates, biological systems, saturated organometallic complexes, and hydrated and solvated species.
Statistical mechanics of quasispecies theories of molecular evolution
Munoz Tavera, Enrique
This thesis presents a statistical mechanical analysis of different formulations of quasispecies theory of molecular evolution. These theories, characterized by two different families of models, the Crow-Kimura and the Eigen model, constitute a microscopie description of evolution. These models are most often used for RNA viruses, where a phase transition is predicted, in agreement with experiments, between an organized or quasispecies phase, and a disordered non-selective phase when the mutation rate exceeds a critical value. The methods of statistical mechanics, in particular field-theoretic methods, are employed to obtain analytic solutions to four problems relevant to biological interest. The first chapter presents the study of evolution under a multiple-peak fitness landscape, with biological applications in the study of the proliferation of viruses or cancer under the control of drugs or the immune system. The second chapter studies the effect of incorporating different forms of horizontal gene transfer and two-parent recombination to the classical formulation of quasispecies models. As an example, we study the effect of the sign of epistasis of the fitness landscape on the advantage or disadvantage of recombination for the mean fitness. The third chapter considers the relaxation of the purine/pyrimidine assumption in the classical formulation of the models, by formulating and solving the parallel and Eigen models in the context of a four-letter alphabet. The fourth and final chapter studies finite population effects, both in the presence and in the absence of horizontal gene transfer.
Energy Technology Data Exchange (ETDEWEB)
Tadaki, Kohtaro, E-mail: tadaki@kc.chuo-u.ac.j [Research and Development Initiative, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551 (Japan)
2010-12-01
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp. 425-434, 2008] and [K. Tadaki, Proceedings of LFCS'09, Springer's LNCS, vol. 5407, pp. 422-440, 2009], where we introduced the notion of thermodynamic quantities, such as partition function Z(T), free energy F(T), energy E(T), statistical mechanical entropy S(T), and specific heat C(T), into AIT. We then discovered that, in the interpretation, the temperature T equals to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. Furthermore, we showed that this situation holds for the temperature T itself, which is one of the most typical thermodynamic quantities. Namely, we showed that, for each of the thermodynamic quantities Z(T), F(T), E(T), and S(T) above, the computability of its value at temperature T gives a sufficient condition for T is an element of (0,1) to satisfy the condition that the partial randomness of T equals to T. In this paper, based on a physical argument on the same level of mathematical strictness as normal statistical mechanics in physics, we develop a total statistical mechanical interpretation of AIT which actualizes a perfect correspondence to normal statistical mechanics. We do this by identifying a microcanonical ensemble in the framework of AIT. As a result, we clarify the statistical mechanical meaning of the thermodynamic quantities of AIT.
Problems in probability theory, mathematical statistics and theory of random functions
Sveshnikov, A A
1979-01-01
Problem solving is the main thrust of this excellent, well-organized workbook. Suitable for students at all levels in probability theory and statistics, the book presents over 1,000 problems and their solutions, illustrating fundamental theory and representative applications in the following fields: Random Events; Distribution Laws; Correlation Theory; Random Variables; Entropy & Information; Markov Processes; Systems of Random Variables; Limit Theorems; Data Processing; and more.The coverage of topics is both broad and deep, ranging from the most elementary combinatorial problems through lim
Nonequilibrium statistical thermodynamic theory for viscoelasticity of polymers
Chen, Xiaohong; Tong, Pin; Wang, Ren
1998-01-01
In this paper, we propose a new molecular relaxation mechanism for polymers by considering the change in the actual microscopic structure under macroscopic stress fields. The effects of both intramolecular and intermolecular forces on the inner rotation and the relative slippage of links are taken into account. A constraint potential function, along with a constraint tensor, is introduced to describe the constraint exerted by the surrounding medium. A unified three-dimensional constitutive framework for the viscoelasticity of polymers including thermal effects is established by making use of nonequilibrium statistical thermodynamics, which can be reduced to James and Guth's (1943) non-Gaussian polymer network theory for rubber elasticity. The model compares well with the experimental data for PMMA and plasticized PVC over a wide range of temperatures.
Dynamic statistical models of biological cognition: insights from communications theory
Wallace, Rodrick
2014-10-01
Maturana's cognitive perspective on the living state, Dretske's insight on how information theory constrains cognition, the Atlan/Cohen cognitive paradigm, and models of intelligence without representation, permit construction of a spectrum of dynamic necessary conditions statistical models of signal transduction, regulation, and metabolism at and across the many scales and levels of organisation of an organism and its context. Nonequilibrium critical phenomena analogous to physical phase transitions, driven by crosstalk, will be ubiquitous, representing not only signal switching, but the recruitment of underlying cognitive modules into tunable dynamic coalitions that address changing patterns of need and opportunity at all scales and levels of organisation. The models proposed here, while certainly providing much conceptual insight, should be most useful in the analysis of empirical data, much as are fitted regression equations.
Viscosity Coefficients of a Nematic Mixture: Statistical Theory Approach
Terentjev, E. M.; Osipov, M. A.
1991-09-01
A statistical theory of the rotational diffusion of a molecule in a two-component anisotropic mixture is developed, based on the Fokker-Planck approximation for the one-particle orientational distribution function. The friction constant of the molecular rotation is determined from the threeparticle correlation function, which takes into account interactions A-A, A-B, B-A and B-B between two sorts of molecules. The Leslie coefficients obtained possess a complicated dependence on mixture concentration together with a dependence on temperature and the molecular parameters of the components. In particular, the rotational viscosity coefficient γj is proportional to a polynomial of third-order in concentrations cA and cB with coefficients proportional to exp{JAca + JBcB} √(JACA + JB bcB )
Statistical theory of the many-body nuclear system
De Pace, A
2002-01-01
A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to nuclear matter, in addition to the mean field energies we obtain their fluctuations as well, together with the ones of the wavefunctions, in first order of the expansion in the complexity of the Q-space states. The physics described by the latter is assumed to be random. To extract numerical predictions out of our scheme we develop a schematic version of the approach, which, while much simplified, yields results of significance on the size of the error affecting the mean fields, on the magnitude of the residual effective interaction, on the ground state spectroscopic factor and on the mixing occurring between the vectors spanning the P-space.
Statistics of F-theory flux vacua for particle physics
Energy Technology Data Exchange (ETDEWEB)
Watari, Taizan [Kavli Institute for the Physics and Mathematics of the Universe,University of Tokyo, Kashiwa-no-ha 5-1-5, 277-8583 (Japan)
2015-11-10
Supersymmetric flux compactification of F-theory in the geometric phase yields numerous vacua, and provides an ensemble of low-energy effective theories with a variety of symmetry, matter multiplicity and Lagrangian parameters. Theoretical tools have already been developed so that we can study how the statistics of those flux vacua depend on the choice of symmetry and some of the Lagrangian parameters. In this article, we estimate the fraction of i) vacua that have a U(1) symmetry for spontaneous R-parity violation, and ii) those that realise ideas which achieve hierarchical eigenvalues of the Yukawa matrices. We also learn a lesson that the number of flux vacua is reduced very much when the unbroken U(1){sub Y} symmetry is obtained from a non-trivial Mordell-Weil group, while it is not, when U(1){sub Y} is in SU(5) unification. It also turns out to be likely that vacua with an approximate U(1) symmetry form a locus of accumulation points of the flux vacua distribution.
Statistical approach to the theory of galaxy formation
Energy Technology Data Exchange (ETDEWEB)
Doroshkevich, A.G.; Shandarin, S.F.
1978-11-01
Some topics concerning the development of galaxies and clusters of galaxies from random adiabatic irregularities are discussed. The perturbations would grow according to the nonlinear theory of gravitational instability, wherein the maxima of the largest principle value lambdaatsub llat of the deformation tensor partialS/sub i//partialq/sub k/ act as singular points. Dense, flattened, pancake-shaped structures would begin to form near these points, and would later evolve into galaxies and galaxy clusters. Parameters of an individual pancake such as its epoch of origin, mass, and temperature will be governed by the value of lambdaatsub llat at the center of the pancake. The distribution function of lambdaatsub llat is derived, and the rate of mass condensation into pancakes as well as the birth rate and space density of pancakes are determined. The statistical properties of individual pancakes are established, including the mean displacement and its dispersion in the neighborhood of the center of the pancake. The analogous characteristics of the deformation tensor and parameters describing the shape of the pancake are given. Possible relationships between young galaxies and quasars are considered from the standpoint of this theory.
Factorization and infrared properties of non-perturbative contributions to DIS structure functions
Ermolaev, B I; Troyan, S I
2010-01-01
Analytical expressions for the non-perturbative components of the hadronic scattering amplitudes and the DIS structure functions are not usually obtained from theoretical considerations, but are introduced phenomenologically by fitting the data. We derive some restrictions for such contributions from the general concepts of factorization and integrability. These restrictions are obtained in the context of both k_T and collinear factorizations. We also show that the use of the collinear factorization basically makes the DIS structure functions be dependent on the factorization scale. Our analysis shows that singular factors of the type x^{-a} in the initial parton densities can be used for the singlet component of the structure function F_1, provided a <1, but excludes the use of them for the other structure functions. The restrictions for the non-perturbative contributions we obtain can also be applied to other QCD reactions at high energies.
Non-perturbative Contributions from Complexified Solutions in $\\mathbb{C}P^{N-1}$ Models
Fujimori, Toshiaki; Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
2016-01-01
We discuss the non-perturbative contributions from real and complex saddle point solutions in the $\\mathbb{C}P^1$ quantum mechanics with fermionic degrees of freedom, using the Lefschetz thimble formalism beyond the gaussian approximation. We find bion solutions, which correspond to (complexified) instanton-antiinstanton configurations stabilized in the presence of the fermionic degrees of freedom. By computing the one-loop determinants in the bion backgrounds, we obtain the leading order contributions from both the real and complex bion solutions. To incorporate quasi zero modes which become nearly massless in a weak coupling limit, we regard the bion solutions as well-separated instanton-antiinstanton configurations and calculate a complexified quasi moduli integral based on the Lefschetz thimble formalism. The non-perturbative contributions from the real and complex bions are shown to cancel out in the supersymmetric case and give an (expected) ambiguity in the non-supersymmetric case, which plays a vital ...
Ab Initio Approach to the Non-Perturbative Scalar Yukawa Model
Li, Yang; Maris, P; Vary, J P
2015-01-01
We report on the first non-perturbative calculation of the quenched scalar Yukawa model in the four-body Fock sector truncation. The light-front Hamiltonian approach with a Fock sector dependent renormalization is applied. We study the Fock sector contribution and the electromagnetic form factor in the non-perturbative region. We find that the one- and two-body contributions dominate the Fock space up to coupling $\\alpha\\approx 1.7$. By comparing with lower Fock sector truncations, we show that the form factor converges with respect to the Fock sector expansion. As we approach the coupling $\\alpha \\approx 2.2$, we discover that the four-body contribution rises rapidly and overtakes the two- and three-body contributions.
Ab initio approach to the non-perturbative scalar Yukawa model
Directory of Open Access Journals (Sweden)
Yang Li
2015-09-01
Full Text Available We report on the first non-perturbative calculation of the scalar Yukawa model in the single-nucleon sector up to four-body Fock sector truncation (one “scalar nucleon” and three “scalar pions”. The light-front Hamiltonian approach with a systematic non-perturbative renormalization is applied. We study the n-body norms and the electromagnetic form factor. We find that the one- and two-body contributions dominate up to coupling α≈1.7. As we approach the coupling α≈2.2, we discover that the four-body contribution rises rapidly and overtakes the two- and three-body contributions. By comparing with lower sector truncations, we show that the form factor converges with respect to the Fock sector expansion.
Kostouki, Anna
2009-01-01
Applying a novel non-perturbative functional method framework to a two-dimensional bosonic sigma model with tachyon, dilaton and graviton backgrounds we construct exact (non perturbative in the Regge slope) inflationary solutions, consistent with world-sheet Weyl Invariance. The mechanism for inflation entails a (partial) "alignment" between tachyon and dilaton backgrounds in the solution space. Some cosmological solutions which contain inflationary eras for a short period and interpolate between flat universes in the far past and far future are also discussed. These solutions are characterized by the absence of cosmological horizons, and therefore have well-defined scattering amplitudes. This makes them compatible with a perturbative string framework, and therefore it is these solutions that we consider as self-consistent in our approach. Within the context of the interpolating solutions, string production at the end of inflation (preheating) may also be studied. The advantage of our method is that the solut...
HQET at order 1/m. Pt. 1. Non-perturbative parameters in the quenched approximation
Energy Technology Data Exchange (ETDEWEB)
Blossier, Benoit [Paris XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Della Morte, Michele [Mainz Univ. (Germany). Inst. fuer Kernphysik; Garron, Nicolas [Universidad Autonoma de Madrid (Spain). Dept. Fisica Teorica y Inst. de Fisica Teorica UAM/CSIC; Edinburgh Univ. (United Kingdom). School of Physics and Astronomy - SUPA; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2010-01-15
We determine non-perturbatively the parameters of the lattice HQET Lagrangian and those of heavy-light axial-vector and vector currents in the quenched approximation. The HQET expansion includes terms of order 1/m{sub b}. Our results allow to compute, for example, the heavy-light spectrum and B-meson decay constants in the static approximation and to order 1/m{sub b} in HQET. The determination of the parameters is separated into universal and non-universal parts. The universal results can be used to determine the parameters for various discretizations. The computation reported in this paper uses the plaquette gauge action and the ''HYP1/2'' action for the b-quark described by HQET. The parameters of the currents also depend on the light-quark action, for which we choose non-perturbatively O(a)-improved Wilson fermions. (orig.)
Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD
Fritzsch, Patrick; Tantalo, Nazario
2010-01-01
We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass in O(a) improved two-flavour lattice QCD. We employ the Schr\\"odinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full relativistic QCD action and renormalization problems in HQET can be solved non-perturbatively by a matching to QCD in finite volume. The other region refers to the common parameter range in large-volume simulations of two-flavour lattice QCD, where our results have particular relevance for charm physics applications.
Non-perturbative renormalization of the quark condensate in Ginsparg-Wilson regularizations
Hernández, Pilar; Lellouch, L P; Wittig, H; Hernandez, Pilar; Jansen, Karl; Lellouch, Laurent; Wittig, Hartmut
2001-01-01
We present a method to compute non-perturbatively the renormalization constant of the scalar density for Ginsparg-Wilson fermions. It relies on chiral symmetry and is based on a matching of renormalization group invariant masses at fixed pseudoscalar meson mass, making use of results previously obtained by the ALPHA Collaboration for O(a)-improved Wilson fermions. Our approach is quite general and enables the renormalization of scalar and pseudoscalar densities in lattice regularizations that preserve chiral symmetry and of fermion masses in any regularization. As an application we compute the non-perturbative factor which relates the renormalization group invariant quark condensate to its bare counterpart, obtained with overlap fermions at beta=5.85 in the quenched approximation.
Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
Energy Technology Data Exchange (ETDEWEB)
Dimopoulos, P.; Vladikas, A. [INFN, Sezione di Roma ' ' Tor Vegata' ' (Italy)]|[Universita die Roma ' ' Tor Vegata' ' (Italy). Dipt. die Fisica; Giusti, L.; Pena, C. [European Lab. for Particle Physics (CERN), Geneva (Switzerland); Hernandez, P. [Valencia Univ., Burjassot (Spain). Dpto. de Fisica Teorica and IFIC; Palombi, F.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik; Wennekers, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2006-07-15
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the {delta}S=1 and {delta}S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays. (Orig.)
Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
Dimopoulos, P; Hernández, P; Palombi, Filippo; Peña, C; Vladikas, A; Wennekers, J; Wittig, H
2006-01-01
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the Delta S=1 and Delta S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.
Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
Energy Technology Data Exchange (ETDEWEB)
Dimopoulos, P. [INFN, Sezione di Rome ' Tor Vergata' , c/o Dipartimento di Fisica, Universita di Rome ' Tor Vergata' , Via della Ricerca Scientifica 1, I-00133 Rome (Italy); Giusti, L. [CERN, Physics Department, TH Division, CH-1211 Geneva 23 (Switzerland); Hernandez, P. [Departamento de Fisica Teorica and IFIC, Universitat de Valencia, E-46100 Burjassot (Spain); Palombi, F. [Institut fuer Kernphysik, University of Mainz, D-55099 Mainz (Germany); Pena, C. [CERN, Physics Department, TH Division, CH-1211 Geneva 23 (Switzerland)]. E-mail: carlos.pena.ruano@cern.ch; Vladikas, A. [INFN, Sezione di Rome ' Tor Vergata' , c/o Dipartimento di Fisica, Universita di Rome ' Tor Vergata' , Via della Ricerca Scientifica 1, I-00133 Rome (Italy); Wennekers, J. [DESY, Theory Group, Notkestrasse 85, D-22603 Hamburg (Germany); Wittig, H. [Institut fuer Kernphysik, University of Mainz, D-55099 Mainz (Germany)
2006-09-28
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the {delta}S=1 and {delta}S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.
Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings
Hatsuda, Yasuyuki
2015-01-01
We give some remarks on exact quantization conditions associated with quantized mirror curves of local Calabi-Yau threefolds, conjectured in arXiv:1410.3382. It is shown that they characterize a non-perturbative completion of the refined topological strings in the Nekrasov-Shatashvili limit. We find that the quantization conditions enjoy an exact S-dual invariance. We also discuss Borel summability of the semi-classical spectrum.
Non-perturbative renormalisation of left left four-fermion operators with Neuberger fermions
Dimopoulos, P.; Giusti, L.; Hernández, P.; Palombi, F.; Pena, C.; Vladikas, A.; Wennekers, J.; Wittig, H.
2006-09-01
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the ΔS = 1 and ΔS = 2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.
Factorization and infrared properties of non-perturbative contributions to DIS structure functions
Energy Technology Data Exchange (ETDEWEB)
Ermolaev, B.I. [Ioffe Physico-Technical Institute, St. Petersburg (Russian Federation); Greco, M. [University Roma Tre, Department of Physics (Italy); INFN, Rome (Italy); Troyan, S.I. [St. Petersburg Institute of Nuclear Physics, Gatchina (Russian Federation)
2011-09-15
In this paper we present a new derivation of QCD factorization. We deduce the k{sub T} and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-perturbative contributions and attributing them to the different blobs. After that the convolutions correspond to QCD factorization. Then we reduce this totally unintegrated (basic) factorization first to k{sub T} -factorization and finally to collinear factorization. In order to yield a finite expression for the Compton amplitude, the integration over the loop momentum in the basic factorization must be free of both ultraviolet and infrared singularities. This obvious mathematical requirement leads to theoretical restrictions on the non-perturbative contributions (parton distributions) to the Compton amplitude and the DIS structure functions related to the Compton amplitude through the Optical Theorem. In particular, our analysis excludes the use of the singular factors x{sup -a} (with a >0) in the fits for the quark and gluon distributions because such factors contradict the integrability of the basic convolutions for the Compton amplitude. This restriction is valid for all DIS structure functions in the framework of both k{sub T} -factorization and collinear factorization if we attribute the perturbative contributions only to the upper blob. The restrictions on the non-perturbative contributions obtained in the present paper can easily be extended to other QCD processes where the factorization is exploited. (orig.)
Non-integer Quantum Transition, a True Non-perturbation Effect in Laser-Atom Interaction
Institute of Scientific and Technical Information of China (English)
ZHANG Qi-Ren
2007-01-01
We show that in the quantum transition of an atom interacting with an intense laser of circular frequencyω, the energy difference between the initial and the final states of the atom is not necessarily an integer multiple of the quantum energy (h)ω. This kind of non-integer transition is a true non-perturbation effect in laser-atom interaction.
Non-perturbative effects for the Quark-Gluon Plasma equation of state
Energy Technology Data Exchange (ETDEWEB)
Begun, V. V., E-mail: viktor.begun@gmail.com; Gorenstein, M. I., E-mail: goren@bitp.kiev.ua; Mogilevsky, O. A. [Bogolyubov Institute for Theoretical Physics (Ukraine)
2012-07-15
The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.
Non-perturbative effects for the Quark-Gluon Plasma equation of state
Begun, V. V.; Gorenstein, M. I.; Mogilevsky, O. A.
2012-07-01
The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
Pérez, Enric
2010-01-01
In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later became to be called Bose-Einstein statistics. We discuss Einstein's motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as ...
Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks
Gomez, Sergio; Moreno, Yamir; Arenas, Alex
2011-01-01
Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by proposing a non-perturbative formulation of the heterogeneous mean field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. The non-perturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description at the node level of the epidemic propagation for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. We propose to use the full extension of the approach instead of pruning the expansion to first order, which leads to a non-perturbative formulation that can be solved by fixed point it...
Non-perturbative QCD Effects and the Top Mass at the Tevatron
Wicke, Daniel
2008-01-01
The modelling of non-perturbative effects is an important part of modern collider physics simulations. In hadron collisions there is some indication that the modelling of the interactions of the beam remnants, the underlying event, may require non-trivial colour reconnection effects to be present. We recently introduced a universally applicable toy model of such reconnections, based on hadronising strings. This model, which has one free parameter, has been implemented in the Pythia event generator. We then considered several parameter sets (`tunes'), constrained by fits to Tevatron minimum-bias data, and determined the sensitivity of a simplified top mass analysis to these effects, in exclusive semi-leptonic top events at the Tevatron. A first attempt at isolating the genuine non-perturbative effects gave an estimate of order +-0.5GeV from non-perturbative uncertainties. The results presented here are an update to the original study and include recent bug fixes of Pythia that influenced the tunings investigat...
Order Statistics Theory of Unfolding of Multimeric Proteins
Zhmurov, A.; Dima, R.I.; Barsegov, V.
2010-01-01
Dynamic force spectroscopy has become indispensable for the exploration of the mechanical properties of proteins. In force-ramp experiments, performed by utilizing a time-dependent pulling force, the peak forces for unfolding transitions in a multimeric protein (D)N are used to map the free energy landscape for unfolding for a protein domain D. We show that theoretical modeling of unfolding transitions based on combining the observed first (f1), second (f2), …, Nth (fN) unfolding forces for a protein tandem of fixed length N, and pooling the force data for tandems of different length, n1 molecular characteristics that determine the unfolding micromechanics. We present a simple method of estimation of the parent distribution, ψD(f), based on analyzing the force data for a tandem (D)n of arbitrary length n. Order statistics theory is exemplified through a detailed analysis and modeling of the unfolding forces obtained from pulling simulations of the monomer and oligomers of the all-β-sheet WW domain. PMID:20858442
Perturbative and non-perturbative approaches to the quantum AdS5xS5 superstring
McKeown, Ryan
This dissertation spans perturbative to non-perturbative approaches of testing and using integrability of the IIB superstring in the AdS5xS 5 background. The integrability-based solution of string theories related to AdS n/CFTn-1 dualities relies on the worldsheet S matrix. In chapter 2 we use generalized unitarity to construct the terms with logarithmic dependence on external momenta at one- and two-loop order in the worldsheet S matrix for strings in a general integrable worldsheet theory. We also discuss aspects of calculations as it extends to higher orders. The S-matrix elements are expressed as sums of integrals with coefficients given in terms of tree-level worldsheet four-point scattering amplitudes. Off-diagonal one-loop rational functions, not determined by two-dimensional unitarity cuts, are fixed by symmetry considerations. They play an important role in the determination of the two-loop logarithmic contributions. We illustrate the general analysis by computing the logarithmic terms in the one- and two-loop four-particle S-matrix elements in the massive worldsheet sectors of string theory in AdS5xS5, AdS4xCP 3, AdS3xS3xS3xS 1 and AdS3xS3xT4. We explore the structure of the S matrices and provide explicit evidence for the absence of higher-order logarithms and for the exponentiation of the one-loop dressing phase. In chapter 3 we will construct the full coset space of AdS5xS5 SO4,1xSO 5 in terms of a Gross-Neveu model. After this non-perturbative transformation we have shown the theory to be UV finite at 1 loop and furthermore that it exhibits some non-local integrals of motion through a Lax connection. The integrability of string theory in AdS5xS 5 and of the dilatation operator of N = 4 super-Yang-Mills theory has been used to propose an exact solution to the spectral problem in these theories. Weak coupling perturbation theory both in gauge theory and on the worldsheet has been extensively used to verify this solution. In chapter 4 we demonstrate
Methodes non perturbatives en mecanique quantique et en theorie des champs quantiques
Jirari, Hamza
2001-10-01
Nous construisons un hamiltonien effectif à partir de l'intégrale de chemin via la méthode Monte-Carlo. Cet hamiltonien décrit les phénomènes physiques dans le domaine de basse énergie. Nous déterminons le spectre d'énergie et les fonctions d'ondes de plusieurs systèmes quantiques. Les résultats obtenus montrent que cette nouvelle approche Monte-Carlo hamiltonienne fonctionne. En mécanique quantique, nous suggérons une expression analytique de l'intégrale de chemin en introduisant une action quantique avec des paramètres renormalisés. Nous présentons des résultats numériques pour quelques potentiels locaux. Cette action quantique offre la possibilité de comparer l'évolution classique et quantique et permet de quantifier les instantons classiques et éventuellement le chaos classique. Nous investiguons la QCD sur un réseau bidimensionnel en utilisant une version améliorée des fermions de Wilson. Nous montrons que la théorie améliorée conduit à une réduction significative des erreurs dues à la valeur finie du pas du réseau. Nous calculons le condensat chiral et la masse de l'état lié quark-antiquark. Nous aboutissons à une bonne concordance entre nos résultats numériques et les résultats analytiques du modèle dans le continu.
Some exact results in four-dimensional non-perturbative string theory
Robles-Llana, D.; Rocek, M.; Saueressig, Frank; Theis, U.; Vandoren, S.
2007-01-01
We find the D(−1) and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi–Yau threefolds. These combine with known perturbative and worldsheet instanton corrections into a single modular invariant function that determines the hypermultip
Methodes Non Perturbatives En Mecanique Quantique Et En Theorie Des Champs Quantiques (french Text)
Jirari, H
2001-01-01
Nous construisons un hamiltonien effectif à partir de l'intégrale de chemin via la méthode Monte-Carlo. Cet hamiltonien décrit les phénomènes physiques dans le domaine de basse énergie. Nous déterminons le spectre d'énergie et les fonctions d'ondes de plusieurs systèmes quantiques. Les résultats obtenus montrent que cette nouvelle approche Monte-Carlo hamiltonienne fonctionne. En mécanique quantique, nous suggérons une expression analytique de l'intégrale de chemin en introduisant une action quantique avec des paramètres renormalisés. Nous présentons des résultats numériques pour quelques potentiels locaux. Cette action quantique offre la possibilité de comparer l'évolution classique et quantique et permet de quantifier les instantons classiques et éventuellement le chaos...
Non-perturbative renormalisation of four-fermion operators in $N_f=2$ QCD
Dimopoulos, P; Palombi, Filippo; Papinutto, Mauro; Peña, C; Vladikas, A; Wittig, H
2007-01-01
We present results for the non-perturbative renormalisation of four-fermion operators with two flavours of dynamical quarks. We consider both fully relativistic left current-left current operators, and a full basis for $\\Delta B=2$ operators with static heavy quarks. The renormalisation group running of the operators to high energy scales is computed in the continuum limit for a family of Schroedinger Functional renormalisation schemes, via standard finite size scaling techniques. The total renormalisation factors relating renormalisation group invariant to bare operators are computed for a choice of lattice regularisations.
Non-perturbative Calculation of the Positronium Mass Spectrum in Basis Light-Front Quantization
Wiecki, Paul; Zhao, Xingbo; Maris, Pieter; Vary, James P
2015-01-01
We report on recent improvements to our non-perturbative calculation of the positronium spectrum. Our Hamiltonian is a two-body effective interaction which incorporates one-photon exchange terms, but neglects fermion self-energy effects. This effective Hamiltonian is diagonalized numerically in a harmonic oscillator basis at strong coupling ($\\alpha=0.3$) to obtain the mass eigenvalues. We find that the mass spectrum compares favorably to the Bohr spectrum of non-relativistic quantum mechanics evaluated at this unphysical coupling.
A Non-Perturbative Approach to the Random-Bond Ising Model
Cabra, D C; Mussardo, G; Pujol, P
1997-01-01
We study the N -> 0 limit of the O(N) Gross-Neveu model in the framework of the massless form-factor approach. This model is related to the continuum limit of the Ising model with random bonds via the replica method. We discuss how this method may be useful in calculating correlation functions of physical operators. The identification of non-perturbative fixed points of the O(N) Gross-Neveu model is pursued by its mapping to a WZW model.
Non-perturbative fixed points and renormalization group improved effective potential
Directory of Open Access Journals (Sweden)
A.G. Dias
2014-12-01
Full Text Available The stability conditions of a renormalization group improved effective potential have been discussed in the case of scalar QED and QCD with a colorless scalar. We calculate the same potential in these models assuming the existence of non-perturbative fixed points associated with a conformal phase. In the case of scalar QED the barrier of instability found previously is barely displaced as we approach the fixed point, and in the case of QCD with a colorless scalar not only the barrier is changed but the local minimum of the potential is also changed.
Non-perturbative gluons in diffractive photo-production of J/Psi
Ducati, M B G; Sauter, Werner K.
2001-01-01
The modifications induced in the calculation of the cross section of the diffractive process gamma gamma -> J/Psi J/Psi when the gluon propagator is changed are analyzed. Instead of the usual perturbative gluon propagator, alternative forms obtained using non-perturbative methods like Dyson-Schwinger equations are used to consider in a more consistent way the contributions of the infrared region. The result shows a reduction in the differential cross-section for low momentum transfer once compared with the perturbative result, to be confirmed with future experimental results from TESLA.
Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
Aoki, Y; Christ, N H; Dawson, C; Donnellan, M A; Izubuchi, T; Juttner, A; Li, S; Mawhinney, R D; Noaki, J; Sachrajda, Christopher T C; Soni, A; Tweedie, R J; Yamaguchi, A
2007-01-01
We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-Kbar mixing parameter B_K. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed non-perturbatively and then matched perturbatively to the MSbar scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16^3 x 32 lattice volume, the Iwasaki gauge action at beta=2.13 and domain wall fermions with L_s=16.
Stable Non--Perturbative Minimal Models Coupled to 2D Quantum Gravity
Johnson, C; Spence, B; Johnson, Clifford; Morris, Tim; Spence, Bill
1992-01-01
A generalisation of the non--perturbatively stable solutions of string equations which respect the KdV flows, obtained recently for the $(2m-1,2)$ conformal minimal models coupled to two--dimensional quantum gravity, is presented for the $(p,q)$ models. These string equations are the most general string equations compatible with the $q$--th generalised KdV flows. They exhibit a close relationship with the bi-hamiltonian structure in these hierarchies. The Ising model is studied as a particular example, for which a real non-singular numerical solution to the string susceptibility is presented.
Inner Structure of Statistical Gauge Potential in Chern-Simons-Ginzburg-Landau Theory
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Based on the decomposition theory of the U(1) gauge potential, the inner structure of the statistical gauge potential in the Chern-Simons-Ginzburg-Landau (CSGL) theory is studied. We give a new creation mechanism of the statistical gauge potential. Furthermore, making use of the φ-mapping topological current theory, we obtain the precise topological expression of the statistical magnetic field, which takes the topological information of the vortices.
The theory and geological application of ternary statistics
Cooper, D. H.
A statistical procedure for defining the relationship of three interdependent variables was developed. A plotting scheme was devised which would reduce any three variable values to a single representative point. The centroid of a triangle formed by the three input values provided the best definition for such a point. Ternary statistical plots were made of geological data which were previously analyzed using conventional statistical and graphical methods. In instances where multiple plots were needed to define the correlation of three variables, ternary statistical analysis reduced the same correlation to a single plot. Ternary statistical plots emphasized features not shown on the conventional plots. Ternary statistical techniques provided a more complete and less complex approach.
Statistical theory of synaptic connectivity in the neocortex
Escobar, Gina
distributions of spine head volumes and spine lengths from mouse, rat, monkey, and human brains. We develope a statistical theory in which the equilibrium distribution of dendritic spine shapes is governed by the principle of synaptic entropy maximization under a "generalized cost" constraint. We find the generalized cost of dendritic spines and show that it universally depends on the spine shape, i.e. the dependence is the same in all the considered systems. We show that the modulatory and structural plasticity mechanisms in adults are in a statistical equilibrium with each other, the numbers of dendritic spines in different cortical areas are nearly optimally chosen for memory storage, and the distribution of spine shapes is governed by a single parameter -- the effective temperature. Our results suggest that the effective temperature of a cortical area may be viewed as a measure of longevity of stored memories. Finally, we test the hypothesis that the number of spines in the neuropil is chosen to optimize its storage information capacity.
Canfora, Fabrizio; Pais, Pablo; Rosa, Luigi; Zerwekh, Alfonso
2016-01-01
In this paper it is analyzed the compatibility of the non-perturbative equations of state of quarks and gluons arising from the lattice with some natural requirements for self gravitating objects at equilibrium: the existence of an equation of state (namely, the possibility to define the pressure as a function of the energy density), the absence of superluminal propagation and Le Chatelier's principle. It is discussed under which conditions it is possible to extract an equation of state (in the above sense) from the non-perturbative propagators arising from the fits of the last lattice data. In particular, in the quarks case, there is a small but non vanishing range of temperatures in which it is not possible to define a single-valued functional relation between density and pressure. Interestingly enough, a small change of the parameters appearing in the fit of the lattice quark propagator (of around 10\\%) can guarantee the fulfillment of all the three conditions (keeping alive, at the same time, the violatio...
Non-perturbative renormalization of tensor bilinears in Schr\\"odinger Functional schemes
Fritzsch, Patrick; Preti, David
2015-01-01
We present preliminary result for the study of the renormalization group evolution of tensor bilinears in Schr\\"odinger Functional (SF) schemes for $N_f=0$ and $N_f=2$ QCD with non-perturbatively $\\mathcal{O}(a)$-improved Wilson fermions. First $N_f=2+1$ results (proceeding in parallel with the ongoing computation of the running quark masses [1] are also discussed. A one-loop perturbative calculation of the discretisation effects for the relevant step scaling functions has been carried out for both Wilson and $\\mathcal{O}(a)$-improved actions and for a large number of lattice resolutions. We also calculate the two-loop anomalous dimension in SF schemes for tensor currents through a scheme matching procedure with RI and $\\overline{\\rm MS}$. Thanks to the SF iterative procedure the non-perturbative running over two orders of magnitude in energy scales, as well as the corresponding Renormalization Group Invariant operators, have been determined.
From charge motion in general magnetic fields to the non perturbative gyrokinetic equation
Energy Technology Data Exchange (ETDEWEB)
Di Troia, C., E-mail: claudio.ditroia@enea.it [ENEA Unità tecnica Fusione, C.R. Frascati, Via E. Fermi 45, 00044 Frascati, Rome (Italy)
2015-04-15
The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem, even if it has not been solved until now, apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field; the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.
Statistical Mechanics of the Community Detection Problem: Theory and Application
Hu, Dandan
We study phase transitions in spin glass type systems and in related computational problems. In the current work, we focus on the "community detection" problem when cast in terms of a general Potts spin glass type problem. We report on phase transitions between solvable and unsolvable regimes. Solvable region may further split into easy and hard phases. Spin glass type phase transitions appear at both low and high temperatures. Low temperature transitions correspond to an order by disorder type effect wherein fluctuations render the system ordered or solvable. Separate transitions appear at higher temperatures into a disordered (or an unsolvable) phases. Different sorts of randomness lead to disparate behaviors. We illustrate the spin glass character of both transitions and report on memory effects. We further relate Potts type spin systems to mechanical analogs and suggest how chaotic-type behavior in general thermodynamic systems can indeed naturally arise in hard-computational problems and spin-glasses. In this work, we also examine large networks (with a power law distribution in cluster size) that have a large number of communities. We infer that large systems at a constant ratio of q to the number of nodes N asymptotically tend toward insolvability in the limit of large N for any positive temperature. We further employ multivariate Tutte polynomials to show that increasing q emulates increasing T for a general Potts model, leading to a similar stability region at low T. We further apply the replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. The problem is cast as identifying tightly bound clusters against a background. Within our multiresolution approach, we compute information theory based correlations among multiple solutions of the same graph over a range of resolutions. Significant multiresolution
Fuzzy statistical decision-making theory and applications
Kabak, Özgür
2016-01-01
This book offers a comprehensive reference guide to fuzzy statistics and fuzzy decision-making techniques. It provides readers with all the necessary tools for making statistical inference in the case of incomplete information or insufficient data, where classical statistics cannot be applied. The respective chapters, written by prominent researchers, explain a wealth of both basic and advanced concepts including: fuzzy probability distributions, fuzzy frequency distributions, fuzzy Bayesian inference, fuzzy mean, mode and median, fuzzy dispersion, fuzzy p-value, and many others. To foster a better understanding, all the chapters include relevant numerical examples or case studies. Taken together, they form an excellent reference guide for researchers, lecturers and postgraduate students pursuing research on fuzzy statistics. Moreover, by extending all the main aspects of classical statistical decision-making to its fuzzy counterpart, the book presents a dynamic snapshot of the field that is expected to stimu...
Lattice methods and effective field theory
Nicholson, Amy N
2016-01-01
Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply these techniques to nuclear Effective Field Theory (EFT), a non-relativistic theory for nuclei involving the nucleons as the basic degrees of freedom. The lattice formulation of [1,2] for so-called pionless EFT is discussed in detail, with portions of code included to aid the reader in code development. Systematic and statistical uncertainties of these methods are discussed at length, and extensions beyond pionless EFT are introduced in the final Section.
Theory of overdispersion in counting statistics caused by fluctuating probabilities
Semkow, T M
1999-01-01
It is shown that the random Lexis fluctuations of probabilities such as probability of decay or detection cause the counting statistics to be overdispersed with respect to the classical binomial, Poisson, or Gaussian distributions. The generating and the distribution functions for the overdispersed counting statistics are derived. Applications to radioactive decay with detection and more complex experiments are given, as well as distinguishing between the source and background, in the presence of overdispersion. Monte-Carlo verifications are provided.
Statistical theory of neutral protein evolution by random site mutations
Indian Academy of Sciences (India)
Arnab Bhattacherjee; Parbati Biswas
2009-09-01
Understanding the features of the protein conformational space represents a key component to characterize protein structural evolution at the molecular level. This problem is approached in a twofold manner; simple lattice models are used to represent protein structures with the ability of a protein sequence to fold into the lowest energy native conformation, quantified as the foldability, which measures the fitness of the sequence. Alternatively, a self-consistent mean-field based theory is developed to evaluate the protein neutrality through random single-point and multiple-point mutations by calculating the pair-wise probability profile of the amino acid residues in a library of sequences, consistent with a particular foldability criterion. The theory predicts the change in sequence plasticity with the foldability criterion and also correlates the effect of hydrophobic residues on the variation of the free energy surface of the protein as a function of the number of cumulative mutations. The results obtained from the theory are compared with the exact enumeration results of 3 × 3 × 3 lattice protein and also with some small real proteins chosen from the protein databank. An excellent match of the results obtained from theory and exact enumeration with those of real proteins validates the range of applicability of the theory. The theory may provide a new perspective in de novo protein design, in-vivo/in-vitro protein evolution and site-directed mutagenesis experiments.
Sub-poissonian statistics as an experimental test for the contextuality of quantum theory
Arnoldus, H.F.; Dieks, Dennis; Nienhuis, G.
1984-01-01
It is argued that the phenomenon of sub-poissonian statistics can be regarded as experimental evidence for the contextual character of quantum theory. To this end, it is shown that the statistics predicted by non-contextual hidden-variable theories must satisfy certain inequalities which are a kind
Applying Sociocultural Theory to Teaching Statistics for Doctoral Social Work Students
Mogro-Wilson, Cristina; Reeves, Michael G.; Charter, Mollie Lazar
2015-01-01
This article describes the development of two doctoral-level multivariate statistics courses utilizing sociocultural theory, an integrative pedagogical framework. In the first course, the implementation of sociocultural theory helps to support the students through a rigorous introduction to statistics. The second course involves students…
Theorems on Estimating Perturbative Coefficients in Quantum Field Theory and Statistical Physics
Energy Technology Data Exchange (ETDEWEB)
Samuel, Mark
2003-06-25
The authors present rigorous proofs for several theorems on using Pade approximants to estimate coefficients in Perturbative Quantum Field Theory and Statistical Physics. As a result, they find new trigonometric and other identities where the estimates based on this approach are exact. They discuss hypergeometric functions, as well as series from both Perturbative Quantum Field Theory and Statistical Physics.
A Non-Perturbative Gauge-Invariant QCD: Ideal vs. Realistic QCD
Fried, H M; Sheu, Y -M
2011-01-01
A basic distinction, long overlooked, between the conventional, "idealistic" formulation of QCD, and a more "realistic" formulation is brought into focus by a rigorous, non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of exact Fradkin representations for the Green's functional $\\mathbf{G}_{c}(x,y|A)$ and the vacuum functional $\\mathbf{L}[A]$. The quanta of all (Abelian) quantized fields may be expected to obey standard quantum-mechanical measurement properties, perfect position dependence at the cost of unknown momenta, and vice-versa, but this is impossible for quarks since they always appear asymptotically in bound states, and their transverse position or momenta can never, in principle, be exactly measured. Violation of this principle produces an absurdity in the exact evaluation of each and every QCD amplitude. We here suggest a phenomenological change in the basic QCD Lagrangian, such that a limitation of transverse precision is automatical...
Energy Technology Data Exchange (ETDEWEB)
Aydin, A; Stiffell, P B, E-mail: a.aydin@sussex.ac.uk [Centre for Physical Electronics and Quantum Technology, School of Engineering and Design, University of Sussex, Brighton, BN1 9QT (United Kingdom)
2011-06-23
We present results of finite element analysis for simple test structures which demonstrate clearly that the measurement situation is complex. The test structure consists of an open geometry parallel plate capacitor within a screened enclosure. Indeed, the presence of earthed objects, even at considerable distances, is shown to have a significant effect on the field geometry close to the source. These simulations are compared with field measurements made using an ultra-high input impedance sensor, the Electric Potential Sensor. A single experimentally determined calibration factor is all that is required to achieve excellent agreement between experimental measurements and the results of the simulations. Given this, the sensor is capable of mapping accurately, and in a non-perturbative manner, the spatial potential both within and outside of the test structure.
Effects of non-perturbatively improved dynamical fermions in QCD at fixed lattice spacing
Allton, C R; Bowler, K C; Garden, J; Hart, A; Hepburn, D; Irving, A C; Joó, B; Kenway, R D; Maynard, C M; McNeile, C; Michael, C; Pickles, S M; Sexton, J C; Sharkey, K J; Sroczynski, Z; Talevi, M; Teper, M; Wittig, H
2002-01-01
We present results for the static inter-quark potential, lightest glueballs, light hadron spectrum and topological susceptibility using a non-perturbatively improved action on a $16^3\\times 32$ lattice at a set of values of the bare gauge coupling and bare dynamical quark mass chosen to keep the lattice size fixed in physical units ($\\sim 1.7$ fm). By comparing these measurements with a matched quenched ensemble, we study the effects due to two degenerate flavours of dynamical quarks. With the greater control over residual lattice spacing effects which these methods afford, we find some evidence of charge screening and some minor effects on the light hadron spectrum over the range of quark masses studied ($M_{PS}/M_{V}\\ge0.58$). More substantial differences between quenched and unquenched simulations are observed in measurements of topological quantities.
Enea Romano, Antonio; Sanes Negrete, Sergio; Sasaki, Misao; Starobinsky, Alexei A.
2014-06-01
We study effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations of the type predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local underdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of a cosmological constant of the order of 0.6{%},1{%},1.5{%} , respectively. These effects cannot be neglected in the precision cosmology era in which we are entering. Our results can be considered an upper bound for the effect of the monopole component of the local non-linear structure which can arise from primordial curvature perturbations and requires a fully non-perturbative relativistic treatment.
Anisotropic non-perturbative zero modes for passively advected magnetic fields
Lanotte, A
1999-01-01
A first analytical assessment of the role of anisotropic corrections to the isotropic anomalous scaling exponents is given for the $d$-dimensional kinematic dynamo problem in the presence of a mean magnetic field. The velocity advecting the magnetic field changes very rapidly in time and scales with a positive exponent $\\xi$. Inertial-range anisotropic contributions to the scaling exponents of magnetic correlations are associated to zero modes and have been calculated non-perturbatively. For $d=3$, the limits $\\xi\\mapsto 0$ yelds $\\zeta_n=n+ \\xi [(n+2) (2 n^2-7 n-3)]/[2 (3+2 n) (1+2 n)]$ where $n$ is the order in the Legendre polynomial decomposition. Conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made.
Non-perturbative running of quark masses in three-flavour QCD
Campos, Isabel; Pena, Carlos; Preti, David; Ramos, Alberto; Vladikas, Anastassios
2016-01-01
We present our preliminary results for the computation of the non-perturbative running of renormalized quark masses in $N_f = 3$ QCD, between the electroweak and hadronic scales, using standard finite-size scaling techniques. The computation is carried out to very high precision, using massless $\\mathcal{O}(a)$-improved Wilson quarks. Following the strategy adopted by the ALPHA Collaboration for the running coupling, different schemes are used above and below a scale $\\mu_0 \\sim m_b$, which differ by using either the Schr\\"odinger Functional or Gradient Flow renormalized coupling. We discuss our results for the running in both regions, and the procedure to match the two schemes.
Non-perturbative Euler-Heisenberg Lagrangian and Paraelectricity in Magnetized Massless QED
Ferrer, Efrain J; Sanchez, Angel
2012-01-01
Using the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field, we show that the chiral-symmetry-broken phase of massless QED in the presence of a magnetic field exhibits significant paraelectricity. A large anisotropic electric susceptibility develops in the strong-field region, where most of the fermions are confined to their lowest Landau level, and dynamical mass and anomalous magnetic moment are generated via the magnetic catalysis mechanism. The nonperturbative nature of this effect is reflected in the non-analytic dependence of the electric susceptibility on the fine-structure constant. The strong paraelectricity is linked to the electric dipole moments of the particle/anti-particle pairs that form the chiral condensate. The large electric susceptibility can be used to detect the realization of the magnetic catalysis of chiral symmetry breaking in physical systems.
Cichy, Krzysztof; Korcyl, Piotr
2016-01-01
Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on-shell and gauge invariant. The step scaling method allows us to calculate the running of the renormalization constants of quark bilinear operators. We describe here the details of this calculation. The aim of this exploratory study is to identify the feasibility of the X-space scheme when used in small volume simulations required by the step scaling technique. Eventually, we translate our final results to the continuum MSbar scheme and compare against four-loop analytic formulae finding satisfactory agreement.
Disentangling the timescales behind the non-perturbative heavy quark potential
Burnier, Yannis
2012-01-01
The static part of the heavy quark potential has been shown to be closely related to the spectrum of the rectangular Wilson loop. In particular the lowest lying positive frequency peak encodes the late time evolution of the two-body system, characterized by a complex potential. While initial studies assumed a perfect separation of early and late time physics, where a simple Lorentian (Breit-Wigner) shape suffices to describe the spectral peak, we argue that scale decoupling in general is not complete. Thus early time, i.e. non-potential effects, significantly modify the shape of the lowest peak. We derive on general grounds an improved peak distribution that reflects this fact. Application of the improved fit to non-perturbative lattice QCD spectra now yields a potential that is compatible with a transition to a deconfined screening plasma.
Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2002-03-19
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.
Truthing the stretch: Non-perturbative cosmological realizations with multiscale spherical collapse
Neyrinck, Mark C
2015-01-01
Here we present a simple, parameter-free, non-perturbative algorithm that gives low-redshift cosmological particle realizations accurate to few-Megaparsec scales, called muscle (MUltiscale Spherical ColLapse Evolution). It has virtually the same cost as producing N-body-simulation initial conditions, since it works with the 'stretch' parameter {\\psi}, the Lagrangian divergence of the displacement field. It promises to be useful in quickly producing mock catalogs, and to simplify computationally intensive reconstructions of galaxy surveys. muscle applies a spherical-collapse prescription on multiple Gaussian-smoothed scales. It achieves higher accuracy than perturbative schemes (Zel'dovich and 2LPT), and, by including the void-in-cloud process (voids in large-scale collapsing regions), solves problems with a single-scale spherical-collapse scheme. Additionally, we show the behavior of {\\psi} for different morphologies (voids, walls, filaments, and haloes). A Python code to produce these realizations is availab...
Cichy, Krzysztof; Jansen, Karl; Korcyl, Piotr
2016-12-01
Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on-shell and gauge invariant. The step scaling method allows us to calculate the running of the renormalization constants of quark bilinear operators. We describe here the details of this calculation. The aim of this exploratory study is to identify the feasibility of the X-space scheme when used in small volume simulations required by the step scaling technique. Eventually, we translate our final results to the continuum MS ‾ scheme and compare against four-loop analytic formulae finding satisfactory agreement.
Non-Equilibrium Statistical Mechanics Inspired by Modern Information Theory
Directory of Open Access Journals (Sweden)
Oscar C. O. Dahlsten
2013-12-01
Full Text Available A collection of recent papers revisit how to quantify the relationship between information and work in the light of modern information theory, so-called single-shot information theory. This is an introduction to those papers, from the perspective of the author. Many of the results may be viewed as a quantification of how much work a generalized Maxwell’s daemon can extract as a function of its extra information. These expressions do not in general involve the Shannon/von Neumann entropy but rather quantities from single-shot information theory. In a limit of large systems composed of many identical and independent parts the Shannon/von Neumann entropy is recovered.
Log-concave Probability Distributions: Theory and Statistical Testing
DEFF Research Database (Denmark)
An, Mark Yuing
1996-01-01
This paper studies the broad class of log-concave probability distributions that arise in economics of uncertainty and information. For univariate, continuous, and log-concave random variables we prove useful properties without imposing the differentiability of density functions. Discrete...... and multivariate distributions are also discussed. We propose simple non-parametric testing procedures for log-concavity. The test statistics are constructed to test one of the two implicati ons of log-concavity: increasing hazard rates and new-is-better-than-used (NBU) property. The test for increasing hazard...... rates are based on normalized spacing of the sample order statistics. The tests for NBU property fall into the category of Hoeffding's U-statistics...
Fisher information and quantum-classical field theory: classical statistics similarity
Energy Technology Data Exchange (ETDEWEB)
Syska, J. [Department of Field Theory and Particle Physics, Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice (Poland)
2007-07-15
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Minimax theory for a class of nonlinear statistical inverse problems
Ray, Kolyan; Schmidt-Hieber, Johannes
2016-06-01
We study a class of statistical inverse problems with nonlinear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the nonlinearity. This reduces the initial nonlinear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of Hölder smoothness scales that are natural in this setting.
Toward a theory of statistical tree-shape analysis
DEFF Research Database (Denmark)
Feragen, Aasa; Lo, Pechin Chien Pau; de Bruijne, Marleen
2013-01-01
these advantages. Along with the theoretical framework we provide experimental proof-of-concept results on synthetic data trees as well as small airway trees from pulmonary CT scans. This way, we illustrate that our framework has promising theoretical and qualitative properties necessary to build a theory...
On Conditional Statistics in Scalar Turbulence Theory vs. Experiment
Ching, E S C; Podivilov, E V; Procaccia, I; Ching, Emily S.C.; L'vov, Victor S.; Podivilov, Evgeni; Procaccia, Itamar
1996-01-01
We consider turbulent advection of a scalar field $T(\\B.r)$, passive or active, and focus on the statistics of gradient fields conditioned on scalar differences $\\Delta T(R)$ across a scale $R$. In particular we focus on two conditional averages $\\langle\
Di Troia, Claudio
2016-01-01
The non perturbative guiding center transformation [Di Troia C., Phys. Plasmas 22, 042103 (2015)] is extended to the relativistic regime. The single particle dynamic is described in the Minkowski flat space-time. The main solutions are obtained in covariant form: the gyrating particle solutions and the guiding particle solution, both in gyro-kinetic as in MHD orderings. It is shown the relevance of the ideal Ohm's law in the context of the guiding center transformation. Moreover, it is also considered the presence of a gravitational field. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the Kaluza-Klein model.
Kinetic theory of non-hamiltonian statistical ensembles
Directory of Open Access Journals (Sweden)
A.V.Zhukov
2006-01-01
Full Text Available A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in terms of time-dependent dynamic quantities. The generalized transport equations involve the phase-space compressibility in a non-trivial way. Our results are useful in molecular dynamics simulation studies as well as nonequilibrium or quasiclassical approximations of quantum-classical dynamics.
Statistical mechanics of ecological systems: Neutral theory and beyond
Azaele, Sandro; Suweis, Samir; Grilli, Jacopo; Volkov, Igor; Banavar, Jayanth R.; Maritan, Amos
2016-07-01
The simplest theories often have much merit and many limitations, and, in this vein, the value of neutral theory (NT) of biodiversity has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain several patterns observed in the organization of ecosystems. Among ecologists, it had a polarizing effect: There were a few ecologists who were enthusiastic, and there were a larger number who firmly opposed it. Physicists and mathematicians, instead, welcomed the theory with excitement. Indeed, NT spawned several theoretical studies that attempted to explain empirical data and predicted trends of quantities that had not yet been studied. While there are a few reviews of NT oriented toward ecologists, the goal here is to review the quantitative aspects of NT and its extensions for physicists who are interested in learning what NT is, what its successes are, and what important problems remain unresolved. Furthermore, this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. It is proposed to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models are also discussed.
Enhancing the Teaching of Statistics: Portfolio Theory, an Application of Statistics in Finance
Christou, Nicolas
2008-01-01
In this paper we present an application of statistics using real stock market data. Most, if not all, students have some familiarity with the stock market (or at least they have heard about it) and therefore can understand the problem easily. It is the real data analysis that students find interesting. Here we explore the building of efficient…
Enhancing the Teaching of Statistics: Portfolio Theory, an Application of Statistics in Finance
Christou, Nicolas
2008-01-01
In this paper we present an application of statistics using real stock market data. Most, if not all, students have some familiarity with the stock market (or at least they have heard about it) and therefore can understand the problem easily. It is the real data analysis that students find interesting. Here we explore the building of efficient…
Relativistic kinetic theory and non-gaussian statistical
de Oliveira, Z. B. B.; Silva, R.
2016-12-01
The nonextensive statistical mechanics is extended in the special relativity context through a generalization of H-theorem. We show that the Tsallis framework is compatible with the second law of the thermodynamics when the nonadditive effects are consistently introduced on the collisional term of the Boltzmann equation. The proof of the H-theorem follows from using of q-algebra in the generalization of the molecular chaos hypothesis (Stosszahlansatz). A thermodynamic consistency is possible whether the entropic parameter belongs to interval q ∈ [ 0 , 2 ] .
Statistical theory of designed quantum transport across disordered networks.
Walschaers, Mattia; Mulet, Roberto; Wellens, Thomas; Buchleitner, Andreas
2015-04-01
We explain how centrosymmetry, together with a dominant doublet of energy eigenstates in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalization of the chaos-assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behavior of characteristic statistical properties with the size of the network. We show that these analytical predictions compare well to numerical simulations, using Hamiltonians sampled from the Gaussian orthogonal ensemble.
A Statistical Theory of Designed Quantum Transport Across Disordered Networks
Walschaers, Mattia; Wellens, Thomas; Buchleitner, Andreas
2014-01-01
We explain how centrosymmetry, together with a dominant doublet in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalisation of the chaos assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behaviour of characteristic statistical properties with the size of the network.
Issues in biomedical statistics: comparing means under normal distribution theory.
Ludbrook, J
1995-04-01
The test used most commonly in biomedical research to compare means when measurements have been made on a continuous scale is Student's t-test, followed closely by various forms of analysis of variance. These tests require that defined populations have been randomly sampled, but there are other assumptions about populations and samples that must be satisfied. These include: (i) normality of the population distributions; (ii) equal variance in those normal populations; and (iii) statistical independence of the samples. This review offers advice to investigators on how to recognize breaches of the assumptions of normality and equality of variance, and how to deal with them by modifying the usual t-test or by transforming the experimental data. The sample-size also has an important bearing on statistical inferences: (i) if it is too small, the risk of Type II error is inflated; and (ii) inequality of sample size exaggerates the effects of inequality of variance. The assumption of independence is breached if repeated measurements are made serially rather than in random order, but adjustments to analysis of variance can be made to correct for the inflated risk of Type I error. The review also considers the problem of making multiple comparisons of means, and recommends solutions.
The development of ensemble theory. A new glimpse at the history of statistical mechanics
Inaba, Hajime
2015-12-01
This paper investigates the history of statistical mechanics from the viewpoint of the development of the ensemble theory from 1871 to 1902. In 1871, Ludwig Boltzmann introduced a prototype model of an ensemble that represents a polyatomic gas. In 1879, James Clerk Maxwell defined an ensemble as copies of systems of the same energy. Inspired by H.W. Watson, he called his approach "statistical". Boltzmann and Maxwell regarded the ensemble theory as a much more general approach than the kinetic theory. In the 1880s, influenced by Hermann von Helmholtz, Boltzmann made use of ensembles to establish thermodynamic relations. In Elementary Principles in Statistical Mechanics of 1902, Josiah Willard Gibbs tried to get his ensemble theory to mirror thermodynamics, including thermodynamic operations in its scope. Thermodynamics played the role of a "blind guide". His theory of ensembles can be characterized as more mathematically oriented than Einstein's theory proposed in the same year. Mechanical, empirical, and statistical approaches to foundations of statistical mechanics are presented. Although it was formulated in classical terms, the ensemble theory provided an infrastructure still valuable in quantum statistics because of its generality.
Pressure broadening of rotational bands. I - A statistical theory
Rosenkranz, P. W.
1985-01-01
Absorption of electromagnetic waves by rotational transitions of molecules is formulated for the case in which the wave frequency is displaced from resonance by an amount large compared to the reciprocal duration of a typical binary collision, and also large compared to the differences between frequencies of the strong resonances of the gas. In this far-wing limit, Fano's relaxation operator is reduced to a scalar parameter which depends on the frequency displacement. This relaxation parameter is not symmetric with respect to reflection about resonance, but becomes symmetric when multiplied by the factor exp (h/2pi) (omega sub d)/2kT where omega sub d is the frequency displacement. The theory applies to dipolar molecules of any shape, in collisions with either dipolar or quadrupolar molecules.
Statistics of cosmic density profiles from perturbation theory
Bernardeau, Francis; Codis, Sandrine
2013-01-01
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with $\\Lambda$-CDM simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope -- the de...
Quantum theory and statistical thermodynamics principles and worked examples
Hertel, Peter
2017-01-01
This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles – necessarily rather abstract – are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers. Chapters on exceptionally simple, but h...
EVALUATING TEACHING PERFORMANCE. FROM THEORY TO PRACTICE USING STATISTICAL TOOLS
Directory of Open Access Journals (Sweden)
MARE CODRUTA
2011-12-01
Full Text Available The teaching performance is influenced firstly by the quality of the educational system. The universities are trying to raise the expectations regarding the methods used for evaluating the teaching quality. In order for the results to be as much as credible the evaluation must defer to the existing theory and to follow the standardized procedures, starting from some basic principles. The most used framework is represented by the 3P model which contains three parts: 1. The input (factors that come under the students and the professor 2. The learning process (activities focused on learning, teaching methods, practical ability, individual study 3. The outcome (the output of the learning process.This study presents some results of a questionnaire based on the existing economic theory and applied to a sample of master business students from Romania. The students were asked to give grades from 1 to 5 to several aspects related to the educational process. These aspects took into consideration the following: if the didactic activity was interesting for the students/ the relationship between the objectives of the course and the activity evolved/ the clarity of the presentations/ the degree of students' participation required by the teacher/ the methods and materials used/ the availability of the teacher. The average grade is 4.39, indicating a very high level of satisfaction, taking into account that the grades ranged from 1 to 5. For 50% of the students, the average grade was below 4.53, while for the other half it was above the specified value. But one has to see the value returned for the majority of the students. The mode equals 5, meaning that most of the students involved in the analyzed programme are extremely satisfied with the quality of the educational process. With a significance value Sig. = 0.004 /_ 0.01, we can state that there is correlation between the level of satisfaction expressed by the average grade and the number of classes missed
Statistical microeconomics and commodity prices: theory and empirical results.
Baaquie, Belal E
2016-01-13
A review is made of the statistical generalization of microeconomics by Baaquie (Baaquie 2013 Phys. A 392, 4400-4416. (doi:10.1016/j.physa.2013.05.008)), where the market price of every traded commodity, at each instant of time, is considered to be an independent random variable. The dynamics of commodity market prices is given by the unequal time correlation function and is modelled by the Feynman path integral based on an action functional. The correlation functions of the model are defined using the path integral. The existence of the action functional for commodity prices that was postulated to exist in Baaquie (Baaquie 2013 Phys. A 392, 4400-4416. (doi:10.1016/j.physa.2013.05.008)) has been empirically ascertained in Baaquie et al. (Baaquie et al. 2015 Phys. A 428, 19-37. (doi:10.1016/j.physa.2015.02.030)). The model's action functionals for different commodities has been empirically determined and calibrated using the unequal time correlation functions of the market commodity prices using a perturbation expansion (Baaquie et al. 2015 Phys. A 428, 19-37. (doi:10.1016/j.physa.2015.02.030)). Nine commodities drawn from the energy, metal and grain sectors are empirically studied and their auto-correlation for up to 300 days is described by the model to an accuracy of R(2)>0.90-using only six parameters.
Wandering in cities: a statistical physics approach to urban theory
Louf, Rémi
2015-01-01
The amount of data that is being gathered about cities is increasing in size and specificity. However, despite this wealth of information, we still have little understanding of what really drives the processes behind urbanisation. In this thesis we apply some ideas from statistical physics to the study of cities. We first present a stochastic, out-of-equilibrium model of city growth that describes the structure of the mobility pattern of individuals. The model explains the appearance of secondary subcenters as an effect of traffic congestion, and predicts a sublinear increase of the number of centers with population size. Within the framework of this model, we are further able to give a prediction for the scaling exponent of the total distance commuted daily, the total length of the road network, the total delay due to congestion, the quantity of CO2 emitted, and the surface area with the population size of cities. In the third part, we focus on the quantitative description of the patterns of residential segr...
Di-Jet Extinction from Non-Perturbative Quantum Gravity Effects
Kilic, Can
2014-01-01
We study a novel signature of TeV scale quantum gravity that manifests itself as an extinction of hard short distance scattering in QCD processes. The extinction behavior is due to the predominance of high-entropy intermediate states of the underlying quantum gravity theory. We model extinction using a large damping Veneziano form-factor modification of QCD scattering amplitudes that suppresses high pT scattering. We propose and demonstrate the potential of an LHC search for extinction, with a possible reach for the string scale as high as 3 TeV with 7 TeV LHC collision data, and up to 5 TeV from high-statistics 13 TeV data.
Nakamura, Yousuke; Taniguchi, Yusuke; Collaboration, for CP-PACS
2007-01-01
We present non-perturbative renormalization factors for $\\Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ pre...
The Hagedorn structure of the non-perturbative gluon pressure within the mass gap approach to
Gogokhia, V; Vasuth, M
2016-01-01
We have shown in detail that the low-temperature expansion for the non-perturbative gluon pressure has the Hagedorn-type structure. Its exponential spectrum of all the effective gluonic excitations are expressed in terms of the mass gap. It is this which is responsible for the large-scale dynamical structure of the QCD ground state. The gluon pressure properly scaled has a maximum at some characteristic temperature $T=T_c = 266.5 \\ \\MeV$, separating the low- and high temperature regions. The gluon pressure is exponentially suppressed in the $T \\rightarrow 0$ limit. In the $T \\rightarrow T_c$ limit it demonstrates an exponential rise in the number of dynamical degrees of freedom. This makes it possible to identify $T_c$ with the Hagedorn transition temperature $T_h$, i.e., to put $T_h=T_c$. The gluon pressure has a complicated dependence on the mass gap and temperature near $T_c$ and up to approximately $(4-5)T_c$. In the limit of very high temperatures $T \\rightarrow \\infty$ its polynomial character is confir...
Non-perturbative measurement of low-intensity charged particle beams
Fernandes, M.; Geithner, R.; Golm, J.; Neubert, R.; Schwickert, M.; Stöhlker, T.; Tan, J.; Welsch, C. P.
2017-01-01
Non-perturbative measurements of low-intensity charged particle beams are particularly challenging to beam diagnostics due to the low amplitude of the induced electromagnetic fields. In the low-energy antiproton decelerator (AD) and the future extra low energy antiproton rings at CERN, an absolute measurement of the beam intensity is essential to monitor the operation efficiency. Superconducting quantum interference device (SQUID) based cryogenic current comparators (CCC) have been used for measuring slow charged beams in the nA range, showing a very good current resolution. But these were unable to measure fast bunched beams, due to the slew-rate limitation of SQUID devices and presented a strong susceptibility to external perturbations. Here, we present a CCC system developed for the AD machine, which was optimised in terms of its current resolution, system stability, ability to cope with short bunched beams, and immunity to mechanical vibrations. This paper presents the monitor design and the first results from measurements with a low energy antiproton beam obtained in the AD in 2015. These are the first CCC beam current measurements ever performed in a synchrotron machine with both coasting and short bunched beams. It is shown that the system is able to stably measure the AD beam throughout the entire cycle, with a current resolution of 30 {nA}.
Non-Perturbative QCD Coupling and Beta Function from Light Front Holography
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; de Teramond, Guy F.; /Costa Rica U.; Deur, Alexandre; /Jefferson Lab
2010-05-26
The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q{sup 2}). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on {alpha}{sub s}{sup AdS} (Q{sup 2}).
Significance of non-perturbative input to TMD gluon density for hard processes at LHC
Grinyuk, A A; Lykasov, G I; Zotov, N P
2015-01-01
We study the role of the non-perturbative input to the transverse momentum dependent (TMD) gluon density in hard processes at the LHC. We derive the input TMD gluon distribution at low scale mu0^2 ~ 1 GeV^2 from the fit of the inclusive hadron spectra measured at low transverse momenta in pp collisions at the LHC and demonstrate that the best description of these spectra for larger hadron transverse momenta can be achieved by matching the derived TMD gluon distribution with the exact solution of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation obtained at low x and small gluon transverse momenta outside the saturation region. Then, we extend the input TMD gluon density to higher mu^2 numerically using the Catani-Ciafoloni-Fiorani-Marchesini (CCFM) gluon evolution equation. A special attention is put to the phenomenological applications of obtained TMD gluon density to some LHC processes, which are sensitive to the gluon content of a proton.
Non-perturbative over-production of axion-like-particles (ALPs) via derivative interaction
Mazumdar, Anupam
2015-01-01
Axion like particles (ALPs) are quite generic in many scenarios for physics beyond the Standard Model, they are pseudoscalar Nambu-Goldstone bosons, and appear once any global $U(1)$ symmetry is broken spontaneously. The ALPs can gain mass from various non-perturbative quantum effects, such as anomalies or instantons. ALPs can couple to the matter sector incluidng a scalar condensate such as inflaton or moduli field via derivative interactions, which are suppressed by the axion {\\it decay constant}, $f_\\chi$ . Although weakly interacting, the ALPs can be produced abundantly from the coherent oscillations of a homogeneous condensate. In this paper we will study such a scenario where the ALPs can be produced abundantly, and in some cases can even overclose the Universe via odd and even dimensional operators, as long as $f_\\chi/\\Phi_{\\rm I} \\ll 1$, where $\\Phi_{\\rm I}$ denotes the initial amplitude of the coherent oscillations of the scalar condensate, $\\phi$. We will briefly mention how such dangerous overprodu...
Using cosmic neutrinos to search for non-perturbative physics at the Pierre Auger Observatory
Anchordoqui, Luis A; Gora, Dariusz; Paul, Thomas; Roth, Markus; Sarkar, Subir; Winders, Lisa Lee
2010-01-01
The Pierre Auger (cosmic ray) Observatory provides a laboratory for studying fundamental physics at energies far beyond those available at colliders. The Observatory is sensitive not only to hadrons and photons, but can in principle detect ultrahigh energy neutrinos in the cosmic radiation. Interestingly, it may be possible to uncover new physics by analyzing characteristics of the neutrino flux at the Earth. By comparing the rate for quasi-horizontal, deeply penetrating air showers triggered by all types of neutrinos, with the rate for slightly upgoing showers generated by Earth-skimming tau neutrinos, we determine the ratio of events which would need to be detected in order to signal the existence of new non-perturbative interactions beyond the TeV-scale in which the final state energy is dominated by the hadronic component. We use detailed Monte Carlo simulations to calculate the effects of interactions in the Earth and in the atmosphere. We find that observation of 1 Earth-skimming and 10 quasi-horizontal...
Non-Perturbative Four-Point Scattering from First-Quantized Relativistic JWKB
Irizarry-Gelpí, M E
2016-01-01
We apply the quantum mechanical (first-quantized) JWKB approximation to a two-body path integral describing the near-forward scattering of two relativistic, heavy, non-identical, scalar particles in $D$ spacetime dimensions. In contrast to the loop expansion, in $D = 4$ this gives a strong-coupling expansion, and in $D = 3$ a non-perturbative weak-coupling expansion. When the interaction is mediated by massless quanta with spin $N$, we obtain explicit, relativistic results for the scattering amplitude when $N = 0$, $1$ and $2$. In $D = 4$ we find a Regge trajectory function that agrees with the usual quantum mechanical spectrum. We also find an exponentiated infrared divergence that becomes a pure phase factor when the Mandelstam invariants $s$ and $t$ are inside of the physical scattering region. In $D = 3$ we find a singularity whose position along the $s$ axis is dependent on $t$. When the interaction is mediated by a heavy scalar with mass $M$, in $D = 3$ we find an all-order scattering amplitude where th...
Towards a non-perturbative matching of HQET and QCD with dynamical light quarks
Della Morte, Michele; Heitger, Jochen; Meyer, Harvey B.; Simma, Hubert; Sommer, Rainer
2007-01-01
We explain how the strategy of solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume can be implemented to include dynamical fermions. As a primary application, some elements of an HQET computation of the mass of the b-quark beyond the leading order with N_f=2 are outlined. In particular, the matching of HQET and QCD requires relativistic QCD simulations in a volume with L ~ 0.5 fm, which will serve to quantitatively determine the heavy quark mass dependence of heavy-light meson observables in the continuum limit of finite-volume two-flavour lattice QCD. As a preparation for the latter, we report on our determination of the renormalization constants and improvement coefficients relating the renormalized current and subtracted bare quark mass in the relevant weak coupling region. The calculation of these coefficients employs a constant physics condition in the Schroedinger functional scheme, where the box size L is fixed by working at a prescribed value of the renorm...
Mixing of B mesons and Decay Constants with the Non-Perturbatively Improved Action
Becirevic, D; Retico, A; Giménez, V; Giusti, Leonardo; Lubicz, V; Martinelli, G
2001-01-01
Several quantities relevant to phenomenological studies of the mixing ofneutral B mesons are computed on the lattice. Our main results are: f_{Bd}sqrt(B_{Bd})=206(28)(7) MeV, f_{Bs} sqrt(B_{Bs})/f_{Bd}sqrt(B_{Bd})=1.16(7). Wealso obtain the related quantities f_{Bs}sqrt(B{Bs})=237(18)(8) MeV, f_{Bd}=174(22)(+7-0)(-4-0) MeV, f_{Bs}= 204(15)(+7-0)(+3-0) MeV,f_{Bs}/f_{Bd}=1.17(4)(+0-1), f_{Bd}/f_{Ds}=0.74(5). After combining our resultswith the experimental world average (Delta m_d), we predict (Deltam_s)=15.8(2.1)(3.3) ps^{-1}. We have also computed the relevant parameters formixing of neutral D mesons which may be useful in some extensions of theStandard Model. All the quantities were obtained from a quenched simulationwith a non-perturbatively improved Clover action at beta=6.2, corresponding toa lattice spacing 1/a=2.7(1) GeV, on a sample of 200 gauge-fieldconfigurations. A discussion of the main systematic errors is also presented.
Enhancement of Higgs to diphoton decay width in non-perturbative Higgs model
Energy Technology Data Exchange (ETDEWEB)
Haba, Naoyuki [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan); Kaneta, Kunio [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan); Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043 (Japan); Mimura, Yukihiro [Department of Physics, National Taiwan University, Taipei 10617, Taiwan, ROC (China); Takahashi, Ryo, E-mail: ryo.takahasi88@gmail.com [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan)
2013-01-29
We investigate a possibility if a loop diagram via Higgsino can enhance the Higgs to diphoton decay width in supersymmetric models with an extension of Higgs sector. A model with an additional non-renormalizable term of Higgs fields is firstly analyzed where the higher order term can introduce the Higgs coupling to Higgsinos as well as charged Higgs bosons. We point out that a choice of the Higgs coupling to obtain a significant size of enhancement of diphoton decay width reduces the Higgs mass and/or a size of non-renormalizable term needs to be large and a cutoff scale is around the weak scale. Another model in which the Higgsino mass term is generated by a non-perturbative instanton effect via a strong dynamics in a context of SUSY QCD is also suggested. It is shown that the sign of the Higgs coupling to fermions is opposite from perturbative models due to an operator including bosonic fields in the denominator and a constructive contribution to the diphoton decay amplitude can be easily obtained in this kind of model.
Capri, M A L; Fiorentini, D; Guimaraes, M S; Justo, I F; Pereira, A D; Mintz, B W; Palhares, L F; Sobreiro, R F; Sorella, S P
2015-01-01
We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.
Ben-Haim, E; Roudeau, Patrick; Savoy-Navarro, Aurore; Stocchi, A; Bambade, Ph.
2004-01-01
Using recent measurements of the b-quark fragmentation distribution obtained in $e^+e^- \\to b \\bar{b}$ events registered at the Z pole, the non-perturbative QCD component of the distribution has been extracted independently of any hadronic physics modelling. This distribution depends only on the way the perturbative QCD component has been defined. When the perturbative QCD component is taken from a parton shower Monte-Carlo, the non-perturbative QCD component is rather similar with those obtained from the Lund or Bowler models. When the perturbative QCD component is the result of an analytic NLL computation, the non-perturbative QCD component has to be extended in a non-physical region and thus cannot be described by any hadronic modelling. In the two examples used to characterize these two situations, which are studied at present, it happens that the extracted non-perturbative QCD distribution has the same shape, being simply translated to higher-x values in the second approach, illustrating the ability of t...
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2015-01-01
The coefficient c_A required for O(a) improvement of the axial current in lattice QCD with N_f=3 flavors of Wilson fermions and the tree-level Symanzik-improved gauge action is determined non-perturbatively. The standard improvement condition using Schroedinger functional boundary conditions is employed at constant physics for a range of couplings relevant for simulations at lattice spacings of ~ 0.09 fm and below. We define the improvement condition projected onto the zero topological charge sector of the theory, in order to avoid the problem of possibly insufficient tunneling between topological sectors in our simulations at the smallest bare coupling. An interpolation formula for c_A(g_0^2) is provided together with our final results.
Boyle, P A; Lytle, A T
2011-01-01
We compute the renormalization factors of four-quark operators needed for the study of $K\\to\\pi\\pi$ decay in the $\\Delta I=3/2$ channel. We evaluate the Z-factors at a low energy scale ($\\mu_0=1.145 \\GeV$) using four different non-exceptional RI-SMOM schemes on a large, coarse lattice ($a\\sim 0.14\\fm$) on which the bare matrix elements are also computed. Then we compute the universal, non-perturbative, scale evolution matrix of these renormalization factors between $\\mu_0$ and $3\\GeV$. We give the numerical results for the different steps of the computation in two different non-exceptional lattice schemes, and the connection to $\\msbar$ at $3\\GeV$ is made using one-loop perturbation theory.
The Rhetoric of Investment Theory : The Story of Statistics and Predictability
T. Pistorius (Thomas)
2016-01-01
markdownabstractUncertainty is a feeling of anxiety and a part of culture since the dawn of civilization. Civilizations have invented numerous ways to cope with uncertainty, statistics is one of those technologies. The rhetoric as the discourse of investment theory uncovers that the theory of statis
Balder, E.J.
1980-01-01
By employing fundamental results from “geometric” functional analysis and the theory of multifunctions we formulate a general model for (nonsequential) statistical decision theory, which extends Wald's classical model. From central results that hold for the model we derive a general theorem on the e
The Rhetoric of Investment Theory : The Story of Statistics and Predictability
T. Pistorius (Thomas)
2016-01-01
markdownabstractUncertainty is a feeling of anxiety and a part of culture since the dawn of civilization. Civilizations have invented numerous ways to cope with uncertainty, statistics is one of those technologies. The rhetoric as the discourse of investment theory uncovers that the theory of statis
The Rhetoric of Investment Theory : The Story of Statistics and Predictability
T. Pistorius (Thomas)
2016-01-01
markdownabstractUncertainty is a feeling of anxiety and a part of culture since the dawn of civilization. Civilizations have invented numerous ways to cope with uncertainty, statistics is one of those technologies. The rhetoric as the discourse of investment theory uncovers that the theory of
Institute of Scientific and Technical Information of China (English)
ZHANG Qi-Ren
2007-01-01
We show that the quantum world with non-local states and original statistics is statistically separable.According to relativistic dynamics, the super-luminal signal transmission is impossible. The present quantum theory is therefore consistent with the relativity and the causality.
Developing Econometrics Statistical Theories and Methods with Applications to Economics and Business
Tong, Hengqing; Huang, Yangxin
2011-01-01
Statistical Theories and Methods with Applications to Economics and Business highlights recent advances in statistical theory and methods that benefit econometric practice. It deals with exploratory data analysis, a prerequisite to statistical modelling and part of data mining. It provides recently developed computational tools useful for data mining, analysing the reasons to do data mining and the best techniques to use in a given situation.Provides a detailed description of computer algorithms.Provides recently developed computational tools useful for data miningHighlights recent advances in
AdS/QCD, LIight-Front Holography, and the Non-perturbative Running Coupling
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; de Teramond, Guy; /Costa Rica U.; Deur, Alexandre; /Jefferson Lab
2010-04-29
The combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states. The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. The eigenvalues give the hadronic spectrum, and the eigenmodes represent the probability distributions of the hadronic constituents at a given scale. A positive-sign confining dilaton background modifying AdS space gives a very good account of meson and baryon spectroscopy and form factors. The light-front holographic mapping of this model also leads to a non-perturbative effective coupling {alpha}{sub s}{sup Ads} (Q{sup 2}) which agrees with the effective charge defined by the Bjorken sum rule and lattice simulations. It displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD.
Transition Form Factors: A Unique Opportunity to Connect Non-Perturbative Strong Interactions to QCD
Energy Technology Data Exchange (ETDEWEB)
Gothe, Ralf W. [University of South Carolina, Columbia, SC (United States)
2014-01-01
Meson-photoproduction measurements and their reaction-amplitude analyses can establish more sensitively, and in some cases in an almost model-independent way, nucleon excitations and non-resonant reaction amplitudes. However, to investigate the strong interaction from explored — where meson-cloud degrees of freedom contribute substantially to the baryon structure — to still unexplored distance scales — where quark degrees of freedom dominate and the transition from dressed to current quarks occurs — we depend on experiments that allow us to measure observables that are probing this evolving non-perturbative QCD regime over its full range. Elastic and transition form factors are uniquely suited to trace this evolution by measuring elastic electron scattering and exclusive single-meson and double-pion electroproduction cross sections off the nucleon. These exclusive measurements will be extended to higher momentum transfers with the energy-upgraded CEBAF beam at JLab to study the quark degrees of freedom, where their strong interaction is responsible for the ground and excited nucleon state formations. After establishing unprecedented high-precision data, the imminent next challenge is a high-quality analysis to extract these relevant electrocoupling parameters for various resonances that then can be compared to state-of-the-art models and QCD-based calculations. Recent results will demonstrate the status of the analysis and of their theoretical descriptions, and an experimental and theoretical outlook will highlight what shall and may be achieved in the new era of the 12-GeV upgraded transition form factor program.
State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory
Directory of Open Access Journals (Sweden)
Stefano Bellucci
2014-01-01
Full Text Available We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.
Reaction dynamics and statistical theory for the growth of hydrogen bonding clusters
Institute of Scientific and Technical Information of China (English)
WANG; Haijun; BA; Xinwu(巴信武); ZHAO; Min(赵敏)
2002-01-01
The similarities between the formation of hydrogen bonds and polycondensation reactions are stated from the statistical viewpoint, and then taking the hydrogen bonding system of AaDd type as an example, the growing process of hydrogen bonding clusters is investigated in terms of the theory of reaction dynamics and statistical theory for polymeric reactions. The two methods lead to the same conclusions, stating that the statistical theory for polymerization is applicable to the hydrogen bonding systems. Based on this consideration, the explicit relationship between the conversions of proton-donors and proton-acceptors and the Gibbs free energy of the system under study is given. Furthermore, the sol-gel phase transition is predicted to take place in some hydrogen bonding systems, and the corresponding generalized scaling laws describing this kind of phase transition are obtained.
State-space Geometry, Statistical Fluctuations and Black Holes in String Theory
Bellucci, Stefano
2011-01-01
We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a new perspective of black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic state-space geometric meaning of the statistical fluctuations, local and global stability conditions and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, \\textit{viz.}, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory. Keywords: Intrinsic Geometry; ...
Direct Numerical Test of the Statistical Mechanical Theory of Hydrophobic Interactions
Chaudhari, M I; Ashbaugh, H S; Pratt, L R
2013-01-01
This work tests the statistical mechanical theory of hydrophobic interactions, isolates consequences of excluded volume interactions, and obtains B2 for those purposes. Cavity methods that are particularly appropriate for study of hydrophobic interactions between atomic-size hard spheres in liquid water are developed and applied to test aspects of the Pratt-Chandler (PC) theory that have not been tested. Contact hydrophobic interactions between Ar-size hard-spheres in water are significantly more attractive than predicted by the PC theory. The corresponding results for the osmotic second virial coefficient are attractive (B2 <0), and more attractive with increasing temperature (Delta B2/Delta T < 0) in the temperature range 300K < T < 360K. This information has not been available previously, but is essential for development of the molecular-scale statistical mechanical theory of hydrophobic interactions, particularly for better definition of the role of attractive intermolecular interactions assoc...
Non-perturbative four-wave mixing in InSb with intense off-resonant multi-THz pulses
Directory of Open Access Journals (Sweden)
Huber R.
2013-03-01
Full Text Available High-field multi-THz pulses are employed to analyze the coherent nonlinear response of the narrow-gap semiconductor InSb which is driven off-resonantly. Field-resolved four-wave mixing signals manifest the onset of a non-perturbative regime of Rabi flopping at external amplitudes above 5 MV/cm per pulse. Simulations based on a two-level quantum system confirm these experimental results.
Di-Photon excess in the 2HDM: hasting towards the instability and the non-perturbative regime
Bertuzzo, Enrico; Taoso, Marco
2016-01-01
We challenge the interpretation of the di-photon excess recently observed by both ATLAS and CMS in a two Higgs doublet framework. Due to the large enhancement necessary to obtain the observed di-photon signal, a large number of colored and charged vector-like fermions are called for. We find that even before the hypercharge gauge coupling becomes non perturbative, the one loop effects of these fermions abruptly drive the scalar potential to instability.
A non-perturbative real-space renormalization group scheme for the spin-1/2 XXX Heisenberg model
Degenhard, Andreas
1999-01-01
In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct non-perturbative renormalization group transformations for the spin-1/2 XXX Heisenberg model in the finite temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behaviour in the temperature depende...
Hayslett, H T
1991-01-01
Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text the
Statistical methods of discrimination and classification advances in theory and applications
Choi, Sung C
1986-01-01
Statistical Methods of Discrimination and Classification: Advances in Theory and Applications is a collection of papers that tackles the multivariate problems of discriminating and classifying subjects into exclusive population. The book presents 13 papers that cover that advancement in the statistical procedure of discriminating and classifying. The studies in the text primarily focus on various methods of discriminating and classifying variables, such as multiple discriminant analysis in the presence of mixed continuous and categorical data; choice of the smoothing parameter and efficiency o
Predicting adsorption isotherms using a two-dimensional statistical associating fluid theory
Martinez, Alejandro; Castro, Martin; McCabe, Clare; Gil-Villegas, Alejandro
2007-02-01
A molecular thermodynamics approach is developed in order to describe the adsorption of fluids on solid surfaces. The new theory is based on the statistical associating fluid theory for potentials of variable range [A. Gil-Villegas et al., J. Chem. Phys. 106, 4168 (1997)] and uses a quasi-two-dimensional approximation to describe the properties of adsorbed fluids. The theory is tested against Gibbs ensemble Monte Carlo simulations and excellent agreement with the theoretical predictions is achieved. Additionally the authors use the new approach to describe the adsorption isotherms for nitrogen and methane on dry activated carbon.
Energy Technology Data Exchange (ETDEWEB)
Mello, P.A.; Pereyra, P.; Seligman, T.H.
1985-05-01
Ensembles of scattering S-matrices have been used in the past to describe the statistical fluctuations exhibited by many nuclear-reaction cross sections as a function of energy. In recent years, there have been attempts to construct these ensembles explicitly in terms of S, by directly proposinng a statistical law for S. In the present paper, it is shown that, for an arbitrary number of channels, one can incorporate, in the ensemble of S-matrices, the conditions of flux conservation, time-reversal invariance, causality, ergodicity, and the requirement that the ensemble average coincide with the optical scattering matrix. Since these conditions do not specify the ensemble uniquely, the ensemble that has maximum information-entropy is dealt with among those that satisfy the above requirements. Some applications to few-channel problems and comparisons to Monte-Carlo calculations are presented.
Links to sources of cancer-related statistics, including the Surveillance, Epidemiology and End Results (SEER) Program, SEER-Medicare datasets, cancer survivor prevalence data, and the Cancer Trends Progress Report.
The N/D method with non-perturbative left-hand-cut discontinuity and the S10NN partial wave
Entem, D. R.; Oller, J. A.
2017-10-01
In this letter we introduce an integral equation that allows to calculate the exact left-hand-cut discontinuity for an uncoupled S-wave partial-wave amplitude in potential scattering for a given finite-range potential. In particular this is applied here to the S10 nucleon-nucleon (NN) partial wave. The calculation of Δ (A) is completely fixed by the potential because short-range physics (corresponding to integrated out degrees of freedom within the low-energy Effective Field Theory) does not contribute to Δ (A). The results obtained from the N / D method for a partial-wave amplitude are rigorous, since now the discontinuities along the left-hand cut and right-hand cut are exactly known. This solves in this case the open question with respect to the N / D method and the effect on the final result of the non-perturbative iterative diagrams in the evaluation of Δ (A). The solution of this problem also implies the equivalence of the N / D method and the Lippmann-Schwinger (LS) equation for the nonsingular one-pion exchange S10NN potential (Yukawa potential). The equivalence between the N / D method with one extra subtraction and the LS equation renormalized with one counterterm or with subtractive renormalization also holds for the singular attractive S10NN potentials calculated by including higher orders in Chiral Perturbation Theory (ChPT). However, the N / D method is more flexible and, rather straightforwardly, it allows to evaluate partial-wave amplitudes with a higher number of extra subtractions, that we fix in terms of shape parameters within the effective range expansion. We give results up to three extra subtractions in the N / D method, which provide a rather accurate reproduction of the S10NN phase shifts when the NNLO ChPT potential is employed. Our new method then provides a general theory to renormalize non-perturbatively singular and regular potentials in scattering that can be extended to higher partial waves as well as to coupled channel scattering.
Statistical mechanics and field theory. [Path integrals, lattices, pseudofree vertex model
Energy Technology Data Exchange (ETDEWEB)
Samuel, S.A.
1979-05-01
Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks. 64 references.
Hasenfratz, Anna
2009-01-01
Monte Carlo Renormalization Group (MCRG) methods were designed to study the non-perturbative phase structure and critical behavior of statistical systems and quantum field theories. I adopt the 2-lattice matching method used extensively in the 1980's and show how it can be used to predict the existence of non-perturbative fixed points and their related critical exponents in many flavor SU(3) gauge theories. This work serves to test the method and I study relatively well understood systems: the $N_f=0$, 4 and 16 flavor models. The pure gauge and $N_f=4$ systems are confining and chirally broken and the MCRG method can predict their bare step scaling functions. Results for the $N_f=16$ model indicate the existence of an infrared fixed point with nearly marginal gauge coupling. I present preliminary results for the scaling dimension of the mass at this new fixed point.
Non-perturbative evaluation of cSW for smeared link clover fermion and Iwasaki gauge action
Taniguchi, Yusuke
2013-01-01
We performed a rough estimate of the non-perturbative value of the clover term coefficient cSW for the APE stout link Wilson fermion. We varied the number of smearings from Nsmear=1 to 6 and adopted beta values roughly corresponding to the lattice spacing of 0.1 fm. We used the Schroedinger functional technique for an evaluation of cSW and found that cSW decreases monotonically as we increase Nsmear but has a 10% order of deviation from the tree level value for Nsmear=6.
Energy Technology Data Exchange (ETDEWEB)
Kaneko, T.; Hashimoto, S. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Graduate Univ. for Advanced Studies, Tsukuba, Ibaraki (Japan); Aoki, S. [Tsukuba Univ., Ibaraki (Japan). Graduate School of Pure and Applied Sciences]|[Brookhaven National Laboratory, Upton, NY (United States). Riken BNL Research Center; Della Morte, M. [CERN, Physics Dept., Geneva (Switzerland); Hoffmann, R. [Colorado Univ., Boulder, CO (United States). Dept. of Physics; Sommer, R. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2007-03-15
We perform a non-perturbative determination of the improvement coefficient c{sub A} to remove O(a) discretization errors in the axial vector current in three-flavor lattice QCD with the Iwasaki gauge action and the standard O(a)-improved Wilson quark action. An improvement condition with a good sensitivity to c{sub A} is imposed at constant physics. Combining our results with the perturbative expansion, c{sub A} is now known rather precisely for a{sup -1}>or similar 1.6 GeV. (orig.)
A generalization of random matrix theory and its application to statistical physics.
Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H
2017-02-01
To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.
Directory of Open Access Journals (Sweden)
J. D. Pandey
2012-12-01
Full Text Available Thermodynamic properties of liquids and liquid mixtures play very important role in understanding the nature of molecular interactions occurring in the system. In the present work different thermodynamic properties of 15 pure liquids and 34 equimolar binary liquid mixtures of benzene, toluene, p-xylene, chlorobenzene and 1-chloronaphthalene with linear and branched alkanes have been computed with the help of Flory’s statistical theory (FST, Hard sphere equation of state (HSE and Hole theory (HT simultaneously. The calculated values are compared with the experimental findings collected from literature and quite satisfactory results are obtained.
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Ave. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
Novaes, Marcel
2015-06-01
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = - iħS†dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO
Heisenberg, Lavinia; Bartelmann, Matthias
2010-01-01
Subject of this paper is a careful and detailed analysis of the PINOCCHIO algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field $\\delta_{\\rm l}$ is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position $\\bmath{q}$ and each smoothing radius $R$, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian Perturbation Theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++ and optimised the construction of halo merging histories. Comparin...
Renormalization-group theory for finite-size scaling in extreme statistics.
Györgyi, G; Moloney, N R; Ozogány, K; Rácz, Z; Droz, M
2010-04-01
We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.
Non-perturbative test of the Witten-Veneziano formula from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Goethe-Universität, Institut für Theoretische Physik,Max-von-Laue-Straße 1, Frankfurt a.M., D-60438 (Germany); NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Adam Mickiewicz University, Faculty of Physics,Umultowska 85, Poznan, 61-614 (Poland); Garcia-Ramos, Elena [NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Humboldt Universität zu Berlin,Newtonstr. 15, Berlin, D-12489 (Germany); Jansen, Karl [NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Ottnad, Konstantin [Institut für Strahlen- und Kernphysik (Theorie),Nussallee 14-16, Bonn 53115 Germania (Germany); Urbach, Carsten [Institut für Strahlen- und Kernphysik (Theorie),Nussallee 14-16, Bonn 53115 Germania (Germany); Bethe Center for Theoretical Physics,Nussallee 12, Universität Bonn, Bonn, D-53115 (Germany); Collaboration: The ETM collaboration
2015-09-03
We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with N{sub f}=2+1+1 dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU(2) chiral limits we compare both sides and find good agreement within uncertainties.
Non-perturbative test of the Witten-Veneziano formula from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, Elena [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Ottnad, Konstantin; Urbach, Carsten [Bonn Univ. (Germany). Institut fuer Strahlen- und Kernphysik; Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Collaboration: The ETM collaboration
2015-10-15
We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with N{sub f}=2 +1+1 dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU(2) chiral limits we compare both sides and find good agreement within uncertainties.
Statistical theory for transition and sustainment of the improved confinement state
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I [Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580 (Japan); Itoh, Kimitaka [National Institute for Fusion Science, Toki 509-5292 (Japan); Yagi, Masatoshi [Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580 (Japan); Toda, Shinichiro [National Institute for Fusion Science, Toki 509-5292 (Japan)
2004-05-01
The occurrence of stochastic transitions is investigated in the presence of triggers by turbulence noise and external events. The probability of observing the transition is calculated assuming that the global controlling parameters change in time. This is another important prediction of statistical theory in addition to the long time average. This explains the feature of transient response of the system with stochastic transitions. The interpretation of the experimental threshold database is discussed.
Modeling of aqueous electrolyte solutions with perturbed-chain statistical associated fluid theory
DEFF Research Database (Denmark)
Cameretti, Luca F.; Sadowski, Gabriele; Mollerup, Jørgen
2005-01-01
The vapor pressures and liquid densities of single-salt electrolyte solutions containing NaCl, LiCl, KCl, NaBr, LiBr, KBr, NaI, LiI, KI, Li2SO4, Na2SO4, and K2SO4 were modeled with an equation of state based on perturbed-chain statistical associated fluid theory (PC-SAFT). The PC-SAFT model...
Bound states of the $\\phi^4$ model via the Non-Perturbative Renormalization Group
Rose, F; Leonard, F; Delamotte, B
2016-01-01
Using the nonperturbative renormalization group, we study the existence of bound states in the symmetry-broken phase of the scalar $\\phi^4$ theory in all dimensions between two and four and as a function of the temperature. The accurate description of the momentum dependence of the two-point function, required to get the spectrum of the theory, is provided by means of the Blaizot--M\\'endez-Galain--Wschebor approximation scheme. We confirm the existence of a bound state in dimension three, with a mass within 1% of previous Monte-Carlo and numerical diagonalization values.
Non-perturbative analysis of the infrared properties of QED3
Roo, M. de; Stam, K.
1984-01-01
We analyse the Dyson-Schwinger equations of the photon and electron propagator of massless QED3. Although the perturbation expansion in this theory contains infrared divergences, the Dyson-Schwinger equations admit well-defined solutions. Perturbative infrared divergences are replaced, in the soluti
Borot, Gaëtan
2012-01-01
We propose a conjecture to compute the all-order asymptotic expansion of the colored Jones polynomial of the complement of a hyperbolic knot, J_N(q = exp(2u/N)) when N goes to infinity. Our conjecture claims that the asymptotic expansion of the colored Jones polynomial is a the formal wave function of an integrable system whose semiclassical spectral curve S would be the SL_2(C) character variety of the knot (the A-polynomial), and is formulated in the framework of the topological recursion. It takes as starting point the proposal made recently by Dijkgraaf, Fuji and Manabe (who kept only the perturbative part of the wave function, and found some discrepancies), but it also contains the non-perturbative parts, and solves the discrepancy problem. These non-perturbative corrections are derivatives of Theta functions associated to S, but the expansion is still in powers of 1/N due to the special properties of A-polynomials. We provide a detailed check for the figure-eight knot and the once-punctured torus bundle...
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
Aoki, S; Ishizuka, N; Izubuchi, T; Kanaya, K; Kuramashi, Y; Murano, K; Namekawa, Y; Okawa, M; Taniguchi, Y; Ukawa, A; Ukita, N; Yoshié, T
2010-01-01
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the MS-bar scheme is safely carried out. For numerical simulations we adopted the Iwasaki gauge action and non-perturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. The regularization independent step scaling function of the quark mass for the Nf=2+1 QCD is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large sca...
Werbos, P J
2003-01-01
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement operator. A previous paper defined a classical density matrix R encoding the statistical moments of an ensemble of states of classical second-order Hamiltonian field theory. It proved Tr(RQ)=E(Q), etc., for the usual field operators as defined by Weinberg, and it proved that those observables of the classical system obey the usual Heisenberg dynamic equation. However, R itself obeys dynamics different from the usual Liouville equation! This paper derives those dynamics, and calculates the discrepancy between CFT and normal form QFT in predicting general observables g(Q,P). There is some preliminary evidence for the conjecture that the discrepancies disappear in equilibrium states (bound states and scattering states) for finite bosonic field theories. Even if not, they appea...
A statistical mechanical model for mass stability in the SHP theory
Horwitz, Lawrence P.
2017-05-01
We construct a model for a particle in the framework of the theory of Stueckelberg, Horwitz and Piron (SHP) as an ensemble of events subject to the laws of covariant classical equilibrium statistical mechanics. The canonical and grand canonical ensembles are constructed without an a priori constraint on the total mass of the system. We show that the total mass of the system, corresponding the mass of this particle is determined by a chemical potential. This model has the property that under perturbation, such as collisions in the SHP theory for which the final asymptotic mass of an elementary event is not constrained by the basic theory, the particle returns to its equilibrium mass value. A mechanism similar to the Maxwell construction for more than one equilibrium mass state may result in several possible masses in the final state.
A Statistical Mechanical Model for Mass Stability in the SHP Theory
Horwitz, Lawrence
2016-01-01
We construct a model for a particle in the framework of the theory of Stueckelberg, Horwitz and Piron (SHP) as an ensemble of events subject to the laws of covariant classical equilibrium statistical mechanics. The canonical and grand canonical emsembles are constructed without an a priori constraint on the total mass of the system. We show that the total mass of the system, corresponding to the mass of this particle, is determined by a chemical potential. This model has the property that under perturbation, such as collisions in the SHP theory for which the final asymptotic mass of an elementary event is not constrained by the basic theory, the particle returns to its equilibrium mass value. A mechanism similar to the Maxwell construction for more than one equlibrium mass state may result in several possible masses in the final state.
Pitard, Francis F
1993-01-01
Pierre Gy's Sampling Theory and Sampling Practice, Second Edition is a concise, step-by-step guide for process variability management and methods. Updated and expanded, this new edition provides a comprehensive study of heterogeneity, covering the basic principles of sampling theory and its various applications. It presents many practical examples to allow readers to select appropriate sampling protocols and assess the validity of sampling protocols from others. The variability of dynamic process streams using variography is discussed to help bridge sampling theory with statistical process control. Many descriptions of good sampling devices, as well as descriptions of poor ones, are featured to educate readers on what to look for when purchasing sampling systems. The book uses its accessible, tutorial style to focus on professional selection and use of methods. The book will be a valuable guide for mineral processing engineers; metallurgists; geologists; miners; chemists; environmental scientists; and practit...
Henderson, Douglas
2010-01-01
Henry Eyring was, and still is, a towering figure in science. Some aspects of his life and science, beginning in Mexico and continuing in Arizona, California, Wisconsin, Germany, Princeton, and finally Utah, are reviewed here. Eyring moved gradually from quantum theory toward statistical mechanics and the theory of liquids, motivated in part by his desire to understand reactions in condensed matter. Significant structure theory, while not as successful as Eyring thought, is better than his critics realize. Eyring won many awards. However, most chemists are surprised, if not shocked, that he was never awarded a Nobel Prize. He joined Lise Meitner, Rosalind Franklin, John Slater, and others, in an even more select group, those who should have received a Nobel Prize but did not.
MANAGERIAL DECISION IN INNOVATIVE EDUCATION SYSTEMS STATISTICAL SURVEY BASED ON SAMPLE THEORY
Directory of Open Access Journals (Sweden)
Gheorghe SĂVOIU
2012-12-01
Full Text Available Before formulating the statistical hypotheses and the econometrictesting itself, a breakdown of some of the technical issues is required, which are related to managerial decision in innovative educational systems, the educational managerial phenomenon tested through statistical and mathematical methods, respectively the significant difference in perceiving the current qualities, knowledge, experience, behaviour and desirable health, obtained through a questionnaire applied to a stratified population at the end,in the educational environment, either with educational activities, or with simultaneously managerial and educational activities. The details having to do with research focused on the survey theory, turning into a working tool the questionnaires and statistical data that are processed from those questionnaires, are summarized below.
The N/D method with non-perturbative left-hand-cut discontinuity and the $^1S_0$ $NN$ partial wave
Entem, D R
2016-01-01
In this letter we deduce an integral equation that allows to calculate the exact left-hand-cut discontinuity for an uncoupled $S$-wave partial-wave amplitude in potential scattering for a given finite-range potential. The results obtained from the $N/D$ method for the partial-wave amplitude are rigorous, since now the discontinuities along the left-hand cut and right-hand cut are exactly known. This solves the open question with respect to the $N/D$ method and the effect on the final result of the non-perturbative iterative diagrams in the evaluation of $\\Delta(A)$. A big advantage of the method is that short-range physics (corresponding to integrated out degrees of freedom within low-energy Effective Field Theory) does not contribute to $\\Delta(A)$ and it manifests through the extra subtractions that are implemented within the method. We show the equivalence of the $N/D$ method and the Lippmann-Schwinger (LS) equation for a nonsingular $^1S_0$ $NN$ potential (Yukawa potential). The equivalence between the $N...
The applications of Complexity Theory and Tsallis Non-extensive Statistics at Solar Plasma Dynamics
Pavlos, George
2015-04-01
As the solar plasma lives far from equilibrium it is an excellent laboratory for testing complexity theory and non-equilibrium statistical mechanics. In this study, we present the highlights of complexity theory and Tsallis non extensive statistical mechanics as concerns their applications at solar plasma dynamics, especially at sunspot, solar flare and solar wind phenomena. Generally, when a physical system is driven far from equilibrium states some novel characteristics can be observed related to the nonlinear character of dynamics. Generally, the nonlinearity in space plasma dynamics can generate intermittent turbulence with the typical characteristics of the anomalous diffusion process and strange topologies of stochastic space plasma fields (velocity and magnetic fields) caused by the strange dynamics and strange kinetics (Zaslavsky, 2002). In addition, according to Zelenyi and Milovanov (2004) the complex character of the space plasma system includes the existence of non-equilibrium (quasi)-stationary states (NESS) having the topology of a percolating fractal set. The stabilization of a system near the NESS is perceived as a transition into a turbulent state determined by self-organization processes. The long-range correlation effects manifest themselves as a strange non-Gaussian behavior of kinetic processes near the NESS plasma state. The complex character of space plasma can also be described by the non-extensive statistical thermodynamics pioneered by Tsallis, which offers a consistent and effective theoretical framework, based on a generalization of Boltzmann - Gibbs (BG) entropy, to describe far from equilibrium nonlinear complex dynamics (Tsallis, 2009). In a series of recent papers, the hypothesis of Tsallis non-extensive statistics in magnetosphere, sunspot dynamics, solar flares, solar wind and space plasma in general, was tested and verified (Karakatsanis et al., 2013; Pavlos et al., 2014; 2015). Our study includes the analysis of solar plasma time
Asymptotic distribution of ∆AUC, NRIs, and IDI based on theory of U-statistics.
Demler, Olga V; Pencina, Michael J; Cook, Nancy R; D'Agostino, Ralph B
2017-09-20
The change in area under the curve (∆AUC), the integrated discrimination improvement (IDI), and net reclassification index (NRI) are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues, we unite the ∆AUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ∆AUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ∆AUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ∆AUC, NRIs, or IDI. In the former case, SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ∆AUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ∆AUC. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
The Two-Component Non-Perturbative Pomeron and the G-Universality
Nicolescu, Basarab
2000-01-01
In this communication we present a generalization of the Donnachie-Landshoff model inspired by the recent discovery of a 2-component Pomeron in LLA-QCD by Bartels, Lipatov and Vacca. In particular, we explore a new property, not present in the usual Regge theory - the G-Universality - which signifies the independence of one of the Pomeron components on the nature of the initial and final hadrons. The best description of all the forward hadron-hadron, gamma- gamma and gamma-proton data is obta...
Koopmans' theorem in the statistical Hartree-Fock theory
Energy Technology Data Exchange (ETDEWEB)
Pain, Jean-Christophe, E-mail: jean-christophe.pain@cea.fr [CEA, DAM, DIF, F-91297 Arpajon (France)
2011-07-28
In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. The Hartree-Fock statistical theory has also been applied in the canonical ensemble (Blenski et al 1997 Phys. Rev. E 55 R4889) for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but a restricted version of the theorem can be obtained by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.
How to construct the optimal Bayesian measurement in quantum statistical decision theory
Tanaka, Fuyuhiko
Recently, much more attention has been paid to the study aiming at the application of fundamental properties in quantum theory to information processing and technology. In particular, modern statistical methods have been recognized in quantum state tomography (QST), where we have to estimate a density matrix (positive semidefinite matrix of trace one) representing a quantum system from finite data collected in a certain experiment. When the dimension of the density matrix gets large (from a few hundred to millions), it gets a nontrivial problem. While a specific measurement is often given and fixed in QST, we are also able to choose a measurement itself according to the purpose of QST by using qunatum statistical decision theory. Here we propose a practical method to find the best projective measurement in the Bayesian sense. We assume that a prior distribution (e.g., the uniform distribution) and a convex loss function (e.g., the squared error) are given. In many quantum experiments, these assumptions are not so restrictive. We show that the best projective measurement and the best statistical inference based on the measurement outcome exist and that they are obtained explicitly by using the Monte Carlo optimization. The Grant-in-Aid for Scientific Research (B) (No. 26280005).
Statistical analysis of 4 types of neck whiplash injuries based on classical meridian theory.
Chen, Yemeng; Zhao, Yan; Xue, Xiaolin; Li, Hui; Wu, Xiuyan; Zhang, Qunce; Zheng, Xin; Wang, Tianfang
2015-01-01
As one component of the Chinese medicine meridian system, the meridian sinew (Jingjin, (see text), tendino-musculo) is specially described as being for acupuncture treatment of the musculoskeletal system because of its dynamic attributes and tender point correlations. In recent decades, the therapeutic importance of the sinew meridian has become revalued in clinical application. Based on this theory, the authors have established therapeutic strategies of acupuncture treatment in Whiplash-Associated Disorders (WAD) by categorizing four types of neck symptom presentations. The advantage of this new system is to make it much easier for the clinician to find effective acupuncture points. This study attempts to prove the significance of the proposed therapeutic strategies by analyzing data collected from a clinical survey of various WAD using non-supervised statistical methods, such as correlation analysis, factor analysis, and cluster analysis. The clinical survey data have successfully verified discrete characteristics of four neck syndromes, based upon the range of motion (ROM) and tender point location findings. A summary of the relationships among the symptoms of the four neck syndromes has shown the correlation coefficient as having a statistical significance (P syndrome factors are more related to the Liver, as originally described in classical theory. The hypothesis of meridian sinew syndromes in WAD is clearly supported by the statistical analysis of the clinical trials. This new discovery should be beneficial in improving therapeutic outcomes.
Disorder in Gauge/Gravity Duality, Pole Spectrum Statistics and Random Matrix Theory
Saremi, Omid
2012-01-01
In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist phases where the nearest neighbor spacing distribution of the unfolded pole spectra of generic two-point correlators is Poisson. This closely resembles the localized phase of the Anderson Hamiltonian. We perform two tests on our statistical hypothesis. One is based on a statistic defined in the context of Random Matrix Theory, the so-called $\\bar{\\Delta_3}$, or spectral rigidity, proposed by Dyson and Mehta. The second is a $\\chi$-squared test. In our model, the results of both tests are consistent with the hypothesis that the pole spectra of two-point functions can be at least in two distinct phases; first a regular sequence and second a completely uncorrelated sequence with a Poisson nearest neighbor spacing distribution.
Disorder in gauge/gravity duality, pole spectrum statistics and random matrix theory
Saremi, Omid
2014-05-01
In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist phases where the nearest neighbor spacing distribution of the unfolded pole spectra of generic two-point correlators is Poisson. This closely resembles the localized phase of the Anderson Hamiltonian. We perform two tests on our statistical hypothesis. One is based on a statistic defined in the context of random matrix theory, the so-called \\overline{\\Delta _3}, or spectral rigidity, proposed by Dyson and Mehta. The second is a χ-squared test. In our model, the results of both tests are consistent with the hypothesis that the pole spectra of two-point functions can be at least in two distinct phases; first a regular sequence and second a completely uncorrelated sequence with a Poisson nearest neighbor spacing distribution.
The two-component non-perturbative pomeron and the G-Universality
Energy Technology Data Exchange (ETDEWEB)
Nicolescu, Basarab E-mail: nicolesc@in2p3.fr
2001-04-01
In this communication we present a generalization of the Donnachie-Landshoff model inspired by the recent discovery of a 2-component Pomeron in LLA-QCD by Bartels, Lipatov and Vacca. In particular, we explore a new property, not present in the usual Regge theory - the G-Universality - which signifies the independence of one of the Pomeron components on the nature of the initial and final hadrons. The best description of the p-barp, pp, {pi}{sup {+-}}p, K{sup {+-}}p, {gamma}{gamma} and {gamma}p forward data is obtained when G-universality is imposed. Moreover, the ln{sup 2}s behaviour of the hadron amplitude, first established by Heisenberg, is clearly favoured by the data.
The Two-Component Non-Perturbative Pomeron and the G-Universality
Nicolescu, Basarab
2000-01-01
In this communication we present a generalization of the Donnachie-Landshoff model inspired by the recent discovery of a 2-component Pomeron in LLA-QCD by Bartels, Lipatov and Vacca. In particular, we explore a new property, not present in the usual Regge theory - the G-Universality - which signifies the independence of one of the Pomeron components on the nature of the initial and final hadrons. The best description of all the forward hadron-hadron, gamma- gamma and gamma-proton data is obtained when G-universailty is imposed. Moreover, the maximal (ln)**2 behaviour of the hadron amplitude, first established by Heisenberg, is clearly favoured by the data.
Majda, Andrew J.; Qi, Di
2016-02-01
Turbulent dynamical systems with a large phase space and a high degree of instabilities are ubiquitous in climate science and engineering applications. Statistical uncertainty quantification (UQ) to the response to the change in forcing or uncertain initial data in such complex turbulent systems requires the use of imperfect models due to the lack of both physical understanding and the overwhelming computational demands of Monte Carlo simulation with a large-dimensional phase space. Thus, the systematic development of reduced low-order imperfect statistical models for UQ in turbulent dynamical systems is a grand challenge. This paper applies a recent mathematical strategy for calibrating imperfect models in a training phase and accurately predicting the response by combining information theory and linear statistical response theory in a systematic fashion. A systematic hierarchy of simple statistical imperfect closure schemes for UQ for these problems is designed and tested which are built through new local and global statistical energy conservation principles combined with statistical equilibrium fidelity. The forty mode Lorenz 96 (L-96) model which mimics forced baroclinic turbulence is utilized as a test bed for the calibration and predicting phases for the hierarchy of computationally cheap imperfect closure models both in the full phase space and in a reduced three-dimensional subspace containing the most energetic modes. In all of phase spaces, the nonlinear response of the true model is captured accurately for the mean and variance by the systematic closure model, while alternative methods based on the fluctuation-dissipation theorem alone are much less accurate. For reduced-order model for UQ in the three-dimensional subspace for L-96, the systematic low-order imperfect closure models coupled with the training strategy provide the highest predictive skill over other existing methods for general forced response yet have simple design principles based on a
Supersymmetric SO(N) from a Planck-scale statistical theory
Allen, Roland E
2010-01-01
Several refinements are made in a theory which starts with a Planck-scale statistical picture and ends with supersymmetry and a coupling of fundamental fermions and bosons to SO(N) gauge fields. In particular, more satisfactory treatments are given for (1) the transformation from the initial Euclidean form of the path integral for fermionic fields to the usual Lorentzian form, (2) the corresponding transformation for bosonic fields (which is much less straightforward), (3) the transformation from an initial primitive supersymmetry to the final standard form (containing, e.g., scalar sfermions and their auxiliary fields), (4) the initial statistical picture, and (5) the transformation to an action which is invariant under general coordinate transformations.
Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
Bruno, Mattia; Engel, Georg P; Francis, Anthony; Herdoiza, Gregorio; Horch, Hanno; Korcyl, Piotr; Korzec, Tomasz; Papinutto, Mauro; Schaefer, Stefan; Scholz, Enno E; Simeth, Jakob; Simma, Hubert; Söldner, Wolfgang
2014-01-01
We describe a new set of gauge configurations generated within the CLS effort. These ensembles have N_f=2+1 flavors of non-perturbatively improved Wilson fermions in the sea with the Luescher-Weisz action used for the gluons. Open boundary conditions in time are used to address the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. We give the bare parameters at which the ensembles have been generated and how these parameters have been chosen. Details of the algorithmic setup and its performance are presented as well as measurements of the pion and kaon masses alongside the scale parameter t_0.
Non-perturbative renormalisation of Delta F=2 four-fermion operators in two-flavour QCD
Dimopoulos, P; Palombi, Filippo; Papinutto, Mauro; Peña, C; Vladikas, A; Wittig, H
2008-01-01
Using Schroedinger Functional methods, we compute the non-perturbative renormalisation and renormalisation group running of several four-fermion operators, in the framework of lattice simulations with two dynamical Wilson quarks. Two classes of operators have been targeted: (i) those with left-left current structure and four propagating quark fields/ (ii) all operators containing two static quarks. In both cases, only the parity-odd contributions have been considered, being the ones that renormalise multiplicatively. Our results, once combined with future simulations of the corresponding lattice hadronic matrix elements, may be used for the computation of phenomenological quantities of interest, such as B_K and B_B (the latter also in the static limit).
Non-perturbative renormalisation of {delta}F=2 four-fermion operators in two-flavour QCD
Energy Technology Data Exchange (ETDEWEB)
Dimopoulos, P.; Vladikas, A. [INFN, Sezione di Roma II (Italy)]|[Rome-3 Univ. (Italy). Dipt. di Fisica; Herdoiza, G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Palombi, F.; Papinutto, M. [CERN, Geneva (Switzerland). Physics Dept., TH Division; Pena, C. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica C-XI]|[Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM/CSIC C-XVI; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2007-12-15
Using Schroedinger Functional methods, we compute the non-perturbative renormalisation and renormalisation group running of several four-fermion operators, in the framework of lattice simulations with two dynamical Wilson quarks. Two classes of operators have been targeted: (i) those with left-left current structure and four propagating quark fields; (ii) all operators containing two static quarks. In both cases, only the parity-odd contributions have been considered, being the ones that renormalise multiplicatively. Our results, once combined with future simulations of the corresponding lattice hadronic matrix elements, may be used for the computation of phenomenological quantities of interest, such as B{sub K} and B{sub B} (the latter also in the static limit). (orig.)
Dzhunushaliev, Vladimir
2016-01-01
The contribution of gluon fields to the proton spin is calculated. The calculations are performed following non-perturbative Heisenberg's quantization technique. In our approach a proton is considered as consisting of three quarks connected by three flux tubes. The flux tubes contain colour longitudinal electric and transversal electric and magnetic fields. The longitudinal electric field causes the interaction forces between quarks. The quantum superposition of the transversal fields causes the appearance of the angular momentum density. From our calculations, we obtain that the contribution of the gluon field from the flux tubes to the proton spin is of the order of $15\\%$. The dimensionless relation between the angular momentum and the mass of the gluon fields is obtained. The experimental verification of this relation is discussed. Simple numerical relation between the proton mass, the speed of light and the proton radius, which is of the same order as the Planck constant, is discussed.
Korcyl, Piotr
2016-01-01
We determine quark mass dependent order $a$ improvement terms of the form $b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents, using correlators in coordinate space. We use a set of CLS ensembles comprising non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz gauge action at $\\beta=3.4,3.46,3.55$ and $\\beta=3.7$, corresponding to lattice spacings $a$ ranging from $0.05$ fm to $0.09$ fm. We report the values of the $b_J$ improvement coefficients which are proportional to non-singlet quark mass combinations and also discuss the possibility of determining the $\\bar{b}_J$ coefficients which are proportional to the trace of the quark mass matrix.
Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the Schroedinger functional scheme
Taniguchi, Yusuke
2010-01-01
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy to deep in the high energy perturbative region. The regularization independent step scaling function of the quark mass is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than m_pi=500 MeV and that of PACS-CS collaboration on the physical point using the reweighting technique.
Zimmermann, Jörg; Romesberg, Floyd E
2014-01-01
Vibrational spectroscopy is uniquely able to characterize protein dynamics and microenvironmental heterogeneity because it possesses an inherently high temporal resolution and employs probes of ultimately high structural resolution-the bonds themselves. The use of carbon-deuterium (C-D) bonds as vibrational labels circumvents the spectral congestion that otherwise precludes the use of vibrational spectroscopy to proteins and makes the observation of single vibrations within a protein possible while being wholly non-perturbative. Thus, C-D probes can be used to site-specifically characterize conformational heterogeneity and thermodynamic stability. C-D probes are also uniquely useful in characterizing the electrostatic microenvironment experienced by a specific residue side chain or backbone due to its effect on the C-D absorption frequency. In this chapter we describe the experimental procedures required to use C-D bonds and FT IR spectroscopy to characterize protein dynamics, structural and electrostatic heterogeneity, ligand binding, and folding.
Puhr, M
2016-01-01
We use exactly chiral overlap lattice fermions to investigate the Chiral Separation Effect in quenched QCD at finite density. We employ a recently developed numerical method which allows, for the first time, to address the transport properties of exactly chiral lattice fermions with non-zero chemical potential. Studying the axial current along the external magnetic field, we find a linear dependence consistent with the free fermion result for topologically trivial gauge field configurations. However, for configurations with nontrivial topology in the confinement regime the axial current is strongly suppressed due to contributions of topological modes of the Dirac operator, which suggests that non-perturbative corrections to the Chiral Separation Effect have topological origin.
A microscopic, non-equilibrium, statistical field theory for cosmic structure formation
Bartelmann, Matthias; Fabis, Felix; Berg, Daniel; Kozlikin, Elena; Lilow, Robert; Viermann, Celia
2016-04-01
Building upon the recent pioneering work by Mazenko and by Das and Mazenko, we develop a microscopic, non-equilibrium, statistical field theory for initially correlated canonical ensembles of classical microscopic particles obeying Hamiltonian dynamics. Our primary target is cosmic structure formation, where initial Gaussian correlations in phase space are believed to be set by inflation. We give an exact expression for the generating functional of this theory and work out suitable approximations. We specify the initial correlations by a power spectrum and derive general expressions for the correlators of the density and the response field. We derive simple closed expressions for the lowest-order contributions to the nonlinear cosmological power spectrum, valid for arbitrary wave numbers. We further calculate the bispectrum expected in this theory within these approximations and the power spectrum of cosmic density fluctuations to first order in the gravitational interaction, using a recent improvement of the Zel’dovich approximation. We show that, with a modification motivated by the adhesion approximation, the nonlinear growth of the density power spectrum found in numerical simulations of cosmic structure evolution is reproduced well to redshift zero and for arbitrary wave numbers even within first-order perturbation theory. Our results present the first fully analytic calculation of the nonlinear power spectrum of cosmic structures.
Statistical testing of the full-range leadership theory in nursing.
Kanste, Outi; Kääriäinen, Maria; Kyngäs, Helvi
2009-12-01
The aim of this study is to test statistically the structure of the full-range leadership theory in nursing. The data were gathered by postal questionnaires from nurses and nurse leaders working in healthcare organizations in Finland. A follow-up study was performed 1 year later. The sample consisted of 601 nurses and nurse leaders, and the follow-up study had 78 respondents. Theory was tested through structural equation modelling, standard regression analysis and two-way anova. Rewarding transformational leadership seems to promote and passive laissez-faire leadership to reduce willingness to exert extra effort, perceptions of leader effectiveness and satisfaction with the leader. Active management-by-exception seems to reduce willingness to exert extra effort and perception of leader effectiveness. Rewarding transformational leadership remained as a strong explanatory factor of all outcome variables measured 1 year later. The data supported the main structure of the full-range leadership theory, lending support to the universal nature of the theory.
Xu, Peng; Yao, Dezhong; Luo, Fen
2005-08-01
The registration method based on mutual information is currently a popular technique for the medical image registration, but the computation for the mutual information is complex and the registration speed is slow. In engineering process, a subsampling technique is taken to accelerate the registration speed at the cost of registration accuracy. In this paper a new method based on statistics sample theory is developed, which has both a higher speed and a higher accuracy as compared with the normal subsampling method, and the simulation results confirm the validity of the new method.
Three Dimensional Statistical Field Theory for Density Fluctuations in Heavy-Ion Collsiions
Eggers, H C; Sarcevic, I
1994-01-01
A statistical field theory of particle production is presented using a gaussian functional in three dimensions. Identifying the field with the particle density fluctuation results in zero correlations of order three and higher, while the second order correlation function is of a Yukawa form. A detailed scheme for projecting the theoretical three-dimensional correlation onto data of three and fewer dimensions illustrates how theoretical predictions are tested against experimental moments in the different dimensions. An example given in terms of NA35 parameters should be testable against future NA35 data.
Thomas, J. M.; Hawk, J. D.
1975-01-01
A generalized concept for cost-effective structural design is introduced. It is assumed that decisions affecting the cost effectiveness of aerospace structures fall into three basic categories: design, verification, and operation. Within these basic categories, certain decisions concerning items such as design configuration, safety factors, testing methods, and operational constraints are to be made. All or some of the variables affecting these decisions may be treated probabilistically. Bayesian statistical decision theory is used as the tool for determining the cost optimum decisions. A special case of the general problem is derived herein, and some very useful parametric curves are developed and applied to several sample structures.
Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View
Montanari, Andrea
2007-01-01
These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory, highlighting connections with statistical mechanics. We also stress common concepts with other disciplines dealing with similar problems that can be generically referred to as `large graphical models'. While most of the lectures are devoted to the classical channel coding problem over simple memoryless channels, we present a discussion of more complex channel models. We conclude with an overview of the main open challenges in the field.
Peridynamic theory of solids from the perspective of classical statistical mechanics
Rahman, R.; Foster, J. T.
2015-11-01
In this paper the classical statistical mechanics has been explored in order to develop statistical mechanical framework for peridynamics. Peridynamic equation of motion is known as upscaled Newton's equation. The peridynamic system consists of finite number of nonlocally interacting particles at nano and meso scales. This particle representation of peridynamics can be treated in terms of classical statistical mechanics. Hence, in this work the phase space is constructed based on the PD particle from their evolving momentum pi and positions xi. The statistical ensembles are derived by defining appropriate partition functions. The algorithms for NVE and NPH implemented in the classical molecular dynamics are revisited for equilibrium peridynamic models. The current work introduces Langevin dynamics to the peridynamic theory through fluctuation-dissipation principle. This introduces a heat bath to the peridynamic system which eliminates the ambiguity with the role of temperature in a peridynamic system. Finally, it was seen that the homogenization of a peridynamic model with finite number of particles approaches to a conventional continuum model. The upscaled non-equilibrium peridynamics has potential applications in modeling wide variety of multiscale-multiphysics problems from nano to macro scale or vice versa.
Slaby, Christoph; Könies, Axel; Kleiber, Ralf
2016-09-01
The resonant interaction of shear Alfvén waves with energetic particles is investigated numerically in tokamak and stellarator geometry using a non-perturbative MHD-kinetic hybrid approach. The focus lies on toroidicity-induced Alfvén eigenmodes (TAEs), which are most easily destabilized by a fast-particle population in fusion plasmas. While the background plasma is treated within the framework of an ideal-MHD theory, the drive of the fast particles, as well as Landau damping of the background plasma, is modelled using the drift-kinetic Vlasov equation without collisions. Building on analytical theory, a fast numerical tool, STAE-K, has been developed to solve the resulting eigenvalue problem using a Riccati shooting method. The code, which can be used for parameter scans, is applied to tokamaks and the stellarator Wendelstein 7-X. High energetic-ion pressure leads to large growth rates of the TAEs and to their conversion into kinetically modified TAEs and kinetic Alfvén waves via continuum interaction. To better understand the physics of this conversion mechanism, the connections between TAEs and the shear Alfvén wave continuum are examined. It is shown that, when energetic particles are present, the continuum deforms substantially and the TAE frequency can leave the continuum gap. The interaction of the TAE with the continuum leads to singularities in the eigenfunctions. To further advance the physical model and also to eliminate the MHD continuum together with the singularities in the eigenfunctions, a fourth-order term connected to radiative damping has been included. The radiative damping term is connected to non-ideal effects of the bulk plasma and introduces higher-order derivatives to the model. Thus, it has the potential to substantially change the nature of the solution. For the first time, the fast-particle drive, Landau damping, continuum damping, and radiative damping have been modelled together in tokamak- as well as in stellarator geometry.
A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO
Heisenberg, Lavinia; Schäfer, Björn Malte; Bartelmann, Matthias
2011-10-01
Subject of this paper is a detailed analysis of the PINpointing Orbit-Crossing Collapsed HIerarchical Object (PINOCCHIO) algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field δl is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position q and each smoothing radius R, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian perturbation theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++, recovered the mass function and optimized the construction of halo merging histories. When compared with the output of the Millennium Simulation our results suggest that the PINOCCHIO is well suited for studying relative velocities of merging haloes and is able to reproduce the pairwise velocity distribution.
Nakamura, Y
2007-01-01
We present non-perturbative renormalization factors for $\\Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ previously obtained by the CP-PACS collaboration with the quenched domain-wall QCD(DWQCD). We compare our result with previous ones obtained by perturbative renormalization factors, different renormalization schemes or different quark actions. We also show that chiral symmetry breaking effects in the renormalization factor are numerically small.
Statistical decision theory to relate neurons to behavior in the study of covert visual attention.
Eckstein, Miguel P; Peterson, Matthew F; Pham, Binh T; Droll, Jason A
2009-06-01
Scrutiny of the numerous physiology and imaging studies of visual attention reveal that integration of results from neuroscience with the classic theories of visual attention based on behavioral work is not simple. The different subfields have pursued different questions, used distinct experimental paradigms and developed diverse models. The purpose of this review is to use statistical decision theory and computational modeling to relate classic theories of attention in psychological research to neural observables such as mean firing rate or functional imaging BOLD response, tuning functions, Fano factor, neuronal index of detectability and area under the receiver operating characteristic (ROC). We focus on cueing experiments and attempt to distinguish two major leading theories in the study of attention: limited resources model/increased sensitivity vs. selection/differential weighting. We use Bayesian ideal observer (BIO) modeling, in which predictive cues or prior knowledge change the differential weighting (prior) of sensory information to generate predictions of behavioral and neural observables based on Gaussian response variables and Poisson process neural based models. The ideal observer model can be modified to represent a number of classic psychological theories of visual attention by including hypothesized human attentional limited resources in the same way sequential ideal observer analysis has been used to include physiological processing components of human spatial vision (Geisler, W. S. (1989). Sequential ideal-observer analysis of visual discrimination. Psychological Review 96, 267-314.). In particular we compare new biologically plausible implementations of the BIO and variant models with limited resources. We find a close relationship between the behavioral effects of cues predicted by the models developed in the field of human psychophysics and their neuron-based analogs. Critically, we show that cue effects on experimental observables such as
STATISTICAL ANALYSIS, REPORTS), (*PROBABILITY, REPORTS), INFORMATION THEORY, DIFFERENTIAL EQUATIONS, STATISTICAL PROCESSES, STOCHASTIC PROCESSES, MULTIVARIATE ANALYSIS, DISTRIBUTION THEORY , DECISION THEORY, MEASURE THEORY, OPTIMIZATION
Multivariate meta-analysis: a robust approach based on the theory of U-statistic.
Ma, Yan; Mazumdar, Madhu
2011-10-30
Meta-analysis is the methodology for combining findings from similar research studies asking the same question. When the question of interest involves multiple outcomes, multivariate meta-analysis is used to synthesize the outcomes simultaneously taking into account the correlation between the outcomes. Likelihood-based approaches, in particular restricted maximum likelihood (REML) method, are commonly utilized in this context. REML assumes a multivariate normal distribution for the random-effects model. This assumption is difficult to verify, especially for meta-analysis with small number of component studies. The use of REML also requires iterative estimation between parameters, needing moderately high computation time, especially when the dimension of outcomes is large. A multivariate method of moments (MMM) is available and is shown to perform equally well to REML. However, there is a lack of information on the performance of these two methods when the true data distribution is far from normality. In this paper, we propose a new nonparametric and non-iterative method for multivariate meta-analysis on the basis of the theory of U-statistic and compare the properties of these three procedures under both normal and skewed data through simulation studies. It is shown that the effect on estimates from REML because of non-normal data distribution is marginal and that the estimates from MMM and U-statistic-based approaches are very similar. Therefore, we conclude that for performing multivariate meta-analysis, the U-statistic estimation procedure is a viable alternative to REML and MMM. Easy implementation of all three methods are illustrated by their application to data from two published meta-analysis from the fields of hip fracture and periodontal disease. We discuss ideas for future research based on U-statistic for testing significance of between-study heterogeneity and for extending the work to meta-regression setting.
Knoester, J.; Himbergen, J.E. Van
1987-01-01
The incorporation is studied of the orientation factor occurring in the complete Förster rate of incoherent energy transfer, into the theory of concentration self-quenching by statistical pairs of luminescent molecules. Within Burshtein’s theory of hopping transport, exact results for the steady
DEFF Research Database (Denmark)
Karakatsani, Eirini; Kontogeorgis, Georgios; Economou, Ioannis
2006-01-01
Perturbed chain-statistical associating fluid theory (PC-SAFT) was extended rigorously to polar fluids based on the theory of Stell and co-workers [Mol. Phys. 1977, 33, 987]. The new PC-PSAFT was simplified to truncated PC-PSAFT (tPC-PSAFT) so that it can be practical for real polar fluid thermod...
Blanco, Angeles
2011-01-01
This study investigated the usefulness of social cognitive career theory--SCCT (Lent, Brown, and Hackett, 1994) in predicting interests and goals relating to statistics among psychology students. The participants were 1036 Spanish students who completed measurements of statistics-related mastery experiences, self-efficacy, outcome expectations,…
Blanco, Angeles
2011-01-01
This study investigated the usefulness of social cognitive career theory--SCCT (Lent, Brown, and Hackett, 1994) in predicting interests and goals relating to statistics among psychology students. The participants were 1036 Spanish students who completed measurements of statistics-related mastery experiences, self-efficacy, outcome expectations,…
Pavlov; Punegov
2000-05-01
The statistical dynamical theory of X-ray diffraction is developed for a crystal containing statistically distributed microdefects. Fourier-component equations for coherent and diffuse (incoherent) scattered waves have been obtained in the case of so-called triple-crystal diffractometry. New correlation lengths and areas are introduced for characterization of the scattered volume.
Martinez, Rafael; Rodriguez, Francisco de Borja; Camacho, David
2007-01-01
The main contribution of this paper is to design an Information Retrieval (IR) technique based on Algorithmic Information Theory (using the Normalized Compression Distance- NCD), statistical techniques (outliers), and novel organization of data base structure. The paper shows how they can be integrated to retrieve information from generic databases using long (text-based) queries. Two important problems are analyzed in the paper. On the one hand, how to detect "false positives" when the distance among the documents is very low and there is actual similarity. On the other hand, we propose a way to structure a document database which similarities distance estimation depends on the length of the selected text. Finally, the experimental evaluations that have been carried out to study previous problems are shown.
Numerical study of chiral plasma instability within the classical statistical field theory approach
Buividovich, P V
2015-01-01
We report on a numerical study of the real-time dynamics of chirally imbalanced lattice Dirac fermions coupled to dynamical electromagnetic field. To this end we use the classical statistical field theory approach, in which the quantum evolution of fermions is simulated exactly, and electromagnetic fields are treated as classical. Motivated by recent experiments on chirally imbalanced Dirac semimetals, we use the Wilson-Dirac lattice Hamiltonian for fermions in order to model the emergent nature of chiral symmetry at low energies. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring large chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to decay at the expense of nonzero helicity of electromagnetic ...
A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory
Bargigli, Leonardo; Viaggiu, Stefano; Lionetto, Andrea
2016-09-01
We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables {w_{ij}} describing the flow of a given commodity from agent i to agent j. This sequence can be arranged in a nonnegative matrix W which we can regard as the representation of a weighted and directed network or digraph G. Our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations, which are in most cases not fulfilled by real markets. An explicit example with reference to the e-MID interbank credit market is provided.
A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory
Bargigli, Leonardo; Viaggiu, Stefano; Lionetto, Andrea
2016-10-01
We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables {w_{ij}} describing the flow of a given commodity from agent i to agent j. This sequence can be arranged in a nonnegative matrix W which we can regard as the representation of a weighted and directed network or digraph G. Our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations, which are in most cases not fulfilled by real markets. An explicit example with reference to the e-MID interbank credit market is provided.
The new interpretation of support vector machines on statistical learning theory
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is concerned with the theoretical foundation of support vector machines (SVMs). The purpose is to develop further an exact relationship between SVMs and the statistical learning theory (SLT). As a representative, the standard C-support vector classification (C-SVC) is considered here. More precisely, we show that the decision function obtained by C-SVC is just one of the decision functions obtained by solving the optimization problem derived directly from the structural risk minimization principle. In addition, an interesting meaning of the parameter C in C-SVC is given by showing that C corresponds to the size of the decision function candidate set in the structural risk minimization principle.
Won, Chang-Hee; Michel, Anthony N
2008-01-01
This volume - dedicated to Michael K. Sain on the occasion of his seventieth birthday - is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. Written by experts in their respective fields, the chapters are thematically organized into four parts: Part I focuses on statistical control theory, where the cost function is viewed as a random variable and performance is shaped through cost cumulants. In this respect, statistical control generalizes linear-quadratic-Gaussian and H-infinity control. Part II addresses algebraic systems th
Berengut, J C; Dzuba, V A; Flambaum, V V; Gribakin, G F
2015-01-01
The strong mixing of many-electron basis states in excited atoms and ions with open $f$ shells results in very large numbers of complex, chaotic eigenstates that cannot be computed to any degree of accuracy. Describing the processes which involve such states requires the use of a statistical theory. Electron capture into these 'compound resonances' leads to electron-ion recombination rates that are orders of magnitude greater than those of direct, radiative recombination, and cannot be described by standard theories of dielectronic recombination. Previous statistical theories considered this as a two-electron capture process which populates a pair of single-particle orbitals, followed by 'spreading' of the two-electron states into chaotically mixed eigenstates. This method is similar to a configuration-average approach, as it neglects potentially important effects of spectator electrons and conservation of total angular momentum. In this work we develop a statistical theory which considers electron capture in...
A Statistical Analysis of the Minimal SUSY B-L Theory
Ovrut, Burt A; Spinner, Sogee
2014-01-01
The structure of the B-L MSSM theory--specifically, the relevant mass scales and soft supersymmetric breaking parameters--is discussed. The space of initial soft parameters is explored at the high scale using random statistical sampling subject to a constraint on the range of dimensionful parameters. For every chosen initial point, the complete set of renormalization group equations is solved. The low energy results are then constrained to be consistent with present experimental data. It is shown that a large set of initial conditions satisfy these constraints and lead to acceptable low energy particle physics. Each such initial point has explicit predictions, such as the exact physical sparticle spectrum--which is presented for two such points. There are also statistical predictions for the masses of the sparticles and the LSP species which are displayed as histograms. Finally, the fine-tuning of the $\\mu$ parameter--which is always equivalent to or smaller than in the MSSM--is discussed.
Counting statistics of chaotic resonances at optical frequencies: Theory and experiments
Lippolis, Domenico; Wang, Li; Xiao, Yun-Feng
2017-07-01
A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang et al., Phys. Rev. E 93, 040201(R) (2016), 10.1103/PhysRevE.93.040201].
Aspects of string theory compactifications. D-brane statistics and generalised geometry
Energy Technology Data Exchange (ETDEWEB)
Gmeiner, F.
2006-05-26
In this thesis we investigate two different aspects of string theory compactifications. The first part deals with the issue of the huge amount of possible string vacua, known as the landscape. Concretely we investigate a specific well defined subset of type II orientifold compactifications. We develop the necessary tools to construct a very large set of consistent models and investigate their gauge sector on a statistical basis. In particular we analyse the frequency distributions of gauge groups and the possible amount of chiral matter for compactifications to six and four dimensions. In the phenomenologically relevant case of four-dimensional compactifications, special attention is paid to solutions with gauge groups that include those of the standard model, as well as Pati-Salam, SU(5) and flipped SU(5) models. Additionally we investigate the frequency distribution of coupling constants and correlations between the observables in the gauge sector. These results are compared with a recent study of Gepner models. Moreover, we elaborate on questions concerning the finiteness of the number of solutions and the computational complexity of the algorithm. In the second part of this thesis we consider a new mathematical framework, called generalised geometry, to describe the six-manifolds used in string theory compactifications. In particular, the formulation of T-duality and mirror symmetry for nonlinear topological sigma models is investigated. Therefore we provide a reformulation and extension of the known topological A- and B-models to the generalised framework. The action of mirror symmetry on topological D-branes in this setup is presented and the transformation of the boundary conditions is analysed. To extend the considerations to D-branes in type II string theory, we introduce the notion of generalised calibrations. We show that the known calibration conditions of supersymmetric branes in type IIA and IIB can be obtained as special cases. Finally we investigate
Balancing the books – a statistical theory of prospective budgets in Earth System science
Directory of Open Access Journals (Sweden)
J. P. O'Kane
2003-01-01
Full Text Available An honest declaration of the error in a mass, momentum or energy balance, ε, simply raises the question of its acceptability: 'At what value of ε is the attempted balance to be rejected?' Answering this question requires a reference quantity against which to compare ε. This quantity must be a mathematical function of all the data used in making the balance. To deliver this function, a theory grounded in a workable definition of acceptability is essential. A distinction must be drawn between a retrospective balance and a prospective budget in relation to any natural space-filling body. Balances look to the past; budgets look to the future. The theory is built on the application of classical sampling theory to the measurement and closure of a prospective budget. It satisfies R.A. Fisher's 'vital requirement that the actual and physical conduct of experiments should govern the statistical procedure of their interpretation'. It provides a test, which rejects, or fails to reject, the hypothesis that the closing error on the budget, when realised, was due to sampling error only. By increasing the number of measurements, the discrimination of the test can be improved, controlling both the precision and accuracy of the budget and its components. The cost-effective design of such measurement campaigns is discussed briefly. This analysis may also show when campaigns to close a budget on a particular space-filling body are not worth the effort for either scientific or economic reasons. Other approaches, such as those based on stochastic processes, lack this finality, because they fail to distinguish between different types of error in the mismatch between a set of realisations of the process and the measured data. Keywords: balance, budget, sampling, hypothesis test, closing error, Earth System
Saha, Asit; Chatterjee, Prasanta; Chatterjee
2014-08-01
Ion acoustic solitary waves and periodic waves in an unmagnetized plasma with superthermal (kappa-distributed) electrons and positrons are investigated through a non-perturbative approach. Model equations are transformed to a planar dynamical system. Then by using the bifurcations of phase portraits of this planar dynamical system, we have established that our model has solitary wave and periodic wave solutions. We have obtained two analytical solutions for these solitary and periodic waves depending on the parameters. From these solitary wave and periodic wave solutions, we have shown the combined effects of temperature ratio (σ) of electrons and positrons, spectral index (κ), speed of the traveling wave (v), and density ratio (p) of positrons and electrons on the characteristics of ion acoustic solitary and periodic waves. The spectral index, density ratio, speed of the traveling wave, and temperature ratio significantly affect the characteristics of ion acoustic solitary and periodic structures. The present study might be helpful to understand the salient features of nonlinear ion acoustic solitary and periodic structures in the interstellar medium.
Directory of Open Access Journals (Sweden)
V. Bacsó
2015-12-01
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.
Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. IV
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I.; Itoh, Kimitaka [Max-Planck-Institut fuer Plasmaphysik, Garching bei Muenchen (Germany)
2000-02-01
A statistical theory of nonlinear-nonequilibrium plasma state with strongly developed turbulence and with strong inhomogeneity of the system has been developed. A Fokker-Planck equation for the probability distribution function of the magnitude of turbulence is deduced. In the statistical description, both the contributions of thermal excitation and turbulence are kept. From the Fokker-Planck equation, the transition probability between the thermal fluctuation and turbulent fluctuation is derived. With respect to the turbulent fluctuations, the coherent part to a certain test mode is renormalized as the drag to the test mode, and the rest, the incoherent part, is considered to be a random noise. The renormalized operator includes the effect of nonlinear destabilization as well as the decorrelation by turbulent fluctuations. The equilibrium distribution function describes the thermal fluctuation, self-sustained turbulence and the hysteresis between them as a function of the plasma gradient. The plasma inhomogeneity is the controlling parameter that governs time turbulence. The formula of transition probability recovers the Arrhenius law in the thermodynamical equilibrium limit. In the presence of self-noise, the transition probability deviates form the exponential law and provides a power law. Application is made to the submarginal interchange mode turbulence, being induced by the turbulent current-diffusivity, in inhomogeneous plasmas. The power law dependence of the transition probability is obtained on the distance between the pressure gradient and the critical gradient for linear instability. Thus a new type of critical exponent is explicitly deduced in the phenomena of subcritical excitation of turbulence. The method provides an extension of the nonequilibrium statistical physics to the far-nonequilibrium states. (author)
Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. III
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I.; Itoh, Kimitaka [Max-Planck-Institut fuer Plasmaphysik, Garching bei Muenchen (Germany)
2000-02-01
A statistical theory of nonlinear-nonequilibrium plasma state with strongly developed turbulence and with strong inhomogeneity of the system has been developed. A unified theory for both the thermally excited fluctuations and the strongly turbulent fluctuations is presented. With respect to the turbulent fluctuations, the coherent part to a certain test mode is renormalized as the drag to the test mode, and the rest, the incoherent part, is considered to be a random noise. The renormalized operator includes the effect of nonlinear destabilization as well as the decorrelation by turbulent fluctuations. Formulation is presented by deriving an Fokker-Planck equation for the probability distribution function. Equilibrium distribution function of fluctuations is obtained. Transition from the thermal fluctuations, that is governed by the Boltzmann distribution, to the turbulent fluctuation is clarified. The distribution function for the turbulent fluctuation has tail component and the width of which is in the same order as the mean fluctuation level itself. The Lyapunov function is constructed for the strongly turbulent plasma, and it is shown that an approach to a certain equilibrium distribution is assured. The result for the most probable state is expressed in terms of 'minimum renormalized dissipation rate', which is given by the ratio of the nonlinear decorrelation rate of fluctuation energy and the random excitation rate which includes both the thermal noise and turbulent self-noise effects. Application is made for example to the current-diffusive interchange mode turbulence in inhomogeneous plasmas. The applicability of this method covers plasma turbulences in much wider circumstance as well as neutral fluid turbulence. This method of analyzing strong turbulence has successfully extended the principles of statistical physics, i.e., Kubo-formula, Prigogine's principle of minimum entropy production rate. The condition for the turbulence transition is
Fried, H. M.; Tsang, P. H.; Gabellini, Y.; Grandou, T.; Sheu, Y.-M.
2016-11-01
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
Fried, H M; Gabellini, Y; Grandou, T; Sheu, Y-M
2015-01-01
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
Directory of Open Access Journals (Sweden)
Fried H. M.
2016-01-01
Full Text Available A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
Gross, Markus; Gambassi, Andrea; Dietrich, S
2017-08-01
The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter (e.g., the total number of particles), is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., in a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of ε=4-d, where d is the spatial dimension of the bulk, the finite-size contribution to the free energy of the confined system and the associated critical Casimir force are calculated to leading order in ε and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting critical Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, in the canonical case with fixed transverse area the critical Casimir force attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the critical Casimir force both on the temperaturelike and on the fieldlike scaling variables is different in the two ensembles.
Directory of Open Access Journals (Sweden)
James Carifio
2007-01-01
Full Text Available One of the highly questionable effects of educational reform and other curriculum reshaping factors at both the high school, post-secondary and graduate levels has been the shift to teaching compressed, pared-down or abbreviated courses in still needed or required subject-matter that became de-emphasized in the current educational reformation. Research methodology, particularly the highly quantitative and experimental kind and statistics, are two still needed to some degree subject matters that has been especially affected by this demotion and compression movement at the pre-service, in-service, professional development, undergraduate, continuing education and graduate levels, even though the professional areas of education, science, business, politics and most other areas (including history have become far more quantitative and objective research oriented than in the past. Until there are more enlightened policy shifts, effective means of teaching such compressed courses need to be devised and tested, if only to lessen the negative outcomes of such critical courses. This article, therefore, analyzes compressed courses from the point of view of cognitive learning and then describes 5 methods and approaches that were tested to improve the effectiveness of research methodology and statistics courses taught in these formats. Each of the formats helped to reduce student stress and anxiety about the content and its compressed presentation and improved understanding and achievement. The theory and view developed in this article is also applicable to similar compressed courses for scientific and/or technical content which are currently prevalent in allied health and biotechnology areas.
Morgenstern Horing, Norman J
2017-01-01
This book provides an introduction to the methods of coupled quantum statistical field theory and Green's functions. The methods of coupled quantum field theory have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics. This introduction to the subject is intended to facilitate delivery of the material in an easily digestible form to advanced undergraduate physics majors at a relatively early stage of their scientific development. The main mechanism to accomplish this is the early introduction of variational calculus and the Schwinger Action Principle, accompanied by Green's functions. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green's function equations-of-motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and nonequilibrium Green's functions...
Indian Academy of Sciences (India)
Vimla Vyas
2008-04-01
Speeds of sound and densities of three ternary liquid systems namely, toluene + -heptane + -hexane (I), cyclohexane + -heptane + -hexane (II) and -hexane + - heptane + -decane (III) have been measured as a function of the composition at 298.15 K at atmospheric pressure. The experimental isothermal compressibility has been evaluated from measured values of speeds of sound and density. The isothermal compressibility of these mixtures has also been computed theoretically using different models for hard sphere equations of state and Flory's statistical theory. Computed values of isothermal compressibility have been compared with experimental findings. A satisfactory agreement has been observed. The superiority of Flory's statistical theory has been established quite reasonably over hard sphere models.
Quantum Computation and Non-Abelian Statistics in Chern-Simons-Higgs Theory
Brozeguini, J C
2013-01-01
We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum vortex topological excitations occurring in this system and show that self-adjoint (Majorana-like) combinations of these vortices and anti-vortices have in general non-Abelian statistics. The associated unitary monodromy braiding matrices become the required logic gates in the special case when the vortex spin is $s=1/4$. We explicitly construct the vortex field operators, show that they carry both magnetic flux and charge and obtain their euclidean correlation functions by using the method of quantization of topological excitations, which is based on the order-disorder duality. These correlators are in general multivalued, the number of sheets being determined by the vortex spin. This, by its turn, is proportional to the vacuum expectation value of the Higgs field and therefore...
Energy Technology Data Exchange (ETDEWEB)
Ji Peijun [College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029 (China); Feng Wei [College of Life Science and Technology, Beijing University of Chemical Technology, Beijing 100029 (China)]. E-mail: fengwei@mail.buct.edu.cn; Tan Tianwei [College of Life Science and Technology, Beijing University of Chemical Technology, Beijing 100029 (China)
2007-07-15
The density of aqueous solutions of amino acids has been modeled with the statistical associating fluid theory (SAFT) equation of state. The modeling is accomplished by extending the previously developed new method to determine the SAFT parameters for amino acids. The modeled systems include {alpha}-alanine/H{sub 2}O, {beta}-alanine/H{sub 2}O, proline/H{sub 2}O, L-asparagine/H{sub 2}O, L-glutamine/H{sub 2}O, L-histidine/H{sub 2}O, serine/H{sub 2}O, glycine/H{sub 2}O, alanine/H{sub 2}O/sucrose, DL-valine/H{sub 2}O/sucrose, arginine/H{sub 2}O/sucrose, serine/H{sub 2}O/ethylene glycol, and glycine/H{sub 2}O/ethylene glycol. The density of binary solutions of amino acids has been correlated or predicted with a high precision. And then the density of multicomponent aqueous solutions of amino acids has been modeled based on the modeling results of binary systems, and a high accuracy of density calculations has been obtained. Finally, the water activities of DL-valine/H{sub 2}O, glycine/H{sub 2}O, and proline/H{sub 2}O have been predicted without using binary interaction parameters, and good results have been obtained.
Inverse problems with Poisson data: statistical regularization theory, applications and algorithms
Hohage, Thorsten; Werner, Frank
2016-09-01
Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years.
Jiang, Hao; Panagiotopoulos, Athanassios Z.; Economou, Ioannis G.
2016-03-01
Statistical associating fluid theory (SAFT) is used to model CO2 solubilities in single and mixed electrolyte solutions. The proposed SAFT model implements an improved mean spherical approximation in the primitive model to represent the electrostatic interactions between ions, using a parameter K to correct the excess energies ("KMSA" for short). With the KMSA formalism, the proposed model is able to describe accurately mean ionic activity coefficients and liquid densities of electrolyte solutions including Na+, K+, Ca2+, Mg2+, Cl-, Br- and SO42- from 298.15 K to 473.15 K using mostly temperature independent parameters, with sole exception being the volume of anions. CO2 is modeled as a non-associating molecule, and temperature-dependent CO2-H2O and CO2-ion cross interactions are used to obtain CO2 solubilities in H2O and in single ion electrolyte solutions. Without any additional fitting parameters, CO2 solubilities in mixed electrolyte solutions and synthetic brines are predicted, in good agreement with experimental measurements.
Evaporation of Liquid Droplet in Nano and Micro Scales from Statistical Rate Theory.
Duan, Fei; He, Bin; Wei, Tao
2015-04-01
The statistical rate theory (SRT) is applied to predict the average evaporation flux of liquid droplet after the approach is validated in the sessile droplet experiments of the water and heavy water. The steady-state experiments show a temperature discontinuity at the evaporating interface. The average evaporation flux is evaluated by individually changing the measurement at a liquid-vapor interface, including the interfacial liquid temperature, the interfacial vapor temperature, the vapor-phase pressure, and the droplet size. The parameter study shows that a higher temperature jump would reduce the average evaporation flux. The average evaporation flux can significantly be influenced by the interfacial liquid temperature and the vapor-phase pressure. The variation can switch the evaporation into condensation. The evaporation flux is found to remain relative constant if the droplet is larger than a micro scale, while the smaller diameters in nano scale can produce a much higher evaporation flux. In addition, a smaller diameter of droplets with the same liquid volume has a larger surface area. It is suggested that the evaporation rate increases dramatically as the droplet shrinks into nano size.
Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. V
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I. [Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka (Japan); Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2000-10-01
A statistical theory of strong plasma turbulence in nonlinear-nonequilibrium state is extended. By use of the spectral decomposition method, the renormalized propagator is decomposed into the projection operators. The decomposition of fluctuation fields into the least stable branch and other branches is explicitly made. The extended fluctuation dissipation theorem is derived for each decomposed renormalized mode. The decorrelation rate, eddy damping rate, fluctuation level and correlation functions are obtained even in the case that the cross-correlation functions and auto-correlation functions are of the same order of magnitude. The Fokker-Planck equation is reformulated for fluctuation components of each branch. These results are generalization of the previous result. It is confirmed that the solutions, probability distribution function and related transition probability which have been obtained in previous analyses are found valid apart from a numerical coefficient of the order of unity. In order to show the wider applicability, a case of plasma turbulence which is described by the four-field reduced set of equations is also discussed. (author)
A New Statistic for Evaluating Item Response Theory Models for Ordinal Data. CRESST Report 839
Cai, Li; Monroe, Scott
2014-01-01
We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…
Tamborini, Marco
2015-11-01
This paper examines the subversive role of statistics paleontology at the end of the 19th and the beginning of the 20th centuries. In particular, I will focus on German paleontology and its relationship with statistics. I argue that in paleontology, the quantitative method was questioned and strongly limited by the first decade of the 20th century because, as its opponents noted, when the fossil record is treated statistically, it was found to generate results openly in conflict with the Darwinian theory of evolution. Essentially, statistics questions the gradual mode of evolution and the role of natural selection. The main objections to statistics were addressed during the meetings at the Kaiserlich-Königliche Geologische Reichsanstalt in Vienna in the 1880s. After having introduced the statistical treatment of the fossil record, I will use the works of Charles Léo Lesquereux (1806-1889), Joachim Barrande (1799-1833), and Henry Shaler Williams (1847-1918) to compare the objections raised in Vienna with how the statistical treatment of the data worked in practice. Furthermore, I will discuss the criticisms of Melchior Neumayr (1845-1890), one of the leading German opponents of statistical paleontology, to show why, and to what extent, statistics were questioned in Vienna. The final part of this paper considers what paleontologists can derive from a statistical notion of data: the necessity of opening a discussion about the completeness and nature of the paleontological data. The Vienna discussion about which method paleontologists should follow offers an interesting case study in order to understand the epistemic tensions within paleontology surrounding Darwin's theory as well as the variety of non-Darwinian alternatives that emerged from the statistical treatment of the fossil record at the end of the 19th century.
Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations
Lee, Chee Kong; Gong, Jiangbin
2012-01-01
Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study non-canonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte-Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify non-canonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, non-canonical statistics enhances as temperature decreases but vanishes at high temperature.
Directory of Open Access Journals (Sweden)
B. S. Raghuram
1963-07-01
Full Text Available Information theory, which originated in Tele-communication studies, is a branch of Mathematical statistics with many applications of statistical inference. The three fundamental problems are: (i Development of statistical measures of information capacity in a Communication system, (ii the transmission problem of information in a system, and (iii analytical study of reception from a statistical decision point of view. This paper is an attempt to present a comprehensive study of all three aspects. In addition, application of sequential analysis, specially with reference to radar signal detection and range estimation has been briefly discussed. Finally from the point of view of signal reception in the case of a radar, the problem has been considered as a statistical decision study. In conclusion, the computational problems as well as certain comparative studies have been briefly touched upon. Illustrative examples are given and graphs are shown wherever necessary.
Accurate statistical associating fluid theory for chain molecules formed from Mie segments.
Lafitte, Thomas; Apostolakou, Anastasia; Avendaño, Carlos; Galindo, Amparo; Adjiman, Claire S; Müller, Erich A; Jackson, George
2013-10-21
A highly accurate equation of state (EOS) for chain molecules formed from spherical segments interacting through Mie potentials (i.e., a generalized Lennard-Jones form with variable repulsive and attractive exponents) is presented. The quality of the theoretical description of the vapour-liquid equilibria (coexistence densities and vapour pressures) and the second-derivative thermophysical properties (heat capacities, isobaric thermal expansivities, and speed of sound) are critically assessed by comparison with molecular simulation and with experimental data of representative real substances. Our new EOS represents a notable improvement with respect to previous versions of the statistical associating fluid theory for variable range interactions (SAFT-VR) of the generic Mie form. The approach makes rigorous use of the Barker and Henderson high-temperature perturbation expansion up to third order in the free energy of the monomer Mie system. The radial distribution function of the reference monomer fluid, which is a prerequisite for the representation of the properties of the fluid of Mie chains within a Wertheim first-order thermodynamic perturbation theory (TPT1), is calculated from a second-order expansion. The resulting SAFT-VR Mie EOS can now be applied to molecular fluids characterized by a broad range of interactions spanning from soft to very repulsive and short-ranged Mie potentials. A good representation of the corresponding molecular-simulation data is achieved for model monomer and chain fluids. When applied to the particular case of the ubiquitous Lennard-Jones potential, our rigorous description of the thermodynamic properties is of equivalent quality to that obtained with the empirical EOSs for LJ monomer (EOS of Johnson et al.) and LJ chain (soft-SAFT) fluids. A key feature of our reformulated SAFT-VR approach is the greatly enhanced accuracy in the near-critical region for chain molecules. This attribute, combined with the accurate modeling of second
Statistical-mechanical theory of a new analytical equation of state
Song, Yuhua; Mason, E. A.
1989-12-01
We present an analytical equation of state based on statistical-mechanical perturbation theory for hard spheres, using the Weeks-Chandler-Andersen decomposition of the potential and the Carnahan-Starling formula for the pair distribution function at contact, g(d+), but with a different algorithm for calculating the effective hard-sphere diameter. The second virial coefficient is calculated exactly. Two temperature-dependent quantities in addition to the second virial coefficient arise, an effective hard-sphere diameter or van der Waals covolume, and a scaling factor for g(d+). Both can be calculated by simple quadrature from the intermolecular potential. If the potential is not known, they can be determined from the experimental second virial coefficient because they are insensitive to the shape of the potential. Two scaling constants suffice for this purpose, the Boyle temperature and the Boyle volume. These could also be determined from analysis of a number of properties other than the second virial coefficient. Thus the second virial coefficient serves to predict the entire equation of state in terms of two scaling parameters, and hence a number of other thermodynamic properties including the Helmholtz free energy, the internal energy, the vapor pressure curve and the orthobaric liquid and vapor densities, and the Joule-Thomson inversion curve, among others. Since it is effectively a two-parameter equation, the equation of state implies a principle of corresponding states. Agreement with computer-simulated results for a Lennard-Jones (12,6) fluid, and with experimental p-v-T data on the noble gases (except He) is quite good, extending up to the limit of available data, which is ten times the critical density for the (12,6) fluid and about three times the critical density for the noble gases. As expected for a mean-field theory, the prediction of the critical constants is only fair, and of the critical exponents is incorrect. Limited testing on the polyatomic
DEFF Research Database (Denmark)
Liang, Xiaodong; Kontogeorgis, Georgios
2015-01-01
The Perturbed Chain-Statistical Associating Fluid Theory Equation of State (PC-SAFT EOS) has been successfully applied to model phase behavior of various types of systems, while it is also well-known that the PC-SAFT EOS has difficulties in describing some second-order derivative properties. In t...
Stemler, Steven E.; Grigorenko, Elena L.; Jarvin, Linda; Sternberg, Robert J.
2006-01-01
Sternberg's theory of successful intelligence was used to create augmented exams in Advanced Placement Psychology and Statistics. Participants included 1895 high school students from 19 states and 56 schools throughout the U.S. The psychometric results support the validity of creating examinations that assess memory, analytical, creative, and…
Directory of Open Access Journals (Sweden)
Lokenath Debnath
1987-01-01
Ramanujan the Man. A brief account of his life, career, and remarkable mathematical contributions is given to describe the gifted talent of Srinivasa Ramanujan. As an example of his creativity in mathematics, some of his work on the theory of partition of numbers has been presented with its application to statistical mechanics.
Schochet, Peter Z.
2015-01-01
This report presents the statistical theory underlying the "RCT-YES" software that estimates and reports impacts for RCTs for a wide range of designs used in social policy research. The report discusses a unified, non-parametric design-based approach for impact estimation using the building blocks of the Neyman-Rubin-Holland causal…
Institute of Scientific and Technical Information of China (English)
许波; 李浩然; 王从敏; 许映杰; 韩世钧
2005-01-01
1H NMR chemical shifts of binary aqueous mixtures of acylamide, alcohol, dimethyl sulphoxide (DMSO), and acetone are correlated by statistical associating fluid theory (SAFT) association model. The comparison between SAFT association model and Wilson equation shows that the former is better for dealing with aqueous solutions. Finally, the specialties of both models are discussed.
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2016-01-01
We non-perturbatively determine the renormalization factor of the axial vector current in lattice QCD with $N_f=3$ flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity and it is imposed among Schr\\"{o}dinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of $\\approx 0.09$ fm and below. An interpolation formula for $Z_A(g_0^2)$, smoothly connecting the non-perturbative values to the 1-loop expression, is provided together with our final results.
Fast Ion Effects on Fishbones and n=1 Kinks in JET Simulated by a Non-perturbative NOVA-KN Code
Energy Technology Data Exchange (ETDEWEB)
N.N. Gorelenkov; C.Z. Cheng; V.G. Kiptily; M.J. Mantsinen; S.E. Sharapov; the JET-EFDA Contributors
2004-10-28
New global non-perturbative hybrid code, NOVA-KN, and simulations of resonant type modes in JET [Joint European Torus] plasmas driven by energetic H-minority ions are presented. The NOVA-KN code employs the ideal-MHD description for the background plasma and treats non-perturbatively the fast particle kinetic response, which includes the fast ion finite orbit width (FOW) effect. In particular, the n = 1 fishbone mode, which is in precession drift resonance with fast ions, is studied. The NOVA-KN code is applied to model an n = 1 (f = 50-80kHz) MHD activity observed recently in JET low density plasma discharges with high fast ion (H-minority) energy content generated during the ion cyclotron resonance heating (ICRH). This n = 1 MHD activity is interpreted as the instability of the n = 1 precession drift frequency fishbone modes.
Zhang, Yang; Máté, Gabriell; Müller, Patrick; Hillebrandt, Sabina; Krufczik, Matthias; Bach, Margund; Kaufmann, Rainer; Hausmann, Michael; Heermann, Dieter W
2015-01-01
It has been well established that the architecture of chromatin in cell nuclei is not random but functionally correlated. Chromatin damage caused by ionizing radiation raises complex repair machineries. This is accompanied by local chromatin rearrangements and structural changes which may for instance improve the accessibility of damaged sites for repair protein complexes. Using stably transfected HeLa cells expressing either green fluorescent protein (GFP) labelled histone H2B or yellow fluorescent protein (YFP) labelled histone H2A, we investigated the positioning of individual histone proteins in cell nuclei by means of high resolution localization microscopy (Spectral Position Determination Microscopy = SPDM). The cells were exposed to ionizing radiation of different doses and aliquots were fixed after different repair times for SPDM imaging. In addition to the repair dependent histone protein pattern, the positioning of antibodies specific for heterochromatin and euchromatin was separately recorded by SPDM. The present paper aims to provide a quantitative description of structural changes of chromatin after irradiation and during repair. It introduces a novel approach to analyse SPDM images by means of statistical physics and graph theory. The method is based on the calculation of the radial distribution functions as well as edge length distributions for graphs defined by a triangulation of the marker positions. The obtained results show that through the cell nucleus the different chromatin re-arrangements as detected by the fluorescent nucleosomal pattern average themselves. In contrast heterochromatic regions alone indicate a relaxation after radiation exposure and re-condensation during repair whereas euchromatin seemed to be unaffected or behave contrarily. SPDM in combination with the analysis techniques applied allows the systematic elucidation of chromatin re-arrangements after irradiation and during repair, if selected sub-regions of nuclei are
Statistical theory of light nucleus reactions with 1p-shell light nuclei
Xiaojun, Sun; Jingshang, Zhang
2017-09-01
The 1p-shell light elements (Li, Be, B, C, N, and O) had long been selected as the most important materials for improving neutron economy in thermal and fast fission reactors and in the design of accelerator-driven spallation neutron sources. A statistical theory of light nucleus reactions (STLN) is proposed to describe the double-differential cross sections for both neutron and light charged particle induced nuclear reactions with 1p-shell light nuclei. The dynamics of STLN is described by the unified Hauser-Feshbach and exciton model, in which the angular momentum and parity conservations are strictly considered in equilibrium and pre-equilibrium processes. The Coulomb barriers of the incoming and outgoing charged particles, which significantly influence the open channels of the reaction, can be reasonably considered in incident channel and different outgoing channels. In kinematics, the recoiling effects in various emission processes are strictly taken into account. The analytical energy and angular spectra of the reaction products in sequential and simultaneous emission processes are obtained in terms of the new integral formula proposed in our recent paper. Taking 12C(n, xn), 9Be(n, xn), 16O(n, xn), and 9Be(p,xn) reactions as examples, we had calculated the double-differential cross sections of outgoing neutrons and compared with the experimental data. In addition, we had also calculated the partition and total kerma coefficients for 12C(n, xn) and 16O(n, xn) reactions, respectively. The existing experimental data can be remarkably well reproduced by STLN, which had been used to set up file-6 in CENDL database.
Statistical theory and transition in multiple-scale-lengths turbulence in plasmas
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I. [Research Institute for Applied Mechanics, Kyushu Univ., Kasuga, Fukuoka (Japan); Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-06-01
The statistical theory of strong turbulence in inhomogeneous plasmas is developed for the cases where fluctuations with different scale-lengths coexist. Nonlinear interactions in the same kind of fluctuations as well as nonlinear interplay between different classes of fluctuations are kept in the analysis. Nonlinear interactions are modelled as turbulent drag, nonlinear noise and nonlinear drive, and a set of Langevin equations is formulated. With the help of an Ansatz of a large number of degrees of freedom with positive Lyapunov number, Langevin equations are solved and the fluctuation dissipation theorem in the presence of strong plasma turbulence has been derived. A case where two driving mechanisms (one for micro mode and the other for semi-micro mode) coexist is investigated. It is found that there are several states of fluctuations: in one state, the micro mode is excited and the semi-micro mode is quenched; in the other state, the semi-micro mode is excited, and the micro mode remains at finite but suppressed level. New type of turbulence transition is obtained, and a cusp type catastrophe is revealed. A phase diagram is drawn for turbulence which is composed of multiple classes of fluctuations. Influence of the inhomogeneous global radial electric field is discussed. A new insight is given for the physics of internal transport barrier. Finally, the nonlocal heat transport due to the long-wave-length fluctuations, which are noise-pumped by shorter-wave-length ones, is analyzed and the impact on transient transport problems is discussed. (author)
Statistical theory and transition in multiple-scale-length turbulence in plasmas
Energy Technology Data Exchange (ETDEWEB)
Itoh, Sanae-I [Research Institute for Applied Mechanics, Kyushu University, Kasuga (Japan); Itoh, Kimitaka [National Institute for Fusion Science, Toki (Japan)
2001-08-01
The statistical theory of strong turbulence in inhomogeneous plasmas is developed for the cases where fluctuations with different scale lengths coexist. Nonlinear interactions in the same kind of fluctuations as well as nonlinear interplay between different classes of fluctuations are kept in the analysis. Nonlinear interactions are modelled as turbulent drag, nonlinear noise and nonlinear drive, and a set of Langevin equations is formulated. With the help of an Ansatz of a large number of degrees of freedom with positive Lyapunov number, Langevin equations are solved and the fluctuation dissipation theorem in the presence of strong plasma turbulence has been derived. A case where two driving mechanisms (one for the micro mode and the other for semi-micro mode) coexist is investigated. It is found that there are several states of fluctuations: in one state, the micro mode is excited and the semi-micro mode is quenched; in the other state, the semi-micro mode is excited, and the micro mode remains at finite but at a suppressed level. A new type of turbulence transition is obtained, and a cusp-type catastrophe is revealed. A phase diagram is drawn for turbulence which is composed of multiple classes of fluctuations. The influence of the inhomogeneous global radial electric field is discussed. A new insight is given for the physics of the internal transport barrier. Finally, the non-local heat transport due to the long-wavelength fluctuations, which are noise-pumped by shorter-wavelength fluctuations, is analysed and its impact on transient transport problems is discussed. (author)
Extraction of business relationships in supply networks using statistical learning theory.
Zuo, Yi; Kajikawa, Yuya; Mori, Junichiro
2016-06-01
Supply chain management represents one of the most important scientific streams of operations research. The supply of energy, materials, products, and services involves millions of transactions conducted among national and local business enterprises. To deliver efficient and effective support for supply chain design and management, structural analyses and predictive models of customer-supplier relationships are expected to clarify current enterprise business conditions and to help enterprises identify innovative business partners for future success. This article presents the outcomes of a recent structural investigation concerning a supply network in the central area of Japan. We investigated the effectiveness of statistical learning theory to express the individual differences of a supply chain of enterprises within a certain business community using social network analysis. In the experiments, we employ support vector machine to train a customer-supplier relationship model on one of the main communities extracted from a supply network in the central area of Japan. The prediction results reveal an F-value of approximately 70% when the model is built by using network-based features, and an F-value of approximately 77% when the model is built by using attribute-based features. When we build the model based on both, F-values are improved to approximately 82%. The results of this research can help to dispel the implicit design space concerning customer-supplier relationships, which can be explored and refined from detailed topological information provided by network structures rather than from traditional and attribute-related enterprise profiles. We also investigate and discuss differences in the predictive accuracy of the model for different sizes of enterprises and types of business communities.
Extraction of business relationships in supply networks using statistical learning theory
Directory of Open Access Journals (Sweden)
Yi Zuo
2016-06-01
Full Text Available Supply chain management represents one of the most important scientific streams of operations research. The supply of energy, materials, products, and services involves millions of transactions conducted among national and local business enterprises. To deliver efficient and effective support for supply chain design and management, structural analyses and predictive models of customer–supplier relationships are expected to clarify current enterprise business conditions and to help enterprises identify innovative business partners for future success. This article presents the outcomes of a recent structural investigation concerning a supply network in the central area of Japan. We investigated the effectiveness of statistical learning theory to express the individual differences of a supply chain of enterprises within a certain business community using social network analysis. In the experiments, we employ support vector machine to train a customer–supplier relationship model on one of the main communities extracted from a supply network in the central area of Japan. The prediction results reveal an F-value of approximately 70% when the model is built by using network-based features, and an F-value of approximately 77% when the model is built by using attribute-based features. When we build the model based on both, F-values are improved to approximately 82%. The results of this research can help to dispel the implicit design space concerning customer–supplier relationships, which can be explored and refined from detailed topological information provided by network structures rather than from traditional and attribute-related enterprise profiles. We also investigate and discuss differences in the predictive accuracy of the model for different sizes of enterprises and types of business communities.
Mavrantzas, Vlasis G.; Beris, Antony N.; Leermakers, Frans; Fleer, Gerard J.
2005-11-01
Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n1,e and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction φ; both n1,e and φ enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z ⩽2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z =2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z ⩽2l, continuum for distances z >2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.
Madriz Aguilar. Jose Edgar; Reyes, Luz Marina; Moreno, Claudia; Bellini, Mauricio
2013-01-01
We develop a non-perturbative formalism for scalar metric fluctuations from a 5D extended version of General Relativity in vacuum. In this work we concentrate our efforts on calculations valid on large cosmological scales, which are the dominant during the inflationary phase of the universe. The resulting metric on this limit case is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution. We calculate the spectrum of these fluctuations on an ...
Arbuzov, B. A.; Zaitsev, I. V.
2017-09-01
Assuming an existence of the anomalous triple electro-weak bosons interaction being defined by coupling constant λ we calculate its contribution to interactions of the Higgs with pairs of heavy particles. Bearing in mind experimental restrictions - 0.011 production with the Higgs. In calculations we rely on results of the non-perturbative approach to a spontaneous generation of effective interactions, which defines the form-factor of the three-boson anomalous interaction.
Larwin, Karen H.; Larwin, David A.
2011-01-01
Bootstrapping methods and random distribution methods are increasingly recommended as better approaches for teaching students about statistical inference in introductory-level statistics courses. The authors examined the effect of teaching undergraduate business statistics students using random distribution and bootstrapping simulations. It is the…
Larwin, Karen H.; Larwin, David A.
2011-01-01
Bootstrapping methods and random distribution methods are increasingly recommended as better approaches for teaching students about statistical inference in introductory-level statistics courses. The authors examined the effect of teaching undergraduate business statistics students using random distribution and bootstrapping simulations. It is the…
Kalinichenko, Igor; Kazinski, Peter
2014-08-01
The explicit expressions for the one-loop non-perturbative corrections to the gravitational effective action induced by a scalar field on a stationary gravitational background are obtained both at zero and finite temperatures. The perturbative and non-perturbative contributions to the one-loop effective action are explicitly separated. It is proved that, after a suitable renormalization, the perturbative part of the effective action at zero temperature can be expressed in a covariant form solely in terms of the metric and its derivatives. This part coincides with the known large mass expansion of the one-loop effective action. The non-perturbative part of the renormalized one-loop effective action at zero temperature is proved to depend explicitly on the Killing vector defining the vacuum state of quantum fields. This part cannot be expressed in a covariant way through the metric and its derivatives alone. The implications of this result for the structure and symmetries of the effective action for gravity are discussed.
Kalinichenko, I S
2014-01-01
The explicit expressions for the one-loop non-perturbative corrections to the gravitational effective action induced by a scalar field on a stationary gravitational background are obtained both at zero and finite temperatures. The perturbative and non-perturbative contributions to the one-loop effective action are explicitly separated. It is proved that, after a suitable renormalization, the perturbative part of the effective action at zero temperature can be expressed in a covariant form solely in terms of the metric and its derivatives. This part coincides with the known large mass expansion of the one-loop effective action. The non-perturbative part of the renormalized one-loop effective action at zero temperature is proved to depend explicitly on the Killing vector defining the vacuum state of quantum fields. This part cannot be expressed in a covariant way through the metric and its derivatives alone. The implications of this result for the structure and symmetries of the effective action for gravity are...
K. Vela Velupillai
2010-01-01
The digital and information technology revolutions are based on algorithmic mathematics in many of their alternative forms. Algorithmic mathematics per se is not necessarily underpinned by the digital or the discrete only; analogue traditions of algorithmic mathematics have a noble pedigree, even in economics. Constructive mathematics of any variety, computability theory and non-standard analysis are intrinsically algorithmic at their foundations. Economic theory, game theory and mathematical...
Lectures on Matrix Field Theory
Ydri, Badis
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.
Slimani, N.
2002-01-01
Large multi-centre cohort studies have been set up with the aim of increasing the statistical power to detect an association between diet and disease by including study populations varying both in dietary exposures and outcome diseases. However, such studies raise also new statistical and methodolog
Probability theory and statistical applications a profound treatise for self-study
Zörnig, Peter
2016-01-01
This accessible and easy-to-read book provides many examples to illustrate diverse topics in probability and statistics, from initial concepts up to advanced calculations. Special attention is devoted e.g. to independency of events, inequalities in probability and functions of random variables. The book is directed to students of mathematics, statistics, engineering, and other quantitative sciences.
Energy Technology Data Exchange (ETDEWEB)
Blumenfeld, R.
1994-07-01
The evolution of two dimensional interfaces in a Laplacian field is discussed. By mapping the growing region conformally onto the unit disk, the problem is converted to the dynamics of a many-body system. This problem is shown to be Hamiltonian. An extension of the many body approach to a continuous density is discussed. The Hamiltonian structure allows introduction of surface effects as an external field. These results are used to formulate a first-principles statistical theory for the morphology of the interface using statistical mechanics for the many-body system.
Brazhnik, Olga D.; Freed, Karl F.
1996-07-01
The lattice cluster theory (LCT) is extended to enable inclusion of longer range correlation contributions to the partition function of lattice model polymers in the athermal limit. A diagrammatic technique represents the expansion of the partition function in powers of the inverse lattice coordination number. Graph theory is applied to sort, classify, and evaluate the numerous diagrams appearing in higher orders. New general theorems are proven that provide a significant reduction in the computational labor required to evaluate the contributions from higher order correlations. The new algorithm efficiently generates the correction to the Flory mean field approximation from as many as eight sterically interacting bonds. While the new results contain the essential ingredients for treating a system of flexible chains with arbitrary lengths and concentrations, the complexity of our new algorithm motivates us to test the theory here for the simplest case of a system of lattice dimers by comparison to the dimer packing entropies from the work of Gaunt. This comparison demonstrates that the eight bond LCT is exact through order φ5 for dimers in one through three dimensions, where φ is the volume fraction of dimers. A subsequent work will use the contracted diagrams, derived and tested here, to treat the packing entropy for a system of flexible N-mers at a volume fraction of φ on hypercubic lattices.
Statistical and Managerial Techniques for Six Sigma Methodology Theory and Application
Barone, Stefano
2012-01-01
Statistical and Managerial Techniques for Six Sigma Methodology examines the methodology through illustrating the most widespread tool and techniques involved in Six Sigma application. Both managerial and statistical aspects of Six Sigma will be analyzed, allowing the reader to apply these tools in the field. This book offers an insight on variation and risk management, and focuses on the structure and organizational aspects of the Six Sigma projects. It covers six sigma methodology, basic managerial techniques, basic statistical techniques, methods for variation and risk management and advanc
Degenerate U- and V-statistics under weak dependence: Asymptotic theory and bootstrap consistency
Leucht, Anne
2012-01-01
We devise a general result on the consistency of model-based bootstrap methods for U- and V-statistics under easily verifiable conditions. For that purpose, we derive the limit distributions of degree-2 degenerate U- and V-statistics for weakly dependent $\\mathbb{R}^d$-valued random variables first. To this end, only some moment conditions and smoothness assumptions concerning the kernel are required. Based on this result, we verify that the bootstrap counterparts of these statistics have the same limit distributions. Finally, some applications to hypothesis testing are presented.
Instanton Effects in Orientifold ABJM Theory
Moriyama, Sanefumi
2015-01-01
We investigate another supersymmetric Chern-Simons theory called orientifold ABJM theory, which replaces the unitary supergroup structure of the ABJM theory by an orthosymplectic one. The non-perturbative structure of it is completely clarified by considering the duplication of the quiver.
Bruno Del Papa
2014-01-01
This dissertation explores some applications of statistical mechanics and information theory tools to topics of interest in anthropology, social sciences, and economics. We intended to develop mathematical and computational models with empirical and theoretical bases aiming to identify important features of two problems: the transitions between egalitarian and hierarchical societies and the emergence of money in human societies. Anthropological data suggest the existence of a correlation ...
Kawano, T; Hilaire, S
2016-01-01
A model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenm\\"{u}ller. The ensemble average of $S$-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [Phys.Rev.C {\\bf 12}, 744 (1975)] using newly parametrized channel degree-of-freedom $\
Directory of Open Access Journals (Sweden)
Tianhao Wu
2016-09-01
Full Text Available While firm-level and micro issue analysis become an important part in research of international trade, only a few work is concerned about the goodness-of-fit for size distribution of firms. In this paper, we revisit the statistical aspects of firm productivity and sales revenue, in order to compare different definitions of statistical distances. We first deduce the exact form of size distribution of firms by only implementing the assumptions of productivity and demand function, and then introduce the famous g-divergence as well as its statistical implications. We also do the simulation and calibration so as to compare those different divergences, moreover, tests the combined assumptions. We conclude that minimizing Pearson χ2 and Neyman χ2 produces similar results and minimizing Kullback-Leibler divergence is likely to take the expense of other distance measures. Additionally, selection among different statistical distances is much more significant than demand functions
Statistical mechanical theory for and simulations of charged fluids and water
Rodgers, Jocelyn Michelle
Treatment of electrostatic interactions in simulations remains a topic of current research. These interactions are present in most biomolecular simulations, and they remain an expensive part of the simulation. Herein we explore the application of local molecular field (LMF) theory to this problem. Local molecular field theory splits the Coulomb potential 1/r into short-ranged and long-ranged components. The short-ranged component may be treated explicitly in simulations and the long-ranged component is contained in a mean-field-like average external electrostatic potential. In this thesis, the derivations and approximations inherent in using the previously developed LMF theory are explored, and connections to classical electrostatics are made. Further the approach is justified for molecular systems. The application of LMF theory to several systems is explored. First, a simple system of uniformly charged walls with neutralizing counterions is treated via simulations using LMF theory. We then explore systems involving molecular water at ambient conditions. A simple approximation to LMF theory using only the short-ranged component of 1/r is quite powerful for bulk water. A full treatment using LMF theory extends the validity of such spherical truncations to nonuniform systems. This thesis studies the successful treatment of water confined between hydrophobic walls with and without an applied electric field---a system which is a classic example of the failings of spherical truncations in molecular simulations. Additional results exemplify the applicability of LMF simulations to more molecularly realistic simulations. Connection is also made between these simulations of confined water and a related theory of hydrophobicity due to Lum, Chandler, and Weeks (1999).
Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory
2016-05-12
SECURITY CLASSIFICATION OF: Three areas were investigated. First, new memory models of discrete-time and finitely-valued information sources are...computational and storage complexities are proved. Second, a statistical method is developed to estimate the memory depth of discrete-time and continuously...Distribution Unlimited UU UU UU UU 12-05-2016 15-May-2014 14-Feb-2015 Final Report: Statistical Inference on Memory Structure of Processes and Its Applications
Energy Technology Data Exchange (ETDEWEB)
Mannel, T. [Siegen Univ. (Germany). FB 7, Theoretische Physik; Pecjak, B.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pivovarov, A.A. [Siegen Univ. (Germany). FB 7, Theoretische Physik]|[Russian Academy of Sciecnes, Moscow (Russian Federation). Inst. for Nuclear Research
2007-03-15
We use QCD sum rules to compute matrix elements of the {delta}B=2 operators appearing in the heavy-quark expansion of the width difference of the B{sub s} mass eigenstates. Our analysis includes the leading-order operators Q and Q{sub S}, as well as the subleading operators R{sub 2} and R{sub 3}, which appear at next-to-leading order in the 1/m{sub b} expansion. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1-2%. (orig.)
Sadovskii, Michael V
2012-01-01
This volume provides a compact presentation of modern statistical physics at an advanced level. Beginning with questions on the foundations of statistical mechanics all important aspects of statistical physics are included, such as applications to ideal gases, the theory of quantum liquids and superconductivity and the modern theory of critical phenomena. Beyond that attention is given to new approaches, such as quantum field theory methods and non-equilibrium problems.
Mathematical-statistical models and qualitative theories for economic and social sciences
Maturo, Fabrizio; Kacprzyk, Janusz
2017-01-01
This book presents a broad spectrum of problems related to statistics, mathematics, teaching, social science, and economics as well as a range of tools and techniques that can be used to solve these problems. It is the result of a scientific collaboration between experts in the field of economic and social systems from the University of Defence in Brno (Czech Republic), G. d’Annunzio University of Chieti-Pescara (Italy), Pablo de Olavid eUniversity of Sevilla (Spain), and Ovidius University in Constanţa, (Romania). The studies included were selected using a peer-review process and reflect heterogeneity and complexity of economic and social phenomena. They and present interesting empirical research from around the globe and from several research fields, such as statistics, decision making, mathematics, complexity, psychology, sociology and economics. The volume is divided into two parts. The first part, “Recent trends in mathematical and statistical models for economic and social sciences”, collects pap...
Krawczyk, Jaroslaw; Croce, Salvatore; Chakrabarti, Buddhapriya; Tasche, Jos
The surface segregation in polymer mixtures remains a challenging problem for both academic exploration as well as industrial applications. Despite its ubiquity and several theoretical attempts a good agreement between computed and experimentally observed profiles has not yet been achieved. A simple theoretical model proposed in this context by Schmidt and Binder combines Flory-Huggins free energy of mixing with the square gradient theory of wetting of a wall by fluid. While the theory gives us a qualitative understanding of the surface induced segregation and the surface enrichment it lacks the quantitative comparison with the experiment. The statistical associating fluid theory (SAFT) allows us to calculate accurate free energy for a real polymeric materials. In an earlier work we had shown that increasing the bulk modulus of a polymer matrix through which small molecules migrate to the free surface causes reduction in the surface migrant fraction using Schmidt-Binder and self-consistent field theories. In this work we validate this idea by combining mean field theories and SAFT to identify parameter ranges where such an effect should be observable. Department of Molecular Physics, Łódź University of Technology, Żeromskiego 116, 90-924 Łódź, Poland.
An NCME Instructional Module on Item-Fit Statistics for Item Response Theory Models
Ames, Allison J.; Penfield, Randall D.
2015-01-01
Drawing valid inferences from item response theory (IRT) models is contingent upon a good fit of the data to the model. Violations of model-data fit have numerous consequences, limiting the usefulness and applicability of the model. This instructional module provides an overview of methods used for evaluating the fit of IRT models. Upon completing…
A tool for GNSS integrity verification based on statistical extreme value theory
Veerman, H.; Van Kleef, A.; Wokke, F.; Ober, O.; Tiberius, C.C.J.M.; Verhagen, A.A.; Bos, A.; Mieremet, A.
2012-01-01
The paper presents a short introduction to the mathematical theory of the EVT, the consecutive steps that are made in the software tool to address MI probability estimation and proof of range error distribution overbounding. Finally some early results obtained by GIMAT are presented.
Quasi-chemical Theory for the Statistical Thermodynamics of the Hard Sphere Fluid
Pratt, L R; Gómez, M A; Gentile, M E; Pratt, Lawrence R.; Violette, Randall A. La; Gomez, Maria A.; Gentile, Mary E.
2001-01-01
We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situation of hard-core interactions is addressed by considering the binding of solvent molecules to a precisely defined `cavity' in order to assess the probability that the `cavity' is entirely evacuated. The primitive quasi-chemical approximation corresponds to a extension of the Poisson distribution used as a default model in an information theory approach. This primitive quasi-chemical theory is in good qualitative agreement with the observations for the hard sphere fluid of occupancy distributions that are central to quasi-chemical theories but begins to be quantitatively erroneous for the equation of state in the dense liquid regime of $\\rho d^3>$0.6. How the quasi-chemical approach can be iterated to treat correlation effects is addressed. Consideration of neglected correlation effects leads to a simple model for the form of those contributions neglected by the primitive quasi-chemical approximation. These c...
Plasma-statistical models of the atom in the theory of some collisional and radiative processes
Astapenko, VA
2002-01-01
A plasma-statistical model was used to describe collisional and radiative processes involving target ionization, namely, collisional ionization of atoms and incoherent polarization bremsstrahlung. The cross sections of these processes were expressed through the Compton profile of X-ray scattering, f
Basic properties and information theory of Audic-Claverie statistic for analyzing cDNA arrays
Tiňo, Peter
2009-01-01
Background The Audic-Claverie method [1] has been and still continues to be a popular approach for detection of differentially expressed genes in the SAGE framework. The method is based on the assumption that under the null hypothesis tag counts of the same gene in two libraries come from the same but unknown Poisson distribution. The problem is that each SAGE library represents only a single measurement. We ask: Given that the tag count samples from SAGE libraries are extremely limited, how useful actually is the Audic-Claverie methodology? We rigorously analyze the A-C statistic that forms a backbone of the methodology and represents our knowledge of the underlying tag generating process based on one observation. Results We show that the A-C statistic and the underlying Poisson distribution of the tag counts share the same mode structure. Moreover, the K-L divergence from the true unknown Poisson distribution to the A-C statistic is minimized when the A-C statistic is conditioned on the mode of the Poisson distribution. Most importantly, the expectation of this K-L divergence never exceeds 1/2 bit. Conclusion A rigorous underpinning of the Audic-Claverie methodology has been missing. Our results constitute a rigorous argument supporting the use of Audic-Claverie method even though the SAGE libraries represent very sparse samples. PMID:19775462
Cosmic Statistics of Statistics
Szapudi, I.; Colombi, S.; Bernardeau, F.
1999-01-01
The errors on statistics measured in finite galaxy catalogs are exhaustively investigated. The theory of errors on factorial moments by Szapudi & Colombi (1996) is applied to cumulants via a series expansion method. All results are subsequently extended to the weakly non-linear regime. Together with previous investigations this yields an analytic theory of the errors for moments and connected moments of counts in cells from highly nonlinear to weakly nonlinear scales. The final analytic formu...