Mean-field theory for a ferroelectric transition

International Nuclear Information System (INIS)

Dobry, A.; Greco, A.; Stachiotti, M.

1990-01-01

For the treatment of anharmonic models of solids presenting structural transitions, a commonly used approximation is that of self-consistent phonons. Rather than the usual site decoupling, this mean-field theory is based on decoupling of modes in reciprocal space. A self-consistent phonon approximation for the non-linear polarizability model is developed in this work. The model describes the dynamical properties of ferroelectric materials. Phase diagrams as a function of relevant model parameters are presented. An analysis is made of critical behaviour and it is shown that the approximation leads to the same anomalies found in other models. (Author). 9 refs., 3 figs

Thermodynamically self-consistent theory for the Blume-Capel model.

Science.gov (United States)

Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G

2001-04-01

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

MFPred: Rapid and accurate prediction of protein-peptide recognition multispecificity using self-consistent mean field theory.

Directory of Open Access Journals (Sweden)

Aliza B Rubenstein

2017-06-01

Full Text Available Multispecificity-the ability of a single receptor protein molecule to interact with multiple substrates-is a hallmark of molecular recognition at protein-protein and protein-peptide interfaces, including enzyme-substrate complexes. The ability to perform structure-based prediction of multispecificity would aid in the identification of novel enzyme substrates, protein interaction partners, and enable design of novel enzymes targeted towards alternative substrates. The relatively slow speed of current biophysical, structure-based methods limits their use for prediction and, especially, design of multispecificity. Here, we develop a rapid, flexible-backbone self-consistent mean field theory-based technique, MFPred, for multispecificity modeling at protein-peptide interfaces. We benchmark our method by predicting experimentally determined peptide specificity profiles for a range of receptors: protease and kinase enzymes, and protein recognition modules including SH2, SH3, MHC Class I and PDZ domains. We observe robust recapitulation of known specificities for all receptor-peptide complexes, and comparison with other methods shows that MFPred results in equivalent or better prediction accuracy with a ~10-1000-fold decrease in computational expense. We find that modeling bound peptide backbone flexibility is key to the observed accuracy of the method. We used MFPred for predicting with high accuracy the impact of receptor-side mutations on experimentally determined multispecificity of a protease enzyme. Our approach should enable the design of a wide range of altered receptor proteins with programmed multispecificities.

Self-consistent field theory based molecular dynamics with linear system-size scaling

Energy Technology Data Exchange (ETDEWEB)

Richters, Dorothee [Institute of Mathematics and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 9, D-55128 Mainz (Germany); Kühne, Thomas D., E-mail: kuehne@uni-mainz.de [Institute of Physical Chemistry and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 7, D-55128 Mainz (Germany); Technical and Macromolecular Chemistry, University of Paderborn, Warburger Str. 100, D-33098 Paderborn (Germany)

2014-04-07

We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is circumvented by means of a properly modified Langevin equation. The predictive power of the present approach is illustrated using the example of liquid methane under extreme conditions.

Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.

Science.gov (United States)

Chou, Yen-Liang; Ihle, Thomas

2015-02-01

Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media.

Science.gov (United States)

Ma, Manman; Xu, Zhenli

2014-12-28

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media

Energy Technology Data Exchange (ETDEWEB)

Ma, Manman, E-mail: mmm@sjtu.edu.cn; Xu, Zhenli, E-mail: xuzl@sjtu.edu.cn [Department of Mathematics, Institute of Natural Sciences, and MoE Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240 (China)

2014-12-28

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.

Vibrational multiconfiguration self-consistent field theory: implementation and test calculations.

Science.gov (United States)

Heislbetz, Sandra; Rauhut, Guntram

2010-03-28

A state-specific vibrational multiconfiguration self-consistent field (VMCSCF) approach based on a multimode expansion of the potential energy surface is presented for the accurate calculation of anharmonic vibrational spectra. As a special case of this general approach vibrational complete active space self-consistent field calculations will be discussed. The latter method shows better convergence than the general VMCSCF approach and must be considered the preferred choice within the multiconfigurational framework. Benchmark calculations are provided for a small set of test molecules.

Self consistent field theory of virus assembly

Science.gov (United States)

Li, Siyu; Orland, Henri; Zandi, Roya

2018-04-01

The ground state dominance approximation (GSDA) has been extensively used to study the assembly of viral shells. In this work we employ the self-consistent field theory (SCFT) to investigate the adsorption of RNA onto positively charged spherical viral shells and examine the conditions when GSDA does not apply and SCFT has to be used to obtain a reliable solution. We find that there are two regimes in which GSDA does work. First, when the genomic RNA length is long enough compared to the capsid radius, and second, when the interaction between the genome and capsid is so strong that the genome is basically localized next to the wall. We find that for the case in which RNA is more or less distributed uniformly in the shell, regardless of the length of RNA, GSDA is not a good approximation. We observe that as the polymer-shell interaction becomes stronger, the energy gap between the ground state and first excited state increases and thus GSDA becomes a better approximation. We also present our results corresponding to the genome persistence length obtained through the tangent-tangent correlation length and show that it is zero in case of GSDA but is equal to the inverse of the energy gap when using SCFT.

The Plumber’s Nightmare Phase in Diblock Copolymer/Homopolymer Blends. A Self-Consistent Field Theory Study.

KAUST Repository

Martinez-Veracoechea, Francisco J.

2009-11-24

Using self-consistent field theory, the Plumber\\'s Nightmare and the double diamond phases are predicted to be stable in a finite region of phase diagrams for blends of AB diblock copolymer (DBC) and A-component homopolymer. To the best of our knowledge, this is the first time that the P phase has been predicted to be stable using self-consistent field theory. The stabilization is achieved by tuning the composition or conformational asymmetry of the DBC chain, and the architecture or length of the homopolymer. The basic features of the phase diagrams are the same in all cases studied, suggesting a general type of behavior for these systems. Finally, it is noted that the homopolymer length should be a convenient variable to stabilize bicontinuous phases in experiments. © 2009 American Chemical Society.

Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

Energy Technology Data Exchange (ETDEWEB)

Hahn, Y.K., E-mail: ykhahn22@verizon.net

2014-12-15

The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the

The Plumber’s Nightmare Phase in Diblock Copolymer/Homopolymer Blends. A Self-Consistent Field Theory Study.

KAUST Repository

Martinez-Veracoechea, Francisco J.; Escobedo, Fernando A.

2009-01-01

Using self-consistent field theory, the Plumber's Nightmare and the double diamond phases are predicted to be stable in a finite region of phase diagrams for blends of AB diblock copolymer (DBC) and A-component homopolymer. To the best of our

Quark mean field theory and consistency with nuclear matter

International Nuclear Information System (INIS)

Dey, J.; Tomio, L.; Dey, M.; Frederico, T.

1989-01-01

1/N c expansion in QCD (with N c the number of colours) suggests using a potential from meson sector (e.g. Richardson) for baryons. For light quarks a σ field has to be introduced to ensure chiral symmetry breaking ( χ SB). It is found that nuclear matter properties can be used to pin down the χ SB-modelling. All masses, M Ν , m σ , m ω are found to scale with density. The equations are solved self consistently. (author)

Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics

DEFF Research Database (Denmark)

Miyagi, Haruhide; Madsen, Lars Bojer

2013-01-01

We present the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory as a framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme...... well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high...

Relativistic four-component multiconfigurational self-consistent-field theory for molecules

DEFF Research Database (Denmark)

Jensen, Hans Jørgen Aa; Dyall, Kenneth G.; Saue, Trond

1996-01-01

A formalism for relativistic four-component multiconfigurational self-consistent-field calculations on molecules is presented. The formalism parallels a direct second-order restricted-step algorithm developed for nonrelativistic molecular calculations. The presentation here focuses on the differe......A formalism for relativistic four-component multiconfigurational self-consistent-field calculations on molecules is presented. The formalism parallels a direct second-order restricted-step algorithm developed for nonrelativistic molecular calculations. The presentation here focuses...... the memory used by the largest nonrelativistic calculation in the equivalent basis, due to the complex arithmetic. The feasibility of the calculations is then determined more by the disk space for storage of integrals and N-particle expansion vectors....

Quantitative verification of ab initio self-consistent laser theory.

Science.gov (United States)

Ge, Li; Tandy, Robert J; Stone, A D; Türeci, Hakan E

2008-10-13

We generalize and test the recent "ab initio" self-consistent (AISC) time-independent semiclassical laser theory. This self-consistent formalism generates all the stationary lasing properties in the multimode regime (frequencies, thresholds, internal and external fields, output power and emission pattern) from simple inputs: the dielectric function of the passive cavity, the atomic transition frequency, and the transverse relaxation time of the lasing transition.We find that the theory gives excellent quantitative agreement with full time-dependent simulations of the Maxwell-Bloch equations after it has been generalized to drop the slowly-varying envelope approximation. The theory is infinite order in the non-linear hole-burning interaction; the widely used third order approximation is shown to fail badly.

Quark mean field theory and consistency with nuclear matter

International Nuclear Information System (INIS)

Dey, J.; Dey, M.; Frederico, T.; Tomio, L.

1990-09-01

1/N c expansion in QCD (with N c the number of colours) suggests using a potential from meson sector (e.g. Richardson) for baryons. For light quarks a σ field has to be introduced to ensure chiral symmetry breaking ( χ SB). It is found that nuclear matter properties can be used to pin down the χ SB-modelling. All masses, M N , m σ , m ω are found to scale with density. The equations are solved self consistently. (author). 29 refs, 2 tabs

Mean field theory for a balanced hypercolumn model of orientation selectivity in primary visual cortex

DEFF Research Database (Denmark)

Lerchner, Alexander; Sterner, G.; Hertz, J.

2006-01-01

We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn, with a numerical procedure for solving the mean-field equations quantitatively. With our treatment, one can determine self-consistently both the firing rates and the firing correlations...

Diffusion and coupled fluxes in concentrated alloys under irradiation: a self-consistent mean-field approach

International Nuclear Information System (INIS)

Nastar, M.

2008-01-01

When an alloy is irradiated, atomic transport can occur through the two types of defects which are created: vacancies and interstitials. Recent developments of the self-consistent mean field (SCMF) kinetic theory could treat within the same formalism diffusion due to vacancies and interstitials in a multi-component alloy. It starts from a microscopic model of the atomic transport via vacancies and interstitials and yields the fluxes with a complete Onsager matrix of the phenomenological coefficients. The jump frequencies depend on the local environment through a 'broken bond model' such that the large range of frequencies involved in concentrated alloys is produced by a small number of thermodynamic and kinetic parameters. Kinetic correlations are accounted for through a set of time-dependent effective interactions within a non-equilibrium distribution function of the system. The different approximations of the SCMF theory recover most of the previous diffusion models. Recent improvements of the theory were to extend the multi-frequency approach usually restricted to dilute alloys to diffusion in concentrated alloys with jump frequencies depending on local concentrations and to generalize the formalism first developed for the vacancy diffusion mechanism to the more complex diffusion mechanism of the interstitial in the dumbbell configuration. (author)

Adsorption of molecular brushes with polyelectrolyte backbones onto oppositely charged surfaces: A self-consistent field theory

NARCIS (Netherlands)

Feuz, L.; Leermakers, F.A.M.; Textor, M.; Borisov, O.V.

2008-01-01

The two-gradient version of the Scheutjens¿Fleer self-consistent field (SF-SCF) theory is employed to model the interaction between a molecular bottle brush with a polyelectrolyte backbone and neutral hydrophilic side chains and an oppositely charged surface. Our system mimics graft-copolymers with

Persistence length of wormlike micelles composed of ionic surfactants: self-consistent-field predictions

NARCIS (Netherlands)

Lauw, Y.; Leermakers, F.A.M.; Cohen Stuart, M.A.

2007-01-01

The persistence length of a wormlike micelle composed of ionic surfactants CnEmXk in an aqueous solvent is predicted by means of the self-consistent-field theory where CnEm is the conventional nonionic surfactant and X-k is an additional sequence of k weakly charged (pH-dependent) segments. By

Approximate self-consistent potentials for density-functional-theory exchange-correlation functionals

International Nuclear Information System (INIS)

Cafiero, Mauricio; Gonzalez, Carlos

2005-01-01

We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

Science.gov (United States)

Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

2016-07-12

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

Renormalization in self-consistent approximation schemes at finite temperature I: theory

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-07-01

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)

A self-consistent two-dimensional resistive fluid theory of field-aligned potential structures including charge separation and magnetic and velocity shear

International Nuclear Information System (INIS)

Hesse, M.; Birn, J.; Schindler, K.

1990-01-01

A self-consistent two-fluid theory that includes the magnetic field and shear patterns therein is developed to model stationary electrostatic structures with field-aligned potential drops. Shear flow is also included in the theory since this seems to be a prominent feature of the structures of interest. In addition, Ohmic dissipation, a Hall term and pressure gradients in a generalized Ohm's law, modified for cases without quasi-neutrality are included. In the analytic theory, the electrostatic force is balanced by field-aligned pressure gradients, i.e., thermal effects in the direction of the magnetic field, and by pressure gradients and magnetic stresses in the perpendicular direction. Within this theory simple examples of applications are presented to demonstrate the kind of solutions resulting from the model. The results show how the effects of charge separation and shear in the magnetic field and the velocity can be combined to form self-consistent structures such as are found to exist above the aurora, suggested also in association with solar flares

Time independent mean-field theory

International Nuclear Information System (INIS)

Negele, J.W.

1980-02-01

The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures

Liking for Evaluators: Consistency and Self-Esteem Theories

Science.gov (United States)

Regan, Judith Weiner

1976-01-01

Consistency and self-esteem theories make contrasting predictions about the relationship between a person's self-evaluation and his liking for an evaluator. Laboratory experiments confirmed predictions about these theories. (Editor/RK)

Exotic nuclei in self-consistent mean-field models

International Nuclear Information System (INIS)

Bender, M.; Rutz, K.; Buervenich, T.; Reinhard, P.-G.; Maruhn, J. A.; Greiner, W.

1999-01-01

We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei with emphasis on neutron-rich tin isotopes and superheavy nuclei. (c) 1999 American Institute of Physics

Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

Science.gov (United States)

Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

2012-01-21

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

Naturalness of Nonlinear Scalar Self-Couplings in a Relativistic Mean Field Theory for Neutron Stars

International Nuclear Information System (INIS)

Maekawa, Claudio; Razeira, Moises; Vasconcellos, Cesar A. Z.; Dillig, Manfred; Bodmann, Bardo E. J.

2004-01-01

We investigate the role of naturalness in effective field theory. We focus on dense hadronic matter using a generalized relativistic multi-baryon lagrangian density mean field approach which contains nonlinear self-couplings of the σ, δ meson fields and the fundamental baryon octet. We adjust the model parameters to describe bulk static properties of ordinary nuclear matter. Then, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars

Odd-even mass differences from self-consistent mean field theory

International Nuclear Information System (INIS)

Bertsch, G. F.; Bertulani, C. A.; Nazarewicz, W.; Schunck, N.; Stoitsov, M. V.

2009-01-01

We survey odd-even nuclear binding energy staggering using density functional theory with several treatments of the pairing interaction including the BCS, Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami approximation. We calculate the second difference of binding energies and compare the results with 443 measured neutron energy differences in isotope chains and 418 measured proton energy differences in isotone chains. The particle-hole part of the energy functional is taken as the SLy4 Skyrme parametrization, and the pairing part of the functional is based on a contact interaction with possible density dependence. An important feature of the data, reproduced by the theory, is the sharp gap quenching at magic numbers. With the strength of the interaction as a free parameter, the theory can reproduce the data to an rms accuracy of about 0.25 MeV. This is slightly better than a single-parameter phenomenological description but slightly poorer than the usual two-parameter phenomenological form c/A α . The following conclusions can be made about the performance of common parametrization of the pairing interaction: (i) there is a weak preference for a surface-peaked neutron-neutron pairing, which might be attributable to many-body effects, (ii) a larger strength is required in the proton pairing channel than in the neutron pairing channel, and (iii) pairing strengths adjusted to the well-known spherical isotope chains are too weak to give a good overall fit to the mass differences

Mean-field theory and solitonic matter

International Nuclear Information System (INIS)

Cohen, T.D.

1989-01-01

Finite density solitonic matter is considered in the context of quantum field theory. Mean-field theory, which provides a reasonable description for single-soliton properties gives rise to a crystalline description. A heuristic description of solitonic matter is given which shows that the low-density limit of solitonic matter (the limit which is presumably relevant for nuclear matter) does not commute with the mean-field theory limit and gives rise to a Fermi-gas description of the system. It is shown on the basis of a formal expansion of simple soliton models in terms of the coupling constant why one expects mean-field theory to fail at low densities and why the corrections to mean-field theory are nonperturbative. This heuristic description is tested against an exactly solvable 1+1 dimensional model (the sine-Gordon model) and found to give the correct behavior. The relevance of these results to the program of doing nuclear physics based on soliton models is discussed. (orig.)

Probabilistic theory of mean field games with applications

CERN Document Server

Carmona, René

2018-01-01

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...

The nuclear N-body problem and the effective interaction in self-consistent mean-field methods

International Nuclear Information System (INIS)

Duguet, Thomas

2002-01-01

This work deals with two aspects of mean-field type methods extensively used in low-energy nuclear structure. The first study is at the mean-field level. The link between the wave-function describing an even-even nucleus and the odd-even neighbor is revisited. To get a coherent description as a function of the pairing intensity in the system, the utility of the formalization of this link through a two steps process is demonstrated. This two-steps process allows to identify the role played by different channels of the force when a nucleon is added in the system. In particular, perturbative formula evaluating the contribution of time-odd components of the functional to the nucleon separation energy are derived for zero and realistic pairing intensities. Self-consistent calculations validate the developed scheme as well as the derived perturbative formula. This first study ends up with an extended analysis of the odd-even mass staggering in nuclei. The new scheme allows to identify the contribution to this observable coming from different channels of the force. The necessity of a better understanding of time-odd terms in order to decide which odd-even mass formulae extracts the pairing gap the most properly is identified. These terms being nowadays more or less out of control, extended studies are needed to make precise the fit of a pairing force through the comparison of theoretical and experimental odd-even mass differences. The second study deals with beyond mean-field methods taking care of the correlations associated with large amplitude oscillations in nuclei. Their effects are usually incorporated through the GCM or the projected mean-field method. We derive a perturbation theory motivating such variational calculations from a diagrammatic point of view for the first time. Resuming two-body correlations in the energy expansion, we obtain an effective interaction removing the hard-core problem in the context of configuration mixing calculations. Proceeding to a

Self-consistent-field calculations of proteinlike incorporations in polyelectrolyte complex micelles

NARCIS (Netherlands)

Lindhoud, S.; Cohen Stuart, M.A.; Norde, W.; Leermakers, F.A.M.

2009-01-01

Self-consistent field theory is applied to model the structure and stability of polyelectrolyte complex micelles with incorporated protein (molten globule) molecules in the core. The electrostatic interactions that drive the micelle formation are mimicked by nearest-neighbor interactions using

Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions

DEFF Research Database (Denmark)

Als-Nielsen, Jens Aage; Birgenau, R. J.

1977-01-01

By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...... in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated...

General variational many-body theory with complete self-consistency for trapped bosonic systems

International Nuclear Information System (INIS)

Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.

2006-01-01

In this work we develop a complete variational many-body theory for a system of N trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue--generally integro-differential--equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or MCHB(M), where M specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states

Self-consistent Random Phase Approximation applied to a schematic model of the field theory

International Nuclear Information System (INIS)

Bertrand, Thierry

1998-01-01

The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum

Mean-field magnetohydrodynamics and dynamo theory

CERN Document Server

Krause, F

2013-01-01

Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen

Mean field theories and dual variation mathematical structures of the mesoscopic model

CERN Document Server

Suzuki, Takashi

2015-01-01

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics.  spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature.  The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.

Orbital effect of the magnetic field in dynamical mean-field theory

Science.gov (United States)

Acheche, S.; Arsenault, L.-F.; Tremblay, A.-M. S.

2017-12-01

The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate, and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.

Quantum mean-field theory of collective dynamics and tunneling

International Nuclear Information System (INIS)

Negele, J.W.

1981-01-01

A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures

Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems

International Nuclear Information System (INIS)

Sandvik, A.W.

1999-01-01

A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C 0 is modeled by a number of neighboring chains C δ , δ=±1, hor-ellipsis,± , with the edge chains C ±n coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1) -chain Hamiltonian is solved self-consistently for n up to 4 . The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings α behaves as M∼√(α) enhanced by a multiplicative logarithmic correction. copyright 1999 The American Physical Society

Consistency relations in effective field theory

Energy Technology Data Exchange (ETDEWEB)

Munshi, Dipak; Regan, Donough, E-mail: D.Munshi@sussex.ac.uk, E-mail: D.Regan@sussex.ac.uk [Astronomy Centre, School of Mathematical and Physical Sciences, University of Sussex, Brighton BN1 9QH (United Kingdom)

2017-06-01

The consistency relations in large scale structure relate the lower-order correlation functions with their higher-order counterparts. They are direct outcome of the underlying symmetries of a dynamical system and can be tested using data from future surveys such as Euclid. Using techniques from standard perturbation theory (SPT), previous studies of consistency relation have concentrated on continuity-momentum (Euler)-Poisson system of an ideal fluid. We investigate the consistency relations in effective field theory (EFT) which adjusts the SPT predictions to account for the departure from the ideal fluid description on small scales. We provide detailed results for the 3D density contrast δ as well as the scaled divergence of velocity θ-bar . Assuming a ΛCDM background cosmology, we find the correction to SPT results becomes important at k ∼> 0.05 h/Mpc and that the suppression from EFT to SPT results that scales as square of the wave number k , can reach 40% of the total at k ≈ 0.25 h/Mpc at z = 0. We have also investigated whether effective field theory corrections to models of primordial non-Gaussianity can alter the squeezed limit behaviour, finding the results to be rather insensitive to these counterterms. In addition, we present the EFT corrections to the squeezed limit of the bispectrum in redshift space which may be of interest for tests of theories of modified gravity.

Mean field theory for a balanced hypercolumn model of orientation selectivity in primary visual cortex

CERN Document Server

Lerchner, A; Hertz, J; Ahmadi, M

2004-01-01

We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stim...

Dynamical Mean Field Approximation Applied to Quantum Field Theory

CERN Document Server

Akerlund, Oscar; Georges, Antoine; Werner, Philipp

2013-12-04

We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...

Self-consistent field theory of protein adsorption in a non-Gaussian polyelectrolyte brush

NARCIS (Netherlands)

Biesheuvel, P.M.; Leermakers, F.A.M.; Stuart, M.A.C.

2006-01-01

To describe adsorption of globular protein molecules in a polyelectrolyte brush we use the strong-stretching approximation of the Edwards self-consistent field equation, combined with corrections for a non-Gaussian brush. To describe chemical potentials in this mixture of (globular) species of

Spin and orbital exchange interactions from Dynamical Mean Field Theory

Energy Technology Data Exchange (ETDEWEB)

Secchi, A., E-mail: a.secchi@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands); Lichtenstein, A.I., E-mail: alichten@physnet.uni-hamburg.de [Universitat Hamburg, Institut für Theoretische Physik, Jungiusstraße 9, D-20355 Hamburg (Germany); Katsnelson, M.I., E-mail: m.katsnelson@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands)

2016-02-15

We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii–Moriya interaction and other symmetric terms such as dipole–dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms. - Highlights: • We give formulas for the exchange interaction tensor in strongly correlated systems. • Interactions are written in terms of electronic Green's functions and self-energies. • The method is suitable for a Dynamical Mean Field Theory implementation. • No quenching of the orbital magnetic moments is assumed. • Spin and orbital contributions to magnetism can be computed separately.

A new mixed self-consistent field procedure

Science.gov (United States)

Alvarez-Ibarra, A.; Köster, A. M.

2015-10-01

A new approach for the calculation of three-centre electronic repulsion integrals (ERIs) is developed, implemented and benchmarked in the framework of auxiliary density functional theory (ADFT). The so-called mixed self-consistent field (mixed SCF) divides the computationally costly ERIs in two sets: far-field and near-field. Far-field ERIs are calculated using the newly developed double asymptotic expansion as in the direct SCF scheme. Near-field ERIs are calculated only once prior to the SCF procedure and stored in memory, as in the conventional SCF scheme. Hence the name, mixed SCF. The implementation is particularly powerful when used in parallel architectures, since all RAM available are used for near-field ERI storage. In addition, the efficient distribution algorithm performs minimal intercommunication operations between processors, avoiding a potential bottleneck. One-, two- and three-dimensional systems are used for benchmarking, showing substantial time reduction in the ERI calculation for all of them. A Born-Oppenheimer molecular dynamics calculation for the Na+55 cluster is also shown in order to demonstrate the speed-up for small systems achievable with the mixed SCF. Dedicated to Sourav Pal on the occasion of his 60th birthday.

Exact mean-field theory of ionic solutions: non-Debye screening

International Nuclear Information System (INIS)

Varela, L.M.; Garcia, Manuel; Mosquera, Victor

2003-01-01

The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory

Effective Field Theories and the Role of Consistency in Theory Choice

CERN Document Server

Wells, James D

2012-01-01

Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the importance of these attributes pales in comparison with consistency, both observational and mathematical consistency, which propels the effective theory to be superior to its simpler truncated version of finite terms, whether that theory be renormalizable (e.g., Standard Model of particle physics) or nonrenormalizable (e.g., gravity). Some implications for the Large Hadron Collider and beyond are discussed, including comments on how directly acknowledging the preeminence of consistency can affect future theory work.

Self-consistent field theory simulations of polymers on arbitrary domains

Energy Technology Data Exchange (ETDEWEB)

Ouaknin, Gaddiel, E-mail: gaddielouaknin@umail.ucsb.edu [Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070 (United States); Laachi, Nabil; Delaney, Kris [Materials Research Laboratory, University of California, Santa Barbara, CA 93106-5080 (United States); Fredrickson, Glenn H. [Materials Research Laboratory, University of California, Santa Barbara, CA 93106-5080 (United States); Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080 (United States); Department of Materials, University of California, Santa Barbara, CA 93106-5050 (United States); Gibou, Frederic [Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070 (United States); Department of Computer Science, University of California, Santa Barbara, CA 93106-5110 (United States)

2016-12-15

We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refine the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.

Self-consistent field variational cellular method as applied to the band structure calculation of sodium

International Nuclear Information System (INIS)

Lino, A.T.; Takahashi, E.K.; Leite, J.R.; Ferraz, A.C.

1988-01-01

The band structure of metallic sodium is calculated, using for the first time the self-consistent field variational cellular method. In order to implement the self-consistency in the variational cellular theory, the crystal electronic charge density was calculated within the muffin-tin approximation. The comparison between our results and those derived from other calculations leads to the conclusion that the proposed self-consistent version of the variational cellular method is fast and accurate. (author) [pt

1ST-ORDER NONADIABATIC COUPLING MATRIX-ELEMENTS FROM MULTICONFIGURATIONAL SELF-CONSISTENT-FIELD RESPONSE THEORY

DEFF Research Database (Denmark)

Bak, Keld L.; Jørgensen, Poul; Jensen, H.J.A.

1992-01-01

A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response of a ref......A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response...... to the full configuration interaction limit. Comparisons are made with state-averaged MCSCF results for MgH2 and finite-difference configuration interaction by perturbation with multiconfigurational zeroth-order wave function reflected by interactive process (CIPSI) results for BH....

Quantum correlated cluster mean-field theory applied to the transverse Ising model.

Science.gov (United States)

Zimmer, F M; Schmidt, M; Maziero, Jonas

2016-06-01

Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

Mean-field theory of nuclear structure and dynamics

International Nuclear Information System (INIS)

Negele, J.W.

1982-01-01

The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission

Pion condensation in a theory consistent with bulk properties of nuclear matter

International Nuclear Information System (INIS)

Glendenning, N.K.

1980-01-01

A relativistic field theory of nuclear matter is solved for the self-consistent field strengths inthe mean-field approximation. The theory is constrained to reproduce the bulk properties of nuclear matter. A weak pion condensate is compatible with this constraint. At least this is encouraging as concerns the possible existence of a new phase of nuclear matter. In contrast, the Lee-Wick density isomer is probably not compatible with the properties of nuclear matter. 3 figures

Regular and chaotic dynamics in time-dependent relativistic mean-field theory

International Nuclear Information System (INIS)

Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.

1997-01-01

Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society

A self-consistent theory of the magnetic polaron

International Nuclear Information System (INIS)

Marvakov, D.I.; Kuzemsky, A.L.; Vlahov, J.P.

1984-10-01

A finite temperature self-consistent theory of magnetic polaron in the s-f model of ferromagnetic semiconductors is developed. The calculations are based on the novel approach of the thermodynamic two-time Green function methods. This approach consists in the introduction of the ''irreducible'' Green functions (IGF) and derivation of the exact Dyson equation and exact self-energy operator. It is shown that IGF method gives a unified and natural approach for a calculation of the magnetic polaron states by taking explicitly into account the damping effects and finite lifetime. (author)

Communication: A difference density picture for the self-consistent field ansatz

Energy Technology Data Exchange (ETDEWEB)

Parrish, Robert M.; Liu, Fang; Martínez, Todd J., E-mail: toddjmartinez@gmail.com [Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305 (United States); SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)

2016-04-07

We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this “difference self-consistent field (dSCF)” picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TERACHEM SCF implementation.

Communication: A difference density picture for the self-consistent field ansatz

International Nuclear Information System (INIS)

Parrish, Robert M.; Liu, Fang; Martínez, Todd J.

2016-01-01

We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this “difference self-consistent field (dSCF)” picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TERACHEM SCF implementation.

Communication: A difference density picture for the self-consistent field ansatz

Science.gov (United States)

Parrish, Robert M.; Liu, Fang; Martínez, Todd J.

2016-04-01

We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this "difference self-consistent field (dSCF)" picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TeraChem SCF implementation.

Self-assembly behavior of pH- and thermosensitive amphiphilic triblock copolymers in solution: experimental studies and self-consistent field theory simulations.

Science.gov (United States)

Cai, Chunhua; Zhang, Liangshun; Lin, Jiaping; Wang, Liquan

2008-10-09

We investigated, both experimentally and theoretically, the self-assembly behaviors of pH- and thermosensitive poly(L-glutamic acid)- b-poly(propylene oxide)-b-poly(L-glutamic acid) (PLGA-b-PPO-b-PLGA) triblock copolymers in aqueous solution by means of transmission electron microscopy (TEM), scanning electron microscopy (SEM), dynamic light scattering (DLS), circular dichroism (CD), and self-consistent field theory (SCFT) simulations. Vesicles were observed when the hydrophilic PLGA block length is shorter or the pH value of solution is lower. The vesicles were found to transform to spherical micelles when the PLGA block length increases or its conformation changes from helix to coil with increasing the pH value. In addition, increasing temperature gives rise to a decrease in the size of aggregates, which is related to the dehydration of the PPO segments at higher temperatures. The SCFT simulation results show that the vesicles transform to the spherical micelles with increasing the fraction or statistical length of A block in model ABA triblock copolymer, which corresponds to the increase in the PLGA length or its conformation change from helix to coil in experiments, respectively. The SCFT calculations also provide chain distribution information in the aggregates. On the basis of both experimental and SCFT results, the mechanism of the structure change of the PLGA- b-PPO- b-PLGA aggregates was proposed.

Consistent Kaluza-Klein truncations via exceptional field theory

Energy Technology Data Exchange (ETDEWEB)

Hohm, Olaf [Center for Theoretical Physics, Massachusetts Institute of Technology,Cambridge, MA 02139 (United States); Samtleben, Henning [Université de Lyon, Laboratoire de Physique, UMR 5672, CNRS,École Normale Supérieure de Lyon, 46, allée d’Italie, F-69364 Lyon cedex 07 (France)

2015-01-26

We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO(p,q) and CSO(p,q,r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides H{sup p,q}, thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D=11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS{sub 5}×S{sup 5}), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.

Generalized molecular orbital theory: a limited multiconfiguration self-consistent-field-theory

International Nuclear Information System (INIS)

Hall, M.B.

1981-01-01

The generalized molecular orbital (GMO) approach is a limited type of multiconfiguration self-consistent-field (MCSCF) calculation which divides the orbitals of a closed shell molecule into four shells: doubly occupied, strongly occupied, weakly occupied, and unoccupied. The orbitals within each shell have the same occupation number and are associated with the same Fock operator. Thus, the orbital optimization is ideally suited to solution via a coupling operator. The determination of the orbitals is followed by a configuration interaction (CI) calculation within the strongly and weakly occupied shells. Results for BH 3 show a striking similarity between the GMO's and the natural orbitals (NO's) from an all singles and doubles CI calculation. Although the GMO approach would not be accurate for an entire potential surface, results for spectroscopic constants of N 2 show that it is suitable near the equilibrium geometry. This paper describes the use of the GMO technique to determine the primary orbital space, but a potentially important application may be in the determination of a secondary orbital space following a more accurate MCSCF determination of the primary space

Self-consistent field theory for the interactions between keratin intermediate filaments

International Nuclear Information System (INIS)

Akinshina, Anna; Jambon-Puillet, Etienne; Warren, Patrick B; Noro, Massimo G

2013-01-01

Keratins are important structural proteins found in skin, hair and nails. Keratin Intermediate Filaments are major components of corneocytes, nonviable horny cells of the Stratum Corneum, the outermost layer of skin. It is considered that interactions between unstructured domains of Keratin Intermediate Filaments are the key factor in maintaining the elasticity of the skin. We have developed a model for the interactions between keratin intermediate filaments based on self-consistent field theory. The intermediate filaments are represented by charged surfaces, and the disordered terminal domains of the keratins are represented by charged heteropolymers grafted to these surfaces. We estimate the system is close to a charge compensation point where the heteropolymer grafting density is matched to the surface charge density. Using a protein model with amino acid resolution for the terminal domains, we find that the terminal chains can mediate a weak attraction between the keratin surfaces. The origin of the attraction is a combination of bridging and electrostatics. The attraction disappears when the system moves away from the charge compensation point, or when excess small ions and/or NMF-representing free amino acids are added. These results are in concordance with experimental observations, and support the idea that the interaction between keratin filaments, and ultimately in part the elastic properties of the keratin-containing tissue, is controlled by a combination of the physico-chemical properties of the disordered terminal domains and the composition of the medium in the inter-filament region

Self-consistent cluster theory for systems with off-diagonal disorder

International Nuclear Information System (INIS)

Kaplan, T.; Leath, P.L.; Gray, L.J.; Diehl, H.W.

1980-01-01

A self-consistent cluster theory for elementary excitations in systems with diagonal, off-diagonal, and environmental disorder is presented. The theory is developed in augmented space where the configurational average over the disorder is replaced by a ground-state matrix element in a translationally invariant system. The analyticity of the resulting approximate Green's function is proved. Numerical results for the self-consistent single-site and pair approximations are presented for the vibrational and electronic properties of disordered linear chains with diagonal, off-diagonal, and environmental disorder

Time-dependent restricted-active-space self-consistent eld theory: Formulation and application to laser-driven many-electron dynamics

DEFF Research Database (Denmark)

Miyagi, Haruhide; Madsen, Lars Bojer

We have developed a new theoretical framework for time-dependent many-electron problems named time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory. The theory generalizes the multicongurational time-dependent Hartree-Fock (MCTDHF) theory by truncating the expansion...

A finite element approach to self-consistent field theory calculations of multiblock polymers

Energy Technology Data Exchange (ETDEWEB)

Ackerman, David M. [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States); Delaney, Kris; Fredrickson, Glenn H. [Materials Research Laboratory, University of California, Santa Barbara (United States); Ganapathysubramanian, Baskar, E-mail: baskarg@iastate.edu [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States)

2017-02-15

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.

Similarities between Prescott Lecky's theory of self-consistency and Carl Rogers' self-theory.

Science.gov (United States)

Merenda, Peter F

2010-10-01

The teachings of Prescott Lecky on the self-concept at Columbia University in the 1920s and 1930s and the posthumous publications of his book on self-consistency beginning in 1945 are compared with the many publications of Carl Rogers on the self-concept beginning in the early 1940s. Given that Rogers was a graduate student at Columbia in the 1920s and 1930s, the striking similarities between these two theorists, as well as claims attributed to Rogers by Rogers' biographers and writers who have quoted Rogers on his works relating to self-theory, strongly suggest that Rogers borrowed from Lecky without giving him the proper credit. Much of Rogers' writings on the self-concept included not only terms and concepts which were original with Lecky, but at times these were actually identical.

Relativistic fluid theories - Self organization

International Nuclear Information System (INIS)

Mahajan, S.M.; Hazeltine, R.D.; Yoshida, Z.

2003-01-01

Developments in two distinct but related subjects are reviewed: 1) Formulation and investigation of closed fluid theories which transcend the limitations of standard magnetohydrodynamics (MHD), in particular, theories which are valid in the long mean free path limit and in which pressure anisotropy, heat flow, and arbitrarily strong sheared flows are treated consistently, and 2) Exploitation of the two-fluid theories to derive new plasma configurations in which the flow-field is a co-determinant of the overall dynamics; some of these states belong to the category of self-organized relaxed states. Physical processes which may provide a route to self-organization and complexity are also explored. (author)

Self-consistent theory of a harmonic gyroklystron with a minimum Q cavity

International Nuclear Information System (INIS)

Tran, T.M.; Kreischer, K.E.; Temkin, R.J.

1986-01-01

In this paper, the energy extraction stage of the gyroklystron [in Advances in Electronics and Electron Physics, edited by C. Marton (Academic, New York, 1979), Vol. 1, pp. 1--54], with a minimum Q cavity is investigated by using a self-consistent radio-frequency (rf) field model. In the low-field, low-current limit, expressions for the self-consistent field and the resulting energy extraction efficiency are derived analytically for an arbitrary cyclotron harmonic number. To our knowledge, these are the first analytic results for the self-consistent field structure and efficiency of a gyrotron device. The large signal regime analysis is carried out by numerically integrating the coupled self-consistent equations. Several examples in this regime are presented

Band mixing effects in mean field theories

International Nuclear Information System (INIS)

Kuyucak, S.; Morrison, I.

1989-01-01

The 1/N expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model (IBM). Conversely, comparison with the exact IBM results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the E2 transitions among the ground, β and γ bands are incomplete for the spin dependent terms and it is essential to include band mixing effect for a correct (Mikhailov) analysis of E2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the sd and sdg boson models. 17 refs., 7 figs., 8 tabs

Analysis of self-consistency effects in range-separated density-functional theory with Møller-Plesset perturbation theory

DEFF Research Database (Denmark)

Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard

2011-01-01

Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled......-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using Møller-Plesset-type (MP......) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational...

Near-resonant absorption in the time-dependent self-consistent field and multiconfigurational self-consistent field approximations

DEFF Research Database (Denmark)

Norman, Patrick; Bishop, David M.; Jensen, Hans Jørgen Aa

2001-01-01

Computationally tractable expressions for the evaluation of the linear response function in the multiconfigurational self-consistent field approximation were derived and implemented. The finite lifetime of the electronically excited states was considered and the linear response function was shown...... to be convergent in the whole frequency region. This was achieved through the incorporation of phenomenological damping factors that lead to complex response function values....

Quasiparticle self-consistent GW method for the spectral properties of complex materials.

Science.gov (United States)

Bruneval, Fabien; Gatti, Matteo

2014-01-01

The GW approximation to the formally exact many-body perturbation theory has been applied successfully to materials for several decades. Since the practical calculations are extremely cumbersome, the GW self-energy is most commonly evaluated using a first-order perturbative approach: This is the so-called G 0 W 0 scheme. However, the G 0 W 0 approximation depends heavily on the mean-field theory that is employed as a basis for the perturbation theory. Recently, a procedure to reach a kind of self-consistency within the GW framework has been proposed. The quasiparticle self-consistent GW (QSGW) approximation retains some positive aspects of a self-consistent approach, but circumvents the intricacies of the complete GW theory, which is inconveniently based on a non-Hermitian and dynamical self-energy. This new scheme allows one to surmount most of the flaws of the usual G 0 W 0 at a moderate calculation cost and at a reasonable implementation burden. In particular, the issues of small band gap semiconductors, of large band gap insulators, and of some transition metal oxides are then cured. The QSGW method broadens the range of materials for which the spectral properties can be predicted with confidence.

Self-consistent theory of three-dimensional convection in the geomagnetic tail

International Nuclear Information System (INIS)

Birn, J.; Schindler, K.

1983-01-01

The self-consistent theory of time-dependent convection in the earth's magnetotail of Schindler and Birn (1982) is extended to three dimensions to include more realistic tail geometry and three-dimensional flow. We confirm that a steady state solution implies unrealistic tail geometry or large particle or energy losses that are unrealistic during quiet times and conclude therefore that as in the 2-dimensional case the magnetotail becomes time-dependent for typical convection electric fields. Explicit solutions are derived, even analytically, for the three-dimensional flow and the electric and magnetic field in a realistic tail geometry, and quantitative examples are presented. Consequences of time-dependent convection are demonstrated considering two idealized cases of magnetosphere response to solar wind changes: (1) uniform compression as the likely consequence of increasing (static, dynamic or magnetic) solar wind pressure; and (2) compression only in the z direction perpendicular to the plasma sheet as the probable consequence of a dawn to dusk external electric field (E/sub y/>0), corresponding to a southward interplanetary magnetic field component (B/sub z/ 0 with geomagnetic activity. Several other features, already present in the 2-dimensional theory, are confirmed

Regularity theory for mean-field game systems

CERN Document Server

Gomes, Diogo A; Voskanyan, Vardan

2016-01-01

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Regularity Theory for Mean-Field Game Systems

KAUST Repository

Gomes, Diogo A.

2016-09-14

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Regularity Theory for Mean-Field Game Systems

KAUST Repository

Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.

2016-01-01

Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Surface incompressibility from semiclassical relativistic mean field calculations

International Nuclear Information System (INIS)

Patra, S.K.; Centelles, M.; Vinas, X.; Estal, M. del

2002-01-01

By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility K A has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of K A for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made

Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals

International Nuclear Information System (INIS)

Takeda, Hiroyuki; John, Sajeev

2011-01-01

We theoretically demonstrate the population switching of quantum dots (QD's), modeled as two-level atoms in idealized one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) by self-consistent solution of the Maxwell-Bloch equations. In our semiclassical theory, energy states of the electron are quantized, and electron dynamics is described by the atomic Bloch equation, while electromagnetic waves satisfy the classical Maxwell equations. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states (LDOS) and spontaneous emission rates exhibit abrupt changes with frequency, enabling large QD population inversion driven by both continuous and pulsed optical fields. We recapture and generalize this ultrafast population switching using the Maxwell-Bloch equations. Radiative emission from the QD is obtained directly from the surrounding PC geometry using finite-difference time-domain simulation of the electromagnetic field. The atomic Bloch equations provide a source term for the electromagnetic field. The total electromagnetic field, consisting of the external input and radiated field, drives the polarization components of the atomic Bloch vector. We also include a microscopic model for phonon dephasing of the atomic polarization and nonradiative decay caused by damped phonons. Our self-consistent theory captures stimulated emission and coherent feedback effects of the atomic Mollow sidebands, neglected in earlier treatments. This leads to remarkable high-contrast QD-population switching with relatively modest (factor of 10) jump discontinuities in the electromagnetic LDOS. Switching is demonstrated in three separate models of QD's placed (i) in the vicinity of a band edge of a 1D PC, (ii) near a cutoff frequency in a bimodal waveguide channel of a 2D PC, and (iii) in the vicinity of a localized defect mode side coupled to a single-mode waveguide channel in a 2D PC.

Analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field method

Directory of Open Access Journals (Sweden)

N.Yoshida

2007-09-01

Full Text Available An analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field (MOZ-SCF method is presented. MOZ-SCF theory is one of the theories to considering the solvent effects on the solute electronic structure in solution. [Yoshida N. et al., J. Chem. Phys., 2000, 113, 4974] Molecular geometries of water, formaldehyde, acetonitrile and acetone in water are optimized by analytical energy gradient formula. The results are compared with those from the polarizable continuum model (PCM, the reference interaction site model (RISM-SCF and the three dimensional (3D RISM-SCF.

Self-consistent theory of hadron-nucleus scattering. Application to pion physics

International Nuclear Information System (INIS)

Johnson, M.B.

1980-01-01

The requirement of using self-consistent amplitudes to evaluate microscopically the scattering of strongly interacting particles from nuclei is developed. Application of the idea to a simple model of pion-nucleus scattering is made. Numerical results indicate that the expansion of the optical potential converges when evaluated in terms of fully self-consistent quantities. A comparison of the results to a recent determination of the spreading interaction in the phenomenological isobar-hole model shows that the theory accounts for the sign and magnitude of the real and imaginary part of the spreading interaction with no adjusted parameters. The self-consistnt theory has a strong density dependence, and the consequences of this for pion-nucleus scattering are discussed. 18 figures, 1 table

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

International Nuclear Information System (INIS)

Kuchinskii, E. Z.; Nekrasov, I. A.; Sadovskii, M. V.

2008-01-01

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition

A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam

International Nuclear Information System (INIS)

Uhm, H.S.

1994-01-01

A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance z m at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications

Bicontinuous Phases in Diblock Copolymer/Homopolymer Blends: Simulation and Self-Consistent Field Theory

KAUST Repository

Martínez-Veracoechea, Francisco J.

2009-03-10

A combination of particle-based simulations and self-consistent field theory (SCFT) is used to study the stabilization of multiple ordered bicontinuous phases in blends of a diblock copolymer (DBC) and a homopolymer. The double-diamond phase (DD) and plumber\\'s nightmare phase (P) were spontaneously formed in the range of homopolymer volume fraction simulated via coarse-grained molecular dynamics. To the best of our knowledge, this is the first time that such phases have been obtained in continuum-space molecular simulations of DBC systems. Though tentative phase boundaries were delineated via free-energy calculations, macrophase separation could not be satisfactorily assessed within the framework of particle-based simulations. Therefore, SCFT was used to explore the DBC/homopolymer phase diagram in more detail, showing that although in many cases two-phase coexistence of a DBC-rich phase and a homopolymer-rich phase does precede the stability of complex bicontinuous phases the DD phase can be stable in a relatively wide region of the phase diagram. Whereas the P phase was always metastable with respect to macrophase separation under the thermodynamic conditions explored with SCFT, it was sometimes nearly stable, suggesting that full stability could be achieved in other unexplored regions of parameter space. Moreover, even the predicted DD- and P-phase metastability regions were located significantly far from the spinodal line, suggesting that these phases could be observed in experiments as "long-lived" metastable phases under those conditions. This conjecture is also consistent with large-system molecular dynamics simulations that showed that the time scale of mesophase formation is much faster than that of macrophase separation. © 2009 American Chemical Society.

Self-consistent Ginzburg-Landau theory for transport currents in superconductors

DEFF Research Database (Denmark)

Ögren, Magnus; Sørensen, Mads Peter; Pedersen, Niels Falsig

2012-01-01

We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in princi...... in principle also be used for general geometries in three-dimensional superconductors....

Self-consistent mean field forces in turbulent plasmas: Current and momentum relaxation

International Nuclear Information System (INIS)

Hegna, C.C.

1997-08-01

The properties of turbulent plasmas are described using the two-fluid equations. Under some modest assumptions, global constraints for the turbulent mean field forces that act on the ion and electron fluids are derived. These constraints imply a functional form for the parallel mean field forces in the Ohm's law and the momentum balance equation. These forms suggest that the fluctuations attempt to relax the plasma to a state where both the current and the bulk plasma momentum are aligned along the mean magnetic field with proportionality constants that are global constants. Observations of flow profile evolution during discrete dynamo activity in reversed field pinch experiments are interpreted

Symplectic manifolds, coadjoint orbits, and Mean Field Theory

International Nuclear Information System (INIS)

Rosensteel, G.

1986-01-01

Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

Science.gov (United States)

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

Classification of networks of automata by dynamical mean field theory

International Nuclear Information System (INIS)

Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.

1990-01-01

Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)

Self-consistent field theory of tethered polymers: one dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions.

Science.gov (United States)

Suo, Tongchuan; Whitmore, Mark D

2014-11-28

We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a "mushroom" regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ(1/3) scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ(1/3). In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ(1/3). We also compare the results for two different solvents with each other, and with earlier Θ solvent results.

Self-consistent field theory of tethered polymers: One dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions

International Nuclear Information System (INIS)

Suo, Tongchuan; Whitmore, Mark D.

2014-01-01

We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a “mushroom” regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ 1/3 scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ 1/3 . In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ 1/3 . We also compare the results for two different solvents with each other, and with earlier Θ solvent results

Nonlinear mean field theory for nuclear matter and surface properties

International Nuclear Information System (INIS)

Boguta, J.; Moszkowski, S.A.

1983-01-01

Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)

A self-consistent formulation of quantum field theory on S4

International Nuclear Information System (INIS)

Harris, B.A.; Joshi, G.C.

1991-01-01

In this paper, a consistent formulation of field theory on a four-sphere was constructed and a method from which various amplitudes may be calculated is described. The standard results of quantum electrodynamics are derived, providing a valuable check on the validity of this approach, as well as allowing a direct comparison between this and previous work done in the area. It is believed that the matrix element approach offers a new way to deal with some of the more troublesome aspects of previous calculations. In particular one can easily handle the transverse part of the photon propagator which had made the (1 - α) gauge parts difficult to calculate. However the main advantage of this method is the ability to compute functions which involve the contraction of indices across different η integrals. This tends to happen when one has derivative couplings such as those in scalar electrodynamics. 12 refs., 3 figs

Quantum critical point revisited by dynamical mean-field theory

Science.gov (United States)

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.

2017-03-01

Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. We use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. By comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.

Quantum mean-field approximations for nuclear bound states and tunneling

International Nuclear Information System (INIS)

Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge

1979-01-01

A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems

Characterisation of poly(lactic acid): poly(ethyleneoxide) (PLA:PEG) nanoparticles using the self-consistent theory modelling approach

NARCIS (Netherlands)

Heald, C.R.; Stolnik, S.; Matteis, De C.; Garnett, M.C.; Illum, L.; Davis, S.S.; Leermakers, F.A.M.

2003-01-01

Self-consistent field (SCF) modelling studies can be used to predict the properties of poly(lactic acid):poly(ethyleneoxide) (PLA:PEG) nanoparticles using the theory developed by Scheutjens and Fleer. Good agreement in the results between experimental and modelled data has been observed previously

Weyl consistency conditions in non-relativistic quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Pal, Sridip; Grinstein, Benjamín [Department of Physics, University of California,San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States)

2016-12-05

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2+1 dimensions with anisotropic scaling exponent z=2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. We comment on possible candidates for a C-theorem in higher dimensions.

Mean-field lattice trees

NARCIS (Netherlands)

Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.

1999-01-01

We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an

Mean field with corrections in lattice gauge theory

International Nuclear Information System (INIS)

Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.

1981-12-01

A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)

Nuclear collective vibrations in extended mean-field theory

Energy Technology Data Exchange (ETDEWEB)

Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)

2003-07-01

The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)

Non-equilibrium mean-field theories on scale-free networks

International Nuclear Information System (INIS)

Caccioli, Fabio; Dall'Asta, Luca

2009-01-01

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks

Self-consistent theory of charged current neutrino-nucleus reactions

Energy Technology Data Exchange (ETDEWEB)

Paar, Nils; Marketin, Tomislav; Vretenar, Dario [Physics Department, Faculty of Science, University Zagreb (Croatia); Ring, Peter [Physik-Department, Technischen Universitaet Muenchen, D-85748 Muenchen (Germany)

2009-07-01

A novel theoretical framework has been introduced for description of neutrino induced reactions with nuclei. The properties of target nuclei are determined in a self-consistent way using relativistic mean-field framework based on effective Lagrangians with density dependent meson-nucleon vertex functions. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described in the relativistic Hartree-Bogolyubov model, and the relevant transitions to excited nuclear states are calculated in the proton-neutron relativistic quasiparticle random phase approximation. This framework has been employed in studies of charged-current neutrino reactions involving nuclei of relevance for neutrino detectors, r-process nuclei, and neutrino-nucleus cross sections averaged over measured neutrino fluxes and supernova neutrino distributions.

Quantum critical point revisited by dynamical mean-field theory

International Nuclear Information System (INIS)

Xu, Wenhu; Kotliar, Gabriel; Rutgers University, Piscataway, NJ; Tsvelik, Alexei M.

2017-01-01

Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.

Accurate X-Ray Spectral Predictions: An Advanced Self-Consistent-Field Approach Inspired by Many-Body Perturbation Theory.

Science.gov (United States)

Liang, Yufeng; Vinson, John; Pemmaraju, Sri; Drisdell, Walter S; Shirley, Eric L; Prendergast, David

2017-03-03

Constrained-occupancy delta-self-consistent-field (ΔSCF) methods and many-body perturbation theories (MBPT) are two strategies for obtaining electronic excitations from first principles. Using the two distinct approaches, we study the O 1s core excitations that have become increasingly important for characterizing transition-metal oxides and understanding strong electronic correlation. The ΔSCF approach, in its current single-particle form, systematically underestimates the pre-edge intensity for chosen oxides, despite its success in weakly correlated systems. By contrast, the Bethe-Salpeter equation within MBPT predicts much better line shapes. This motivates one to reexamine the many-electron dynamics of x-ray excitations. We find that the single-particle ΔSCF approach can be rectified by explicitly calculating many-electron transition amplitudes, producing x-ray spectra in excellent agreement with experiments. This study paves the way to accurately predict x-ray near-edge spectral fingerprints for physics and materials science beyond the Bethe-Salpether equation.

Consistent constraints on the Standard Model Effective Field Theory

International Nuclear Information System (INIS)

Berthier, Laure; Trott, Michael

2016-01-01

We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S,T analysis is modified by the theory errors we include as an illustrative example.

Self-consistent theory of finite Fermi systems and radii of nuclei

International Nuclear Information System (INIS)

Saperstein, E. E.; Tolokonnikov, S. V.

2011-01-01

Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ ch (r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

The numerical multiconfiguration self-consistent field approach for atoms; Der numerische Multiconfiguration Self-Consistent Field-Ansatz fuer Atome

Energy Technology Data Exchange (ETDEWEB)

Stiehler, Johannes

1995-12-15

The dissertation uses the Multiconfiguration Self-Consistent Field Approach to specify the electronic wave function of N electron atoms in a static electrical field. It presents numerical approaches to describe the wave functions and introduces new methods to compute the numerical Fock equations. Based on results computed with an implemented computer program the universal application, flexibility and high numerical precision of the presented approach is shown. RHF results and for the first time MCSCF results for polarizabilities and hyperpolarizabilities of various states of the atoms He to Kr are discussed. In addition, an application to interpret a plasma spectrum of gallium is presented. (orig.)

Self-assembled structures of amphiphilic ionic block copolymers: Theory, self-consistent field modeling and experiment

NARCIS (Netherlands)

Borisov, O.V.; Zhulina, E.B.; Leermakers, F.A.M.; Muller, A.H.E.

2011-01-01

We present an overview of statistical thermodynamic theories that describe the self-assembly of amphiphilic ionic/hydrophobic diblock copolymers in dilute solution. Block copolymers with both strongly and weakly dissociating (pH-sensitive) ionic blocks are considered. We focus mostly on structural

Modification of linear response theory for mean-field approximations

NARCIS (Netherlands)

Hütter, M.; Öttinger, H.C.

1996-01-01

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

Self-consistent model of confinement

International Nuclear Information System (INIS)

Swift, A.R.

1988-01-01

A model of the large-spatial-distance, zero--three-momentum, limit of QCD is developed from the hypothesis that there is an infrared singularity. Single quarks and gluons do not propagate because they have infinite energy after renormalization. The Hamiltonian formulation of the path integral is used to quantize QCD with physical, nonpropagating fields. Perturbation theory in the infrared limit is simplified by the absence of self-energy insertions and by the suppression of large classes of diagrams due to vanishing propagators. Remaining terms in the perturbation series are resummed to produce a set of nonlinear, renormalizable integral equations which fix both the confining interaction and the physical propagators. Solutions demonstrate the self-consistency of the concepts of an infrared singularity and nonpropagating fields. The Wilson loop is calculated to provide a general proof of confinement. Bethe-Salpeter equations for quark-antiquark pairs and for two gluons have finite-energy solutions in the color-singlet channel. The choice of gauge is addressed in detail. Large classes of corrections to the model are discussed and shown to support self-consistency

Self-consistent quark bags

International Nuclear Information System (INIS)

Rafelski, J.

1979-01-01

After an introductory overview of the bag model the author uses the self-consistent solution of the coupled Dirac-meson fields to represent a bound state of strongly ineteracting fermions. In this framework he discusses the vivial approach to classical field equations. After a short description of the used numerical methods the properties of bound states of scalar self-consistent Fields and the solutions of a self-coupled Dirac field are considered. (HSI) [de

Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer

Directory of Open Access Journals (Sweden)

Ying Jiang

2017-02-01

Full Text Available This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials.

First principles molecular dynamics without self-consistent field optimization

International Nuclear Information System (INIS)

Souvatzis, Petros; Niklasson, Anders M. N.

2014-01-01

We present a first principles molecular dynamics approach that is based on time-reversible extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The optimization-free dynamics keeps the computational cost to a minimum and typically provides molecular trajectories that closely follow the exact Born-Oppenheimer potential energy surface. Only one single diagonalization and Hamiltonian (or Fockian) construction are required in each integration time step. The proposed dynamics is derived for a general free-energy potential surface valid at finite electronic temperatures within hybrid density functional theory. Even in the event of irregular functional behavior that may cause a dynamical instability, the optimization-free limit represents a natural starting guess for force calculations that may require a more elaborate iterative electronic ground state optimization. Our optimization-free dynamics thus represents a flexible theoretical framework for a broad and general class of ab initio molecular dynamics simulations

Self-consistent Random Phase Approximation applied to a schematic model of the field theory; Approximation des phases aleatoires self-consistante appliquee a un modele schematique de la theorie des champs

Energy Technology Data Exchange (ETDEWEB)

Bertrand, Thierry [Inst. de Physique Nucleaire, Lyon-1 Univ., 69 - Villeurbanne (France)

1998-12-11

The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum 40 refs., 33 figs., 14 tabs.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles

Science.gov (United States)

Elizondo-Aguilera, L. F.; Zubieta Rico, P. F.; Ruiz-Estrada, H.; Alarcón-Waess, O.

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, Fl m ,l m(k ,t ) and Flm ,l m S(k ,t ) , are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density nl m(k ,t ) and the translational (α =T ) and rotational (α =R ) current densities jlm α(k ,t ) . Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by Sl m ,l m(k ) . Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γT and γR, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

Science.gov (United States)

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Macroscopic self-consistent model for external-reflection near-field microscopy

International Nuclear Information System (INIS)

Berntsen, S.; Bozhevolnaya, E.; Bozhevolnyi, S.

1993-01-01

The self-consistent macroscopic approach based on the Maxwell equations in two-dimensional geometry is developed to describe tip-surface interaction in external-reflection near-field microscopy. The problem is reduced to a single one-dimensional integral equation in terms of the Fourier components of the field at the plane of the sample surface. This equation is extended to take into account a pointlike scatterer placed on the sample surface. The power of light propagating toward the detector as the fiber mode is expressed by using the self-consistent field at the tip surface. Numerical results for trapezium-shaped tips are presented. The authors show that the sharper tip and the more confined fiber mode result in better resolution of the near-field microscope. Moreover, it is found that the tip-surface distance should not be too small so that better resolution is ensured. 14 refs., 10 figs

Self-interaction error in density functional theory: a mean-field correction for molecules and large systems

International Nuclear Information System (INIS)

Ciofini, Ilaria; Adamo, Carlo; Chermette, Henry

2005-01-01

Corrections to the self-interaction error which is rooted in all standard exchange-correlation functionals in the density functional theory (DFT) have become the object of an increasing interest. After an introduction reminding the origin of the self-interaction error in the DFT formalism, and a brief review of the self-interaction free approximations, we present a simple, yet effective, self-consistent method to correct this error. The model is based on an average density self-interaction correction (ADSIC), where both exchange and Coulomb contributions are screened by a fraction of the electron density. The ansatz on which the method is built makes it particularly appealing, due to its simplicity and its favorable scaling with the size of the system. We have tested the ADSIC approach on one of the classical pathological problem for density functional theory: the direct estimation of the ionization potential from orbital eigenvalues. A large set of different chemical systems, ranging from simple atoms to large fullerenes, has been considered as test cases. Our results show that the ADSIC approach provides good numerical values for all the molecular systems, the agreement with the experimental values increasing, due to its average ansatz, with the size (conjugation) of the systems

Analytical relativistic self-consistent-field calculations for atoms

International Nuclear Information System (INIS)

Barthelat, J.C.; Pelissier, M.; Durand, P.

1980-01-01

A new second-order representation of the Dirac equation is presented. This representation which is exact for a hydrogen atom is applied to approximate analytical self-consistent-field calculations for atoms. Results are given for the rare-gas atoms from helium to radon and for lead. The results compare favorably with numerical Dirac-Hartree-Fock solutions

Covariant density functional theory beyond mean field and applications for nuclei far from stability

International Nuclear Information System (INIS)

Ring, P

2010-01-01

Density functional theory provides a very powerful tool for a unified microscopic description of nuclei all over the periodic table. It is not only successful in reproducing bulk properties of nuclear ground states such as binding energies, radii, or deformation parameters, but it also allows the investigation of collective phenomena, such as giant resonances and rotational excitations. However, it is based on the mean field concept and therefore it has its limits. We discuss here two methods based based on covariant density functional theory going beyond the mean field concept, (i) models with an energy dependent self energy allowing the coupling to complex configurations and a quantitative description of the width of giant resonances and (ii) methods of configuration mixing between Slater determinants with different deformation and orientation providing are very successful description of transitional nuclei and quantum phase transitions.

Fostering Personal Meaning and Self-Relevance: A Self-Determination Theory Perspective on Internalization

Science.gov (United States)

Vansteenkiste, Maarten; Aelterman, Nathalie; De Muynck, Gert-Jan; Haerens, Leen; Patall, Erika; Reeve, Johnmarshall

2018-01-01

Central to self-determination theory (SDT) is the notion that autonomously motivated learning relates to greater learning benefits. While learners' intrinsic motivation has received substantial attention, learners also display volitional learning when they come to endorse the personal meaning or self-relevance of the learning task. In Part I of…

Development of mean field theories in nuclear physics and in desordered media

International Nuclear Information System (INIS)

Orland, Henri.

1981-04-01

This work, in two parts, deals with the development of mean field theories in nuclear physics (nuclei in balance and collisions of heavy ions) as well as in disordered media. In the first part, two different ways of tackling the problem of developments around mean field theories are explained. Possessing an approach wave function for the system, the natural idea for including the correlations is to develop the exact wave function of the system around the mean field wave function. The first two chapters show two different ways of dealing with this problem: the perturbative approach - Hartree-Fock equations with two body collisions and functional methods. In the second part: mean field theory for spin glasses. The problem for spin glasses is to construct a physically acceptable mean field theory. The importance of this problem in statistical mechanics is linked to the fact that the mean field theory provides a qualitative description of the low temperature phase and is the starting point needed for using more sophisticated methods (renormalization group). Two approaches to this problem are presented, one based on the Sherrington-Kirkpatrick model and the other based on a model of spins with purely local disorder and competitive interaction between the spins [fr

Modeling polymer-induced interactions between two grafted surfaces: comparison between interfacial statistical associating fluid theory and self-consistent field theory.

Science.gov (United States)

Jain, Shekhar; Ginzburg, Valeriy V; Jog, Prasanna; Weinhold, Jeffrey; Srivastava, Rakesh; Chapman, Walter G

2009-07-28

The interaction between two polymer grafted surfaces is important in many applications, such as nanocomposites, colloid stabilization, and polymer alloys. In our previous work [Jain et al., J. Chem. Phys. 128, 154910 (2008)], we showed that interfacial statistical associating fluid density theory (iSAFT) successfully calculates the structure of grafted polymer chains in the absence/presence of a free polymer. In the current work, we have applied this density functional theory to calculate the force of interaction between two such grafted monolayers in implicit good solvent conditions. In particular, we have considered the case where the segment sizes of the free (sigma(f)) and grafted (sigma(g)) polymers are different. The interactions between the two monolayers in the absence of the free polymer are always repulsive. However, in the presence of the free polymer, the force either can be purely repulsive or can have an attractive minimum depending upon the relative chain lengths of the free (N(f)) and grafted polymers (N(g)). The attractive minimum is observed only when the ratio alpha = N(f)/N(g) is greater than a critical value. We find that these critical values of alpha satisfy the following scaling relation: rho(g) square root(N(g)) beta(3) proportional to alpha(-lambda), where beta = sigma(f)/sigma(g) and lambda is the scaling exponent. For beta = 1 or the same segment sizes of the free and grafted polymers, this scaling relation is in agreement with those from previous theoretical studies using self-consistent field theory (SCFT). Detailed comparisons between iSAFT and SCFT are made for the structures of the monolayers and their forces of interaction. These comparisons lead to interesting implications for the modeling of nanocomposite thermodynamics.

Finite discrete field theory

International Nuclear Information System (INIS)

Souza, Manoelito M. de

1997-01-01

We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)

Self-organizing physical fields and gravity

International Nuclear Information System (INIS)

Pestov, I.B.

2009-01-01

It is shown that the Theory of Self-Organizing Physical Fields provides the adequate and consistent consideration of the gravitational phenomena. The general conclusion lies in the fact that the essence of gravidynamics is the new field concept of time and the general covariant law of energy conservation which in particular means that dark energy is simply the energy of the gravitational field. From the natural geometrical laws of gravidynamics the dynamical equations of the gravitational field are derived. Two exact solutions of these equations are obtained. One of them represents a shock gravitational wave and the other represents the Universe filled up with the gravitational energy only. These solutions are compared with the Schwarzschild and Friedmann solutions in the Einstein general theory of relativity

General Relativistic Mean Field Theory for rotating nuclei

Energy Technology Data Exchange (ETDEWEB)

Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki

1998-03-01

The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)

Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report

International Nuclear Information System (INIS)

Wadia, Spenta R.

2009-01-01

We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)

Quantum Critical Point revisited by the Dynamical Mean Field Theory

Science.gov (United States)

Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei

Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. Our results reveal a substantial difference with the calculations based on the Spin-Fermion model which indicates that the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor. The authors are supported by Center for Computational Design of Functional Strongly Correlated Materials and Theoretical Spectroscopy under DOE Grant DE-FOA-0001276.

Bosons system with finite repulsive interaction: self-consistent field method

International Nuclear Information System (INIS)

Renatino, M.M.B.

1983-01-01

Some static properties of a boson system (T = zero degree Kelvin), under the action of a repulsive potential are studied. For the repulsive potential, a model was adopted consisting of a region where it is constant (r c ), and a decay as 1/r (r > r c ). The self-consistent field approximation used takes into account short range correlations through a local field corrections, which leads to an effective field. The static structure factor S(q-vector) and the effective potential ψ(q-vector) are obtained through a self-consistent calculation. The pair-correlation function g(r-vector) and the energy of the collective excitations E(q-vector) are also obtained, from the structure factor. The density of the system and the parameters of the repulsive potential, that is, its height and the size of the constant region were used as variables for the problem. The results obtained for S(q-vector), g(r-vector) and E(q-vector) for a fixed ratio r o /r c and a variable λ, indicates the raising of a system structure, which is more noticeable when the potential became more repulsive. (author)

Mean-field theory of differential rotation in density stratified turbulent convection

Science.gov (United States)

Rogachevskii, I.

2018-04-01

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.

Self-consistent hybrid functionals for solids: a fully-automated implementation

Science.gov (United States)

Erba, A.

2017-08-01

A fully-automated algorithm for the determination of the system-specific optimal fraction of exact exchange in self-consistent hybrid functionals of the density-functional-theory is illustrated, as implemented into the public Crystal program. The exchange fraction of this new class of functionals is self-consistently updated proportionally to the inverse of the dielectric response of the system within an iterative procedure (Skone et al 2014 Phys. Rev. B 89, 195112). Each iteration of the present scheme, in turn, implies convergence of a self-consistent-field (SCF) and a coupled-perturbed-Hartree-Fock/Kohn-Sham (CPHF/KS) procedure. The present implementation, beside improving the user-friendliness of self-consistent hybrids, exploits the unperturbed and electric-field perturbed density matrices from previous iterations as guesses for subsequent SCF and CPHF/KS iterations, which is documented to reduce the overall computational cost of the whole process by a factor of 2.

Self-consistent theory of hadron-nucleus scattering. Application to pion physics

International Nuclear Information System (INIS)

Johnson, M.B.

1981-01-01

The first part of this set of two seminars will consist of a review of several of the important accomplishments made in the last few years in the field of pion-nucleus physics. Next I discuss some questions raised by these accomplishments and show that for some very natural reasons the commonly employed theoretical methods cannot be applied to answer these questions. This situation leads to the idea of self-consistency, which is first explained in a general context. The remainder of the seminars are devoted to illustrating the idea within a simple multiple-scattering model for the case of pion scattering. An evaluation of the effectiveness of the self-consistent requirment to produce a solution to the model is made, and a few of the questions raised by recent accomplishments in the field of pion physics are addressed in the model. Finally, the results of the model calculation are compared to experimental data and implications of the results discussed. (orig./HSI)

Self-consistent electrodynamic scattering in the symmetric Bragg case

International Nuclear Information System (INIS)

Campos, H.S.

1988-01-01

We have analyzed the symmetric Bragg case, introducing a model of self consistent scattering for two elliptically polarized beams. The crystal is taken as a set of mathematical planes, each of them defined by a surface density of dipoles. We have considered the mesofield and the epifield differently from that of the Ewald's theory and, we assumed a plane of dipoles and the associated fields as a self consistent scattering unit. The exact analytical treatment when applied to any two neighbouring planes, results in a general and self consistent Bragg's equation, in terms of the amplitude and phase variations. The generalized solution for the set of N planes was obtained after introducing an absorption factor in the incident radiation, in two ways: (i) the analytical one, through a rule of field similarity, which says that the incidence occurs in both faces of the all crystal planes and also, through a matricial development with the Chebyshev polynomials; (ii) using the numerical solution we calculated, iteratively, the reflectivity, the reflection phase, the transmissivity, the transmission phase and the energy. The results are showed through reflection and transmission curves, which are characteristics as from kinematical as dynamical theories. The conservation of the energy results from the Ewald's self consistency principle is used. In the absorption case, the results show that it is not the only cause for the asymmetric form in the reflection curves. The model contains basic elements for a unified, microscope, self consistent, vectorial and exact formulation for interpretating the X ray diffraction in perfect crystals. (author)

Self-consistent equilibria in cylindrical reversed-field pinch

International Nuclear Information System (INIS)

Lo Surdo, C.; Paccagnella, R.; Guo, S.

1995-03-01

The object of this work is to study the self-consistent magnetofluidstatic equilibria of a 2-region (plasma + gas) reversed-field pinch (RFP) in cylindrical approximation (namely, with vanishing inverse aspect ratio). Differently from what happens in a tokamak, in a RFP a significant part of the plasma current is driven by a dynamo electric field (DEF), in its turn mainly due to plasma turbulence. So, it is worked out a reasonable mathematical model of the above self-consistent equilibria under the following main points it has been: a) to the lowest order, and according to a standard ansatz, the turbulent DEF say ε t , is expressed as a homogeneous transform of the magnetic field B of degree 1, ε t =(α) (B), with α≡a given 2-nd rank tensor, homogeneous of degree 0 in B and generally depending on the plasma state; b) ε t does not explicitly appear in the plasma energy balance, as it were produced by a Maxwell demon able of extract the corresponding Joule power from the plasma. In particular, it is showed that, if both α and the resistivity tensor η are isotropic and constant, the magnetic field is force-free with abnormality equal to αη 0 /η, in the limit of vanishing β; that is, the well-known J.B. Taylor'result is recovered, in this particular conditions, starting from ideas quite different from the usual ones (minimization of total magnetic energy under constrained total elicity). Finally, the general problem is solved numerically under circular (besides cylindrical) symmetry, for simplicity neglecting the existence of gas region (i.e., assuming the plasma in direct contact with the external wall)

A mean field theory of coded CDMA systems

International Nuclear Information System (INIS)

Yano, Toru; Tanaka, Toshiyuki; Saad, David

2008-01-01

We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems

A mean field theory of coded CDMA systems

Energy Technology Data Exchange (ETDEWEB)

Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp

2008-08-15

We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Towards a unification of the hierarchical reference theory and the self-consistent Ornstein-Zernike approximation.

Science.gov (United States)

Reiner, A; Høye, J S

2005-12-01

The hierarchical reference theory and the self-consistent Ornstein-Zernike approximation are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase coexistence and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal, we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity, we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable mean spherical approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions that any closure to the Ornstein-Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.

On the derivation of effective field theories

International Nuclear Information System (INIS)

Uzunov, Dimo I.

2004-12-01

A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of cumulant expansion leads to a new point of view on the effective field theories. The proposed approach can be used for a systematic treatment of fluctuation effects of various length scales and, perhaps, for the development of a new coarse graining procedure. We outline and justify our method by some preliminary calculations. Concrete results are given for the critical temperature and the Landau parameters of the φ 4 -theory - the field counterpart of the Ising model. An important unresolved problem of the modern theory of phase transitions - the problem for the calculation of the true critical temperature, is considered within the framework of the present approach. A comprehensive description of the ground state properties of many-body systems is also demonstrated. (author)

Electron confinement in quantum nanostructures: Self-consistent Poisson-Schroedinger theory

International Nuclear Information System (INIS)

Luscombe, J.H.; Bouchard, A.M.; Luban, M.

1992-01-01

We compute the self-consistent electron states and confining potential, V(r,T), for laterally confined cylindrical quantum wires at a temperature T from a numerical solution of the coupled Poisson and Schroedinger (PS) equations. Finite-temperature effects are included in the electron density function, n(r,T), via the single-particle density matrix in the grand-canonical ensemble using the self-consistent bound states. We compare our results for a GaAs quantum wire with those obtained previously [J. H. Luscombe and M. Luban, Appl. Phys. Lett. 57, 61 (1990)] from a finite-temperature Thomas-Fermi (TF) approximation. We find that the TF results agree well with those of the more realistic, but also more computationally intensive PS theory, except for low temperatures or for cases where the quantum wire is almost, but not totally, depleted due to a combination of either small geometry, surface boundary conditions, or low doping concentrations. In the latter situations, the number of subbands that are populated is relatively small, and both n(r,T) and V(r,T) exhibit Friedel-type oscillations. Otherwise the TF theory, which is based on free-particle states, is remarkably accurate. We also present results for the partial electron density functions associated with the angular momentum quantum numbers, and discuss their role in populating the quantum wire

Induced boson self couplings in four-fermion and Yukawa theories

International Nuclear Information System (INIS)

Tamvakis, K.K.

1978-01-01

Theories of self-interacting fermion fields are expanded in a mean field expansion in terms of boson collective variables. Divergences can be absorbed in a renormalized mass and a renormalized Yukawa-type coupling to all orders in the mean field expansion. The cubic and quartic collective boson self-couplings required by renormalization are fixed in terms of the renormalized Yukawa coupling. This fixing is demonstrated by use of the Callan-Symanzik equations. These theories are formally equivalent to Yukawa-type theories, expanded the same way, with the boson self-couplings constrained to be functions of the Yukawa coupling

Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory

NARCIS (Netherlands)

Aarts, G.; Smit, J.

2000-01-01

As a toy model for dynamics in nonequilibrium quantum field theory we consider the abelian Higgs model in 1+1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function

Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory

International Nuclear Information System (INIS)

Janda, A.

2006-01-01

We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)

Self-consistent velocity dependent effective interactions

International Nuclear Information System (INIS)

Kubo, Takayuki; Sakamoto, Hideo; Kammuri, Tetsuo; Kishimoto, Teruo.

1993-09-01

The field coupling method is extended to a system with a velocity dependent mean potential. By means of this method, we can derive the effective interactions which are consistent with the mean potential. The self-consistent velocity dependent effective interactions are applied to the microscopic analysis of the structures of giant dipole resonances (GDR) of 148,154 Sm, of the first excited 2 + states of Sn isotopes and of the first excited 3 - states of Mo isotopes. It is clarified that the interactions play crucial roles in describing the splitting of the resonant structure of GDR peaks, in restoring the energy weighted sum rule values, and in reducing B (Eλ) values. (author)

Mean field theory of nuclei and shell model. Present status and future outlook

International Nuclear Information System (INIS)

Nakada, Hitoshi

2003-01-01

Many of the recent topics of the nuclear structure are concerned on the problems of unstable nuclei. It has been revealed experimentally that the nuclear halos and the neutron skins as well as the cluster structures or the molecule-like structures can be present in the unstable nuclei, and the magic numbers well established in the stable nuclei disappear occasionally while new ones appear. The shell model based on the mean field approximation has been successfully applied to stable nuclei to explain the nuclear structure as the finite many body system quantitatively and it is considered as the standard model at present. If the unstable nuclei will be understood on the same model basis or not is a matter related to fundamental principle of nuclear structure theories. In this lecture, the fundamental concept and the framework of the theory of nuclear structure based on the mean field theory and the shell model are presented to make clear the problems and to suggest directions for future researches. At first fundamental properties of nuclei are described under the subtitles: saturation and magic numbers, nuclear force and effective interactions, nuclear matter, and LS splitting. Then the mean field theory is presented under subtitles: the potential model, the mean field theory, Hartree-Fock approximation for nuclear matter, density dependent force, semiclassical mean field theory, mean field theory and symmetry, Skyrme interaction and density functional, density matrix expansion, finite range interactions, effective masses, and motion of center of mass. The subsequent section is devoted to the shell model with the subtitles: beyond the mean field approximation, core polarization, effective interaction of shell model, one-particle wave function, nuclear deformation and shell model, and shell model of cross shell. Finally structure of unstable nuclei is discussed with the subtitles: general remark on the study of unstable nuclear structure, asymptotic behavior of wave

Self-consistent-field method and τ-functional method on group manifold in soliton theory. II. Laurent coefficients of soliton solutions for sln and for sun

International Nuclear Information System (INIS)

Nishiyama, Seiya; Providencia, Joao da; Komatsu, Takao

2007-01-01

To go beyond perturbative method in terms of variables of collective motion, using infinite-dimensional fermions, we have aimed to construct the self-consistent-field (SCF) theory, i.e., time dependent Hartree-Fock theory on associative affine Kac-Moody algebras along the soliton theory. In this paper, toward such an ultimate goal we will reconstruct a theoretical frame for a υ (external parameter)-dependent SCF method to describe more precisely the dynamics on the infinite-dimensional fermion Fock space. An infinite-dimensional fermion operator is introduced through Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent and a Υ-periodic potential. As an illustration, we derive explicit expressions for the Laurent coefficients of soliton solutions for sl n and for su n on infinite-dimensional Grassmannian. The associative affine Kac-Moody algebras play a crucial role to determine the dynamics on the infinite-dimensional fermion Fock space

Conserving gapless mean-field theory for weakly interacting Bose gases

International Nuclear Information System (INIS)

Kita, Takafumi

2006-01-01

This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function Ψ and the Nambu Green's function G for the quasiparticle field. Imposing its stationarity respect to Ψ and G yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: 'conserving' and 'gapless'. The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length a and particle mass m to clarify its basic thermodynamic properties under two complementary conditions of constant density n and constant pressure p. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near T c inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature T c shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case T c increases from the ideal gas value T 0 as T c /T 0 =1+2.33an 1/3 , whereas it decreases in the latter as T c /T 0 =1-3.84a(mp/2πℎ 2 ) 1/5 . Temperature dependences of basic thermodynamic quantities are clarified explicitly. (author)

Self-Consistent-Field Method and τ-Functional Method on Group Manifold in Soliton Theory: a Review and New Results

Directory of Open Access Journals (Sweden)

Seiya Nishiyama

2009-01-01

Full Text Available The maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a collective submanifold in which a canonicity condition makes the collective variables to be an orthogonal coordinate-system. For this aim we adopt a concept of curvature unfamiliar in the conventional time-dependent (TD self-consistent field (SCF theory. Our basic idea lies in the introduction of a sort of Lagrange manner familiar to fluid dynamics to describe a collective coordinate-system. This manner enables us to take a one-form which is linearly composed of a TD SCF Hamiltonian and infinitesimal generators induced by collective variable differentials of a canonical transformation on a group. The integrability condition of the system read the curvature C = 0. Our method is constructed manifesting itself the structure of the group under consideration. To go beyond the maximaly-decoupled method, we have aimed to construct an SCF theory, i.e., υ (external parameter-dependent Hartree-Fock (HF theory. Toward such an ultimate goal, the υ-HF theory has been reconstructed on an affine Kac-Moody algebra along the soliton theory, using infinite-dimensional fermion. An infinite-dimensional fermion operator is introduced through a Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent potential with a Υ-periodicity. A bilinear equation for the υ-HF theory has been transcribed onto the corresponding τ-function using the regular representation for the group and the Schur-polynomials. The υ-HF SCF theory on an infinite-dimensional Fock space F∞ leads to a dynamics on an infinite-dimensional Grassmannian Gr∞ and may describe more precisely such a dynamics on the group manifold. A finite-dimensional Grassmannian is identified with a Gr�

Nonequilibrium dynamical mean-field theory

Energy Technology Data Exchange (ETDEWEB)

Eckstein, Martin

2009-12-21

The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)

Nonequilibrium dynamical mean-field theory

International Nuclear Information System (INIS)

Eckstein, Martin

2009-01-01

The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)

Self-consistent one-gluon exchange in soliton bag models

International Nuclear Information System (INIS)

Dodd, L.R.; Adelaide Univ.; Williams, A.G.

1988-01-01

The treatment of soliton bag models as two-point boundary value problems is extended to include self-consistent one-gluon exchange interactions. The colour-magnetic contribution to the nucleon-delta mass splitting is calculated self-consistently in the mean-field, one-gluon-exchange approximation for the Friedberg-Lee and Nielsen-Patkos models. Small glueball mass parameters (m GB ∝ 500 MeV) are favoured. Comparisons with previous calculations are made. (orig.)

Superconducting and other phases in organic high polymers of polyacenic carbon skeletons. II. The mean field method

International Nuclear Information System (INIS)

Kimura, M.; Kawabe, H.; Nishikawa, K.; Aono, S.

1986-01-01

Ordered phases such as CDW, SDW, and the singlet superconductivity(SSC) are predicted by means of a mean field theory. The electronic Hamiltonian is linearized by introducing order parameters which are expected to arise, and these order parameters are determined self-consistently. The behaviors of gap, transition temperature, and condensation energy are greatly different from those of BCS theory. The coexistence of the various phases is discussed. Aside from a very special case the single phase is most stable

Self-consistent equilibrium in a cylindrical, dissipative reverse field pinch

International Nuclear Information System (INIS)

Guo, S.C.; Paccagnella, R.

1994-01-01

One of the authors (C.L.S.) recently proposed a dissipative model to self-consistently solve the equilibrium problem in a free-boundary plasma column under cylindrical symmetry. In the present paper, on one hand the problem is strongly specialized to circular symmetry and to Ohm's and Fourier's laws without off-diagonal contributions; on the other hand, it is generalized by adding a dynamo effective electric field E d in Ohm's law, based on the standard turbulent model. This seems appropriate enough to study RFP equilibria, since it is well known that a stationary and cylindrically symmetric RFP is incompatible with a classical Ohm's law. Reasonably, only numerical solutions are expected to be accessible in general; but the further simplified problem with scalar and constant electric resistivity and constant dynamo coefficient α (E d =αB) can be solved analytically by elementary means. (author) 4 refs., 2 figs

Coarse grainings and irreversibility in quantum field theory

International Nuclear Information System (INIS)

Anastopoulos, C.

1997-01-01

In this paper we are interested in studying coarse graining in field theories using the language of quantum open systems. Motivated by the ideas of Hu and Calzetta on correlation histories we employ the Zwanzig projection technique to obtain evolution equations for relevant observables in self-interacting scalar field theories. Our coarse-graining operation consists in concentrating solely on the evolution of the correlation functions of degree less than n, a treatment which corresponds to the familiar truncation of the BBKGY hierarchy at the nth level. We derive the equations governing the evolution of mean-field and two-point functions thus identifying the terms corresponding to dissipation and noise. We discuss possible applications of our formalism, the emergence of classical behavior, and the connection to the decoherent histories framework. copyright 1997 The American Physical Society

Self-consistency in Capital Markets

Science.gov (United States)

Benbrahim, Hamid

2013-03-01

Capital Markets are considered, at least in theory, information engines whereby traders contribute to price formation with their diverse perspectives. Regardless whether one believes in efficient market theory on not, actions by individual traders influence prices of securities, which in turn influence actions by other traders. This influence is exerted through a number of mechanisms including portfolio balancing, margin maintenance, trend following, and sentiment. As a result market behaviors emerge from a number of mechanisms ranging from self-consistency due to wisdom of the crowds and self-fulfilling prophecies, to more chaotic behavior resulting from dynamics similar to the three body system, namely the interplay between equities, options, and futures. This talk will address questions and findings regarding the search for self-consistency in capital markets.

Time-dependent density functional theory (TD-DFT) coupled with reference interaction site model self-consistent field explicitly including spatial electron density distribution (RISM-SCF-SEDD)

Energy Technology Data Exchange (ETDEWEB)

Yokogawa, D., E-mail: d.yokogawa@chem.nagoya-u.ac.jp [Department of Chemistry, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602 (Japan); Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8602 (Japan)

2016-09-07

Theoretical approach to design bright bio-imaging molecules is one of the most progressing ones. However, because of the system size and computational accuracy, the number of theoretical studies is limited to our knowledge. To overcome the difficulties, we developed a new method based on reference interaction site model self-consistent field explicitly including spatial electron density distribution and time-dependent density functional theory. We applied it to the calculation of indole and 5-cyanoindole at ground and excited states in gas and solution phases. The changes in the optimized geometries were clearly explained with resonance structures and the Stokes shift was correctly reproduced.

Lopsidedness of Self-consistent Galaxies Caused by the External Field Effect of Clusters

Energy Technology Data Exchange (ETDEWEB)

Wu, Xufen [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, 230026 (China); Wang, Yougang [Key Laboratory of Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012 (China); Feix, Martin [CNRS, UMR 7095 and UPMC, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, F-75014 Paris (France); Zhao, HongSheng, E-mail: xufenwu@ustc.edu.cn [School of Physics and Astronomy, University of St Andrews, North Haugh, Fife, KY16 9SS (United Kingdom)

2017-08-01

Adopting Schwarzschild’s orbit-superposition technique, we construct a series of self-consistent galaxy models, embedded in the external field of galaxy clusters in the framework of Milgrom’s MOdified Newtonian Dynamics (MOND). These models represent relatively massive ellipticals with a Hernquist radial profile at various distances from the cluster center. Using N -body simulations, we perform a first analysis of these models and their evolution. We find that self-gravitating axisymmetric density models, even under a weak external field, lose their symmetry by instability and generally evolve to triaxial configurations. A kinematic analysis suggests that the instability originates from both box and nonclassified orbits with low angular momentum. We also consider a self-consistent isolated system that is then placed in a strong external field and allowed to evolve freely. This model, just like the corresponding equilibrium model in the same external field, eventually settles to a triaxial equilibrium as well, but has a higher velocity radial anisotropy and is rounder. The presence of an external field in the MOND universe generically predicts some lopsidedness of galaxy shapes.

Lopsidedness of Self-consistent Galaxies Caused by the External Field Effect of Clusters

Science.gov (United States)

Wu, Xufen; Wang, Yougang; Feix, Martin; Zhao, HongSheng

2017-08-01

Adopting Schwarzschild’s orbit-superposition technique, we construct a series of self-consistent galaxy models, embedded in the external field of galaxy clusters in the framework of Milgrom’s MOdified Newtonian Dynamics (MOND). These models represent relatively massive ellipticals with a Hernquist radial profile at various distances from the cluster center. Using N-body simulations, we perform a first analysis of these models and their evolution. We find that self-gravitating axisymmetric density models, even under a weak external field, lose their symmetry by instability and generally evolve to triaxial configurations. A kinematic analysis suggests that the instability originates from both box and nonclassified orbits with low angular momentum. We also consider a self-consistent isolated system that is then placed in a strong external field and allowed to evolve freely. This model, just like the corresponding equilibrium model in the same external field, eventually settles to a triaxial equilibrium as well, but has a higher velocity radial anisotropy and is rounder. The presence of an external field in the MOND universe generically predicts some lopsidedness of galaxy shapes.

Fully self-consistent GW calculations for molecules

DEFF Research Database (Denmark)

Rostgaard, Carsten; Jacobsen, Karsten Wedel; Thygesen, Kristian Sommer

2010-01-01

We calculate single-particle excitation energies for a series of 34 molecules using fully self-consistent GW, one-shot G0W0, Hartree-Fock (HF), and hybrid density-functional theory (DFT). All calculations are performed within the projector-augmented wave method using a basis set of Wannier...... functions augmented by numerical atomic orbitals. The GW self-energy is calculated on the real frequency axis including its full frequency dependence and off-diagonal matrix elements. The mean absolute error of the ionization potential (IP) with respect to experiment is found to be 4.4, 2.6, 0.8, 0.4, and 0...

Coherent states field theory in supramolecular polymer physics

Science.gov (United States)

Fredrickson, Glenn H.; Delaney, Kris T.

2018-05-01

In 1970, Edwards and Freed presented an elegant representation of interacting branched polymers that resembles the coherent states (CS) formulation of second-quantized field theory. This CS polymer field theory has been largely overlooked during the intervening period in favor of more conventional "auxiliary field" (AF) interacting polymer representations that form the basis of modern self-consistent field theory (SCFT) and field-theoretic simulation approaches. Here we argue that the CS representation provides a simpler and computationally more efficient framework than the AF approach for broad classes of reversibly bonding polymers encountered in supramolecular polymer science. The CS formalism is reviewed, initially for a simple homopolymer solution, and then extended to supramolecular polymers capable of forming reversible linkages and networks. In the context of the Edwards model of a non-reacting homopolymer solution and one and two-component models of telechelic reacting polymers, we discuss the structure of CS mean-field theory, including the equivalence to SCFT, and show how weak-amplitude expansions (random phase approximations) can be readily developed without explicit enumeration of all reaction products in a mixture. We further illustrate how to analyze CS field theories beyond SCFT at the level of Gaussian field fluctuations and provide a perspective on direct numerical simulations using a recently developed complex Langevin technique.

Gyrokinetic field theory

International Nuclear Information System (INIS)

Sugama, H.

1999-08-01

The Lagrangian formulation of the gyrokinetic theory is generalized in order to describe the particles' dynamics as well as the self-consistent behavior of the electromagnetic fields. The gyrokinetic equation for the particle distribution function and the gyrokinetic Maxwell's equations for the electromagnetic fields are both derived from the variational principle for the Lagrangian consisting of the parts of particles, fields, and their interaction. In this generalized Lagrangian formulation, the energy conservation property for the total nonlinear gyrokinetic system of equations is directly shown from the Noether's theorem. This formulation can be utilized in order to derive the nonlinear gyrokinetic system of equations and the rigorously conserved total energy for fluctuations with arbitrary frequency. (author)

Semiclassical approximations in a mean-field theory with collision terms

International Nuclear Information System (INIS)

Galetti, D.

1986-01-01

Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt

The numerical multiconfiguration self-consistent field approach for atoms

International Nuclear Information System (INIS)

Stiehler, Johannes

1995-12-01

The dissertation uses the Multiconfiguration Self-Consistent Field Approach to specify the electronic wave function of N electron atoms in a static electrical field. It presents numerical approaches to describe the wave functions and introduces new methods to compute the numerical Fock equations. Based on results computed with an implemented computer program the universal application, flexibility and high numerical precision of the presented approach is shown. RHF results and for the first time MCSCF results for polarizabilities and hyperpolarizabilities of various states of the atoms He to Kr are discussed. In addition, an application to interpret a plasma spectrum of gallium is presented. (orig.)

Consistent guiding center drift theories

International Nuclear Information System (INIS)

Wimmel, H.K.

1982-04-01

Various guiding-center drift theories are presented that are optimized in respect of consistency. They satisfy exact energy conservation theorems (in time-independent fields), Liouville's theorems, and appropriate power balance equations. A theoretical framework is given that allows direct and exact derivation of associated drift-kinetic equations from the respective guiding-center drift-orbit theories. These drift-kinetic equations are listed. Northrop's non-optimized theory is discussed for reference, and internal consistency relations of G.C. drift theories are presented. (orig.)

Structural predictions for Correlated Electron Materials Using the Functional Dynamical Mean Field Theory Approach

Science.gov (United States)

Haule, Kristjan

2018-04-01

The Dynamical Mean Field Theory (DMFT) in combination with the band structure methods has been able to address reach physics of correlated materials, such as the fluctuating local moments, spin and orbital fluctuations, atomic multiplet physics and band formation on equal footing. Recently it is getting increasingly recognized that more predictive ab-initio theory of correlated systems needs to also address the feedback effect of the correlated electronic structure on the ionic positions, as the metal-insulator transition is almost always accompanied with considerable structural distortions. We will review recently developed extension of merger between the Density Functional Theory (DFT) and DMFT method, dubbed DFT+ embedded DMFT (DFT+eDMFT), whichsuccessfully addresses this challenge. It is based on the stationary Luttinger-Ward functional to minimize the numerical error, it subtracts the exact double-counting of DFT and DMFT, and implements self-consistent forces on all atoms in the unit cell. In a few examples, we will also show how the method elucidated the important feedback effect of correlations on crystal structure in rare earth nickelates to explain the mechanism of the metal-insulator transition. The method showed that such feedback effect is also essential to understand the dynamic stability of the high-temperature body-centered cubic phase of elemental iron, and in particular it predicted strong enhancement of the electron-phonon coupling over DFT values in FeSe, which was very recently verified by pioneering time-domain experiment.

BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields

Science.gov (United States)

Dai, Jialiang; Fan, Engui

2018-04-01

We apply BRST method to the self-dual Chern-Simons gauge theory with matter fields and the generators of symmetries of the system from an elegant Lie algebra structure under the operation of Poisson bracket. We discuss four different cases: abelian, nonabelian, relativistic, and nonrelativistic situations and extend the system to the whole phase space including ghost fields. In addition, we obtain the BRST charge of the field system and check its nilpotence of the BRST transformation which plays an important role such as in topological quantum field theory and string theory.

Effects of Dzyaloshinsky–Moriya interaction on magnetism in nanodisks from a self-consistent approach

Energy Technology Data Exchange (ETDEWEB)

Liu, Zhaosen, E-mail: liuzhsnj@yahoo.com [Nanjing University of Information Science and Technology, Department of Applied Physics (China); Ian, Hou, E-mail: houian@umac.mo [University of Macau, Institute of Applied Physics and Materials Engineering, FST (China)

2016-01-15

We give a theoretical study on the magnetic properties of monolayer nanodisks with both Heisenberg exchange and Dzyaloshinsky–Moriya (DM) interactions. In particular, we survey the magnetic effects caused by anisotropy, external magnetic field, and disk size when DM interaction is present by means of a new quantum simulation method facilitated by a self-consistent algorithm based on mean field theory. This computational approach finds that uniaxial anisotropy and transversal magnetic field enhance the net magnetization as well as increase the transition temperature of the vortical phase while preserving the chiralities of the swirly magnetic structures, whereas when the strength of DM interaction is sufficiently strong for a given disk size, magnetic domains appear within the circularly bounded region, which vanish and give in to a single vortex when a transversal magnetic field is applied. The latter confirms the magnetic skyrmions induced by the magnetic field as observed in the experiments.

Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws

International Nuclear Information System (INIS)

Kita, Takafumi

2009-01-01

Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure to construct such approximations systematically by using either an exact relation for the interaction energy or the Hugenholtz-Pines relation to express the thermodynamic potential in a Luttinger-Ward form. Inspection of the self-consistent perturbation expansion up to the third order with respect to the interaction shows that the two relations yield a unique identical result at each order, reproducing the conserving-gapless mean-field theory [T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005)] as the lowest-order approximation. The uniqueness implies that the series becomes exact when infinite terms are retained. We also derive useful expressions for the entropy and superfluid density in terms of Green's function and a set of real-time dynamical equations to describe thermalization of the condensate.

On a gauge theory of the self-dual field and its quantization

International Nuclear Information System (INIS)

Srivastava, P.P.

1990-01-01

A gauge theory of self-dual fields is constructed by adding a Wess-Zumino term to the recently studied formulation based on a second-order scalar field lagrangian carrying with it an auxiliary vector field to take care of the self-duality constraint in a linear fashion. The two versions are quantized using the BRST formulation following the BFV procedure. No violation of microcausality occurs and the action of the ordinary scalar field may not be written as the sum of the actions of the self- and anti-self-dual fields. (orig.)

Some approximate calculations in SU2 lattice mean field theory

International Nuclear Information System (INIS)

Hari Dass, N.D.; Lauwers, P.G.

1981-12-01

Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)

DO SELF-THEORIES EXPLAIN OVERCONFIDENCE AND FINANCIAL RISK TAKING? A field experiment.

OpenAIRE

Bertrand Koebel; André Schmitt; Sandrine Spaeter

2015-01-01

How people develop beliefs about themselves (self-theories) plays an important role on motivation and achievement as shown by Carol Dweck’s life-long research. In this paper, we conduct a field experiment to investigate whether self-theories impact overconfidence and risk taking. Self-theories deal with how an individual perceives some of her attributes such as intelligence, personality or moral character. In this paper, we are interested by how people perceive their mindset (fixed or growth)...

Nonlinear many-body reaction theories from nuclear mean field approximations

International Nuclear Information System (INIS)

Griffin, J.J.

1983-01-01

Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

Instability in relativistic mean-field theories of nuclear matter

International Nuclear Information System (INIS)

Friman, B.L.; Henning, P.A.

1988-01-01

We investigate the stability of the nuclear matter ground state with respect to small-perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion-collisions are discussed briefly. (orig.)

Instability in relativistic mean-field theories of nuclear matter

International Nuclear Information System (INIS)

Friman, B.L.; Henning, P.A.

1988-01-01

We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly. (orig.)

Hartree-type approximation applied to a phi4 field theory

International Nuclear Information System (INIS)

Chang, S.-J.

1976-01-01

Recently, there has been considerable interest in studying the relativistic field theories by means of nonperturbative method. These studies are partially motivated by the now fashionable physical picture that the hadrons are created from an 'abnormal vacuum state'. This abnormal vacuum state is the ground state associated with a spontaneously broken symmetry and is usually characterized by the non-vanishing expectation value of one or more scale fields. Presently, nearly all understandings of hadrons in the above description are based on semi-classical calculations. It is important to know how significant are the effects of the quantum corrections. Some results on the quantum fluctuations in a phi 4 field theory based in a self-consistent Hartree-type approximation are described. (Auth.)

On the hydrodynamic limit of self-consistent field equations

International Nuclear Information System (INIS)

Pauli, H.C.

1980-01-01

As an approximation to the nuclear many-body problem, the hydrodynamical limit of self-consistent field equations is worked out and applied to the treatment of vibrational and rotational motion. Its validity is coupled to the value of a smallness parameter, behaving as 20Asup(-2/3) with the number of nucleons. For finite nuclei, this number is not small enough as compared to 1, and indeed one observes a discrepancy of roughly a factor of 5 between the hydrodynamic frequencies and the relevant experimental numbers. (orig.)

Mean field theory of dynamic phase transitions in ferromagnets

International Nuclear Information System (INIS)

Idigoras, O.; Vavassori, P.; Berger, A.

2012-01-01

We have studied the second order dynamic phase transition (DPT) of the two-dimensional kinetic Ising model by means of numerical calculations. While it is well established that the order parameter Q of the DPT is the average magnetization per external field oscillation cycle, the possible identity of the conjugate field has been addressed only recently. In this work, we demonstrate that our entire set of numerical data is fully consistent with the applied bias field H b being the conjugate field of order parameter Q. For this purpose, we have analyzed the Q(H b )-dependence and we have found that it follows the expected power law behavior with the same critical exponent as the mean field equilibrium case.

Thermodynamically self-consistent integral equations and the structure of liquid metals

International Nuclear Information System (INIS)

Pastore, G.; Kahl, G.

1987-01-01

We discuss the application of the new thermodynamically self-consistent integral equations for the determination of the structural properties of liquid metals. We present a detailed comparison of the structure (S(q) and g(r)) for models of liquid alkali metals as obtained from two thermodynamically self-consistent integral equations and some published exact computer simulation results; the range of states extends from the triple point to the expanded metal. The theories which only impose thermodynamic self-consistency without any fitting of external data show an excellent agreement with the simulation results, thus demonstrating that this new type of integral equation is definitely superior to the conventional ones (hypernetted chain, Percus-Yevick, mean spherical approximation, etc). (author)

Phenomenology of noncommutative field theories

International Nuclear Information System (INIS)

Carone, C D

2006-01-01

Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model

Functional differential equation approach to the large N expansion and mean field perturbation theory

International Nuclear Information System (INIS)

Bender, C.M.; Cooper, F.

1985-01-01

An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi

Mean-field theory of active electrolytes: Dynamic adsorption and overscreening

Science.gov (United States)

Frydel, Derek; Podgornik, Rudolf

2018-05-01

We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.

Relativistic mean field theory for unstable nuclei

International Nuclear Information System (INIS)

Toki, Hiroshi

2000-01-01

We discuss the properties of unstable nuclei in the framework of the relativistic mean field (RMF) theory. We take the RMF theory as a phenomenological theory with several parameters, whose form is constrained by the successful microscopic theory (RBHF), and whose values are extracted from the experimental values of unstable nuclei. We find the outcome with the newly obtained parameter sets (TM1 and TMA) is promising in comparison with various experimental data. We calculate systematically the ground state properties of even-even nuclei up to the drip lines; about 2000 nuclei. We find that the neutron magic shells (N=82, 128) at the standard magic numbers stay at the same numbers even far from the stability line and hence provide the feature of the r-process nuclei. However, many proton magic numbers disappear at the neutron numbers far away from the magic numbers due to the deformations. We discuss how to describe giant resonances for the case of the non-linear coupling terms for the sigma and omega mesons in the relativistic RPA. We mention also the importance of the relativistic effect on the spin observables as the Gamow-Teller strength and the longitudinal and transverse spin responses. (author)

A self-consistency check for unitary propagation of Hawking quanta

Science.gov (United States)

Baker, Daniel; Kodwani, Darsh; Pen, Ue-Li; Yang, I.-Sheng

2017-11-01

The black hole information paradox presumes that quantum field theory in curved space-time can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum-gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman’s analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern is projected is infinitely far away. We argue for an analogous self-consistency check for quantum field theory in curved space-time. We apply it to the propagation of Hawking quanta and test whether ignoring the entanglement with the geometry also becomes arbitrarily reliable in the limit of a large black hole. We present curious results to suggest a negative answer, and we discuss how this loss of naive unitarity in QFT might be related to a solution of the paradox based on the soft-hair-memory effect.

Self-consistent particle distribution of a bunched beam in RF field

CERN Document Server

Batygin, Y K

2002-01-01

An analytical solution for the self-consistent particle equilibrium distribution in an RF field with transverse focusing is found. The solution is attained in the approximation of a high brightness beam. The distribution function in phase space is determined as a stationary function of the energy integral. Equipartitioning of the beam distribution between degrees of freedom follows directly from the choice of the stationary distribution function. Analytical expressions for r-z equilibrium beam profile and maximum beam current in RF field are obtained.

Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory

Energy Technology Data Exchange (ETDEWEB)

Lin, Lin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division

2013-10-28

We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied by the total potential. They can be viewed as preconditioners for a fixed point iteration. We point out different requirements for constructing preconditioners for insulating and metallic systems respectively, and discuss how to construct preconditioners to keep the convergence rate of the fixed point iteration independent of the size of the atomistic system. We propose a new preconditioner that can treat insulating and metallic system in a unified way. The new preconditioner, which we call an elliptic preconditioner, is constructed by solving an elliptic partial differential equation. The elliptic preconditioner is shown to be more effective in accelerating the convergence of a fixed point iteration than the existing approaches for large inhomogeneous systems at low temperature.

On the consistency of quantum geometrodynamics and quantum field theories in the Bohm-de Broglie Interpretation

Energy Technology Data Exchange (ETDEWEB)

Pinto-Neto, N.; Santini, E. Sergio. E-mail: nelsonpn@lafex.cbpf.br; santini@lafex.cbpf.br

2000-12-01

We consider quantum geometrodynamics and parametrized quantum field theories in the frame-work of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work, where a Hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative Hamiltonian method, a concrete example already known in the literature where Lorentz invariance of individual events is broken. (author)

Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: exactly solvable two-site Hubbard model.

Science.gov (United States)

Kutepov, A L

2015-08-12

Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ1 from the first-order perturbation theory, and the exact vertex Γ(E)). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. The results obtained with the exact vertex are directly related to the present open question-which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on perturbation theory (PT) systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.

Theory of field induced incommensurability: CsFeCl3

DEFF Research Database (Denmark)

Lindgård, Per-Anker

1986-01-01

Using correlation theory for the singlet-doublet magnet CsFeCl3 in a magnetic field, a field induced incommensurate ordering along K-M is predicted without invoking dipolar effects. A fully self-consistent RPA theory gives Hc=44 kG in agreement with experiments at T=1.3K. Correlation and dipolar...

Justifying quasiparticle self-consistent schemes via gradient optimization in Baym-Kadanoff theory.

Science.gov (United States)

Ismail-Beigi, Sohrab

2017-09-27

The question of which non-interacting Green's function 'best' describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a realistic manner. Here, we study this question within the framework of Baym-Kadanoff theory, an approach where one locates the stationary point of a total energy functional of the one-particle Green's function in order to find the total ground-state energy as well as all one-particle properties such as the density matrix, chemical potential, or the quasiparticle energy spectrum and quasiparticle wave functions. For the case of the Klein functional, our basic finding is that minimizing the length of the gradient of the total energy functional over non-interacting Green's functions yields a set of self-consistent equations for quasiparticles that is identical to those of the quasiparticle self-consistent GW (QSGW) (van Schilfgaarde et al 2006 Phys. Rev. Lett. 96 226402-4) approach, thereby providing an a priori justification for such an approach to electronic structure calculations. In fact, this result is general, applies to any self-energy operator, and is not restricted to any particular approximation, e.g., the GW approximation for the self-energy. The approach also shows that, when working in the basis of quasiparticle states, solving the diagonal part of the self-consistent Dyson equation is of primary importance while the off-diagonals are of secondary importance, a common observation in the electronic structure literature of self-energy calculations. Finally, numerical tests and analytical arguments show that when the Dyson equation produces multiple quasiparticle solutions corresponding to a single non-interacting state, minimizing the length of the gradient translates into choosing the solution with largest quasiparticle weight.

A self-consistent field study of diblock copolymer/charged particle system morphologies for nanofiltration membranes

International Nuclear Information System (INIS)

Zhang, Bo; Ye, Xianggui; Edwards, Brian J.

2013-01-01

A combination of self-consistent field theory and density functional theory was used to examine the stable, 3-dimensional equilibrium morphologies formed by diblock copolymers with a tethered nanoparticle attached either between the two blocks or at the end of one of the blocks. Both neutral and interacting particles were examined, with and without favorable/unfavorable energetic potentials between the particles and the block segments. The phase diagrams of the various systems were constructed, allowing the identification of three types of ordered mesophases composed of lamellae, hexagonally packed cylinders, and spheroids. In particular, we examined the conditions under which the mesophases could be generated wherein the tethered particles were primarily located within the interface between the two blocks of the copolymer. Key factors influencing these properties were determined to be the particle position along the diblock chain, the interaction potentials of the blocks and particles, the block copolymer composition, and molecular weight of the copolymer

Density dependent hadron field theory

International Nuclear Information System (INIS)

Fuchs, C.; Lenske, H.; Wolter, H.H.

1995-01-01

A fully covariant approach to a density dependent hadron field theory is presented. The relation between in-medium NN interactions and field-theoretical meson-nucleon vertices is discussed. The medium dependence of nuclear interactions is described by a functional dependence of the meson-nucleon vertices on the baryon field operators. As a consequence, the Euler-Lagrange equations lead to baryon rearrangement self-energies which are not obtained when only a parametric dependence of the vertices on the density is assumed. It is shown that the approach is energy-momentum conserving and thermodynamically consistent. Solutions of the field equations are studied in the mean-field approximation. Descriptions of the medium dependence in terms of the baryon scalar and vector density are investigated. Applications to infinite nuclear matter and finite nuclei are discussed. Density dependent coupling constants obtained from Dirac-Brueckner calculations with the Bonn NN potentials are used. Results from Hartree calculations for energy spectra, binding energies, and charge density distributions of 16 O, 40,48 Ca, and 208 Pb are presented. Comparisons to data strongly support the importance of rearrangement in a relativistic density dependent field theory. Most striking is the simultaneous improvement of charge radii, charge densities, and binding energies. The results indicate the appearance of a new ''Coester line'' in the nuclear matter equation of state

Non-local correlations within dynamical mean field theory

Energy Technology Data Exchange (ETDEWEB)

Li, Gang

2009-03-15

The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)

Non-local correlations within dynamical mean field theory

International Nuclear Information System (INIS)

Li, Gang

2009-03-01

The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)

Ab initio, mean field theory and series expansions calculations study of electronic and magnetic properties of antiferromagnetic MnSe alloys

Energy Technology Data Exchange (ETDEWEB)

Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, BP. 63, 46000 Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Mounkachi, O.; El Moussaoui, H. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)

2014-06-01

Self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the MnSe lattice. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn lattices. Magnetic moments considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The zero-field high temperature static susceptibility series of the spin −4.28 nearest-neighbor Ising model on face centered cubic (fcc) and lattices is thoroughly analyzed by means of a power series coherent anomaly method (CAM). The exchange interaction between the magnetic atoms and the Néel temperature are deduced using the mean filed and HTSEs theories. - Highlights: • Ab initio calculations are used to investigate both electronic and magnetic properties of the MnSe alloys. • Obtained data from ab initio calculations are used as input for the HTSEs. • The Néel temperature is obtained for MnSe alloys.

Linking lipid architecture to bilayer structure and mechanics using self-consistent field modelling

International Nuclear Information System (INIS)

Pera, H.; Kleijn, J. M.; Leermakers, F. A. M.

2014-01-01

To understand how lipid architecture determines the lipid bilayer structure and its mechanics, we implement a molecularly detailed model that uses the self-consistent field theory. This numerical model accurately predicts parameters such as Helfrichs mean and Gaussian bending modulus k c and k ¯ and the preferred monolayer curvature J 0 m , and also delivers structural membrane properties like the core thickness, and head group position and orientation. We studied how these mechanical parameters vary with system variations, such as lipid tail length, membrane composition, and those parameters that control the lipid tail and head group solvent quality. For the membrane composition, negatively charged phosphatidylglycerol (PG) or zwitterionic, phosphatidylcholine (PC), and -ethanolamine (PE) lipids were used. In line with experimental findings, we find that the values of k c and the area compression modulus k A are always positive. They respond similarly to parameters that affect the core thickness, but differently to parameters that affect the head group properties. We found that the trends for k ¯ and J 0 m can be rationalised by the concept of Israelachivili's surfactant packing parameter, and that both k ¯ and J 0 m change sign with relevant parameter changes. Although typically k ¯ 0 m ≫0, especially at low ionic strengths. We anticipate that these changes lead to unstable membranes as these become vulnerable to pore formation or disintegration into lipid disks

Three-dimensional loop quantum gravity: towards a self-gravitating quantum field theory

International Nuclear Information System (INIS)

Noui, Karim

2007-01-01

In a companion paper, we have emphasized the role of the Drinfeld double DSU(2) in the context of three-dimensional Riemannian loop quantum gravity coupled to massive spinless point particles. We make use of this result to propose a model for a self-gravitating quantum field theory (massive spinless non-causal scalar field) in three-dimensional Riemannian space. We start by constructing the Fock space of the free self-gravitating field: the vacuum is the unique DSU(2) invariant state, one-particle states correspond to DSU(2) unitary irreducible simple representations and any multi-particles states are obtained as the symmetrized tensor product between simple representations. The associated quantum field is defined by the usual requirement of covariance under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential (the obtained model is a group field theory) and explicitly compute the lowest order terms (in the self-interaction coupling constant λ) of the propagator and of the three-point function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G) to the propagator and to the three-point function

Quasi-Particle Self-Consistent GW for Molecules.

Science.gov (United States)

Kaplan, F; Harding, M E; Seiler, C; Weigend, F; Evers, F; van Setten, M J

2016-06-14

We present the formalism and implementation of quasi-particle self-consistent GW (qsGW) and eigenvalue only quasi-particle self-consistent GW (evGW) adapted to standard quantum chemistry packages. Our implementation is benchmarked against high-level quantum chemistry computations (coupled-cluster theory) and experimental results using a representative set of molecules. Furthermore, we compare the qsGW approach for five molecules relevant for organic photovoltaics to self-consistent GW results (scGW) and analyze the effects of the self-consistency on the ground state density by comparing calculated dipole moments to their experimental values. We show that qsGW makes a significant improvement over conventional G0W0 and that partially self-consistent flavors (in particular evGW) can be excellent alternatives.

Self-consistent areas law in QCD

International Nuclear Information System (INIS)

Makeenko, Yu.M.; Migdal, A.A.

1980-01-01

The problem of obtaining the self-consistent areas law in quantum chromodynamics (QCD) is considered from the point of view of the quark confinement. The exact equation for the loop average in multicolor QCD is reduced to a bootstrap form. Its iterations yield new manifestly gauge invariant perturbation theory in the loop space, reproducing asymptotic freedom. For large loops, the areas law apprears to be a self-consistent solution

The application of mean field theory to image motion estimation.

Science.gov (United States)

Zhang, J; Hanauer, G G

1995-01-01

Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.

Mean-field theory of spin-glasses with finite coordination number

Science.gov (United States)

Kanter, I.; Sompolinsky, H.

1987-01-01

The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.

Relativistic deformed mean-field calculation of binding energy differences of mirror nuclei

International Nuclear Information System (INIS)

Koepf, W.; Barreiro, L.A.

1996-01-01

Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existence of the Okamoto-Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is significantly smaller than the one obtained within state-of-the-art nonrelativistic calculations. (author). 35 refs

Configuration mixing of mean-field states

International Nuclear Information System (INIS)

Bender, M; Heenen, P-H

2005-01-01

Starting from self-consistent mean-field models, we discuss how to include correlations from fluctuations in collective degrees of freedom through symmetry restoration and configuration mixing, which give access to ground-state correlations and collective excitations. As an example for the method, we discuss the spectroscopy of neutron-deficient Pb isotopes

Self-consistent radial sheath

International Nuclear Information System (INIS)

Hazeltine, R.D.

1988-12-01

The boundary layer arising in the radial vicinity of a tokamak limiter is examined, with special reference to the TEXT tokamak. It is shown that sheath structure depends upon the self-consistent effects of ion guiding-center orbit modification, as well as the radial variation of E /times/ B-induced toroidal rotation. Reasonable agreement with experiment is obtained from an idealized model which, however simplified, preserves such self-consistent effects. It is argued that the radial sheath, which occurs whenever confining magnetic field-lines lie in the plasma boundary surface, is an object of some intrinsic interest. It differs from the more familiar axial sheath because magnetized charges respond very differently to parallel and perpendicular electric fields. 11 refs., 1 fig

Nonlinear and self-consistent treatment of ECRH

Energy Technology Data Exchange (ETDEWEB)

Tsironis, C.; Vlahos, L.

2005-07-01

A self-consistent formulation for the nonlinear interaction of electromagnetic waves with relativistic magnetized electrons is applied for the description of the ECRH. In general, electron-cyclotron absorption is the result of resonances between the cyclotron harmonics and the Doppler-shifted waver frequency. The resonant interaction results to an intense wave-particle energy exchange and an electron acceleration, and for that reason it is widely applied in fusion experiments for plasma heating and current drive. The linear theory, for the wave absorption, as well as the quasilinear theory for the electron distribution function, are the most frequently-used tools for the study of wave-particle interactions. However, in many cases the validity of these theories is violated, namely cases where nonlinear effects, like, e. g. particle trapping in the wave field, are dominant in the particle phase-space. Our model consists of electrons streaming and gyrating in a tokamak plasma slab, which is finite in the directions perpendicular to the main magnetic field. The particles interact with an electromagnetic electron-cyclotron wave of the ordinary (O-) or the extraordinary (X-) mode. A set of nonlinear and relativistic equations is derived, which take into account the effects of the charged particle motions on the wave. These consist of the equations of motion for the plasma electrons in the slab, as well as the wave equation in terms of the vector potential. The effect of the electron motions on the temporal evolution of the wave is reflected in the current density source term. (Author)

Nonlinear and self-consistent treatment of ECRH

International Nuclear Information System (INIS)

Tsironis, C.; Vlahos, L.

2005-01-01

A self-consistent formulation for the nonlinear interaction of electromagnetic waves with relativistic magnetized electrons is applied for the description of the ECRH. In general, electron-cyclotron absorption is the result of resonances between the cyclotron harmonics and the Doppler-shifted waver frequency. The resonant interaction results to an intense wave-particle energy exchange and an electron acceleration, and for that reason it is widely applied in fusion experiments for plasma heating and current drive. The linear theory, for the wave absorption, as well as the quasilinear theory for the electron distribution function, are the most frequently-used tools for the study of wave-particle interactions. However, in many cases the validity of these theories is violated, namely cases where nonlinear effects, like, e. g. particle trapping in the wave field, are dominant in the particle phase-space. Our model consists of electrons streaming and gyrating in a tokamak plasma slab, which is finite in the directions perpendicular to the main magnetic field. The particles interact with an electromagnetic electron-cyclotron wave of the ordinary (O-) or the extraordinary (X-) mode. A set of nonlinear and relativistic equations is derived, which take into account the effects of the charged particle motions on the wave. These consist of the equations of motion for the plasma electrons in the slab, as well as the wave equation in terms of the vector potential. The effect of the electron motions on the temporal evolution of the wave is reflected in the current density source term. (Author)

[Studies in quantum field theory

International Nuclear Information System (INIS)

1990-01-01

During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity

Nuclear matter in relativistic mean field theory with isovector scalar meson.

Energy Technology Data Exchange (ETDEWEB)

Kubis, S.; Kutschera, M. [Institute of Nuclear Physics, Cracow (Poland)

1996-12-01

Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)] is studied. While the {delta}-meson field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to {delta}-field to the nuclear symmetry energy is negative. To fit the empirical value, E{sub s}{approx}30 MeV, a stronger {rho}-meson coupling is required than in absence of the {delta}-field. The energy per particle of neutron star matter is than larger at high densities than the one with no {delta}-field included. Also, the proton fraction of {beta}-stable matter increases. Splitting of proton and neutron effective masses due to the {delta}-field can affect transport properties of neutron star matter. (author). 4 refs, 6 figs.

Nuclear matter in relativistic mean field theory with isovector scalar meson

International Nuclear Information System (INIS)

Kubis, S.; Kutschera, M.

1996-12-01

Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)] is studied. While the δ-meson field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to δ-field to the nuclear symmetry energy is negative. To fit the empirical value, E s ∼30 MeV, a stronger ρ-meson coupling is required than in absence of the δ-field. The energy per particle of neutron star matter is than larger at high densities than the one with no δ-field included. Also, the proton fraction of β-stable matter increases. Splitting of proton and neutron effective masses due to the δ-field can affect transport properties of neutron star matter. (author). 4 refs, 6 figs

Self-consistent neutral point current and fields from single particle dynamics

International Nuclear Information System (INIS)

Martin, R.F. Jr.

1988-01-01

In order to begin to build a global model of the magnetotail-auroral region interaction, it is of interest to understand the role of neutral points as potential centers of particle energization in the tail. In this paper, the single particle current is calculated near a magnetic neutral point with magnetotail properties. This is balanced with the Ampere's law current producing the magnetic field to obtain the self-consistent electric field for the problem. Also calculated is the current-electric field relationship and, in the regime where this relation is linear, an effective conductivity. Results for these macroscopic quantities are surprisingly similar to the values calculated for a constant normal field current sheet geometry. Application to magnetotail modeling is discussed. 11 references

Nonstandard approximation schemes for lower dimensional quantum field theories

International Nuclear Information System (INIS)

Fitzpatrick, D.A.

1981-01-01

The purpose of this thesis has been to apply two different nonstandard approximation schemes to a variety of lower-dimensional schemes. In doing this, we show their applicability where (e.g., Feynman or Rayleigh-Schroedinger) approximation schemes are inapplicable. We have applied the well-known mean-field approximation scheme by Guralnik et al. to general lower dimensional theories - the phi 4 field theory in one dimension, and the massive and massless Thirring models in two dimensions. In each case, we derive a bound-state propagator and then expand the theory in terms of the original and bound-state propagators. The results obtained can be compared with previously known results thereby show, in general, reasonably good convergence. In the second half of the thesis, we develop a self-consistent quantum mechanical approximation scheme. This can be applied to any monotonic polynomial potential. It has been applied in detail to the anharmonic oscillator, and the results in several analytical domains are very good, including extensive tables of numerical results

Self-organization of physical fields and spin

International Nuclear Information System (INIS)

Pestov, I.B.

2008-01-01

The subject of the present investigation is the laws of intrinsic self-organization of fundamental physical fields. In the framework of the Theory of Self-Organization the geometrical and physical nature of spin phenomena is uncovered. The key points are spin symmetry (the fundamental realization of the concept of geometrical internal symmetry) and the spinning field (space of defining representation of spin symmetry). It is shown that the essence of spin is the bipolar structure of spin symmetry induced by the gravitational potentials. The bipolar structure provides natural violation of spin symmetry and leads to spinstatics (theory of spinning field outside the time) and spindynamics. The equations of spinstatics and spindynamics are derived. It is shown that Sommerfeld's formula can be derived from the equations of spindynamics and hence the correspondence principle is valid. This means that the Theory of Self-Organization provides the new understanding of spin phenomena

The accuracy of the time-dependent self-consistent-field approximation for inelastic collisions

DEFF Research Database (Denmark)

Henriksen, Niels Engholm; Billing, Gert D.; Hansen, Flemming Yssing

1992-01-01

We study the accuracy of the time-dependent self-consistent-field approximation for collinear inelastic collisions between an atom and a diatomic molecule. Individual state-to-state transition probabilities, total energy transfer. and the global description of the wavefunction is considered...

Does one see gluon condensation after subtraction of mean field perturbation theory from Monte Carlo data

International Nuclear Information System (INIS)

Schlichting, H.

1985-01-01

We do a linearised mean field calculation in axial gauge for the four dimensional mixed fundamental adjoint SU(2) lattice gauge theory and extract the gluon condensate parameter from the expectation values of the plaquette and the action by subtracting mean field perturbation theory from Monte Carlo data. (orig.)

Quasiparticle Lagrangian for the binding energies and self-consistent fields of nuclei in the Fermi-liquid approach

International Nuclear Information System (INIS)

Sapershtein, E.E.; Khodel', V.A.

1981-01-01

The problem of calculating the binding energy and self-consistent field of a nucleus in terms of the effective interaction of quasiparticles at the Fermi surface is solved. It is shown that for this one can go over from the system of N Fermi particles to a system of N interacting quasiparticles described by an effective quasiparticle Lagrangian L/sub q/. It is shown that the corresponding quasiparticle energy is equal to the ground-state energy of the system. The connection between the parameters of the effective Lagrangian and the constants of the quasiparticle interaction introduced in the theory of finite Fermi systems is established

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics

Science.gov (United States)

Nourhani, Amir; Crespi, Vincent H.; Lammert, Paul E.

2015-06-01

We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected. We present a flexible approach to these processes using bias potential as a control parameter field and a locally-open-circuit reference state, carried through in detail for a spherical motor. While the phenomenological flavor makes meaningful contact with experiment easier, required inputs can also conceivably come from, e.g., Frumkin-Butler-Volmer kinetics. Previously obtained results are recovered in the weak-heterogeneity limit and improved small-basis approximations tailored to structural heterogeneity are presented. Under the assumption of weak inhomogeneity, a scaling form is deduced for motor speed as a function of fuel concentration and swimmer size. We argue that this form should be robust and demonstrate a good fit to experimental data.

An effective correlated mean-field theory applied in the spin-1/2 Ising ferromagnetic model

Energy Technology Data Exchange (ETDEWEB)

Roberto Viana, J.; Salmon, Octávio R. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); Ricardo de Sousa, J. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); National Institute of Science and Technology for Complex Systems, Universidade Federal do Amazonas, 3000, Japiim, 69077-000 Manaus, AM (Brazil); Neto, Minos A.; Padilha, Igor T. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil)

2014-11-15

We developed a new treatment for mean-field theory applied in spins systems, denominated effective correlated mean-field (ECMF). We apply this theory to study the spin-1/2 Ising ferromagnetic model with nearest-neighbor interactions on a square lattice. We use clusters of finite sizes and study the criticality of the ferromagnetic system, where we obtain a convergence of critical temperature for the value k{sub B}T{sub c}/J≃2.27905±0.00141. Also the behavior of magnetic and thermodynamic properties, using the condition of minimum energy of the physical system is obtained. - Highlights: • We developed spin models to study real magnetic systems. • We study the thermodynamic and magnetic properties of the ferromagnetism. • We enhanced a mean-field theory applied in spins models.

Self-consistent DFT +U method for real-space time-dependent density functional theory calculations

Science.gov (United States)

Tancogne-Dejean, Nicolas; Oliveira, Micael J. T.; Rubio, Angel

2017-12-01

We implemented various DFT+U schemes, including the Agapito, Curtarolo, and Buongiorno Nardelli functional (ACBN0) self-consistent density-functional version of the DFT +U method [Phys. Rev. X 5, 011006 (2015), 10.1103/PhysRevX.5.011006] within the massively parallel real-space time-dependent density functional theory (TDDFT) code octopus. We further extended the method to the case of the calculation of response functions with real-time TDDFT+U and to the description of noncollinear spin systems. The implementation is tested by investigating the ground-state and optical properties of various transition-metal oxides, bulk topological insulators, and molecules. Our results are found to be in good agreement with previously published results for both the electronic band structure and structural properties. The self-consistent calculated values of U and J are also in good agreement with the values commonly used in the literature. We found that the time-dependent extension of the self-consistent DFT+U method yields improved optical properties when compared to the empirical TDDFT+U scheme. This work thus opens a different theoretical framework to address the nonequilibrium properties of correlated systems.

Fictive impurity approach to dynamical mean field theory

Energy Technology Data Exchange (ETDEWEB)

Fuhrmann, A.

2006-10-15

A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)

Fictive impurity approach to dynamical mean field theory

International Nuclear Information System (INIS)

Fuhrmann, A.

2006-10-01

A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)

Electronic symmetry breaking in polyatomic molecules. Multiconfiguration self-consistent field study of the cyclopropenyl radical C3H3

International Nuclear Information System (INIS)

Hoffmann, M.R.; Laidig, W.D.; Kim, K.S.; Fox, D.J.; Schaefer, H.F. III

1984-01-01

For equilateral triangle geometries (point group D/sub 3h/), the C 3 H 3 radical has a degenerate 2 E'' electronic ground state. Although the 2 A 2 and 2 B 1 components separate in energy for C/sub 2v/ geometries, these two components should have identical energies for equilateral triangle structures. In fact, when approximate wave functions are used and the orbitals not required to transform according to the D/sub 3h/ irreducible representations, an energy separation between the 2 A 2 and 2 B 1 components is observed. At the single configuration self-consistent field (SCF) level of theory this separation is 2.8 kcal with a double-zeta basis set and 2.4 kcal with double-zeta plus polarization. It has been demonstrated that this spurious separation may be greatly reduced using multiconfiguration self-consistent field (up to 7474 variationally optimum configurations) and configuration interaction (up to 60 685 space and spin adapted configurations) techniques. Configurations differing by three and four electrons from the Hartree--Fock reference function are found necessary to reduce the 2 A 2 - 2 B 1 separation to below 0.5 kcal

Double giant resonances in time-dependent relativistic mean-field theory

International Nuclear Information System (INIS)

Ring, P.; Podobnik, B.

1996-01-01

Collective vibrations in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory (RMFT). Isoscalar quadrupole and isovector dipole oscillations that correspond to giant resonances are studied, and possible excitations of higher modes are investigated. We find evidence for modes which can be interpreted as double resonances. In a quantized RMFT they correspond to two-phonon states. (orig.)

Time-odd mean fields in covariant density functional theory: Rotating systems

International Nuclear Information System (INIS)

Afanasjev, A. V.; Abusara, H.

2010-01-01

Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration, and rotational frequency dependencies of their impact on the moments of inertia have been analyzed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean-field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid-body value. On the contrary, superdeformed and hyperdeformed nuclei have the moments of inertia which are close to rigid-body value. The structure of the currents in rotating frame, their microscopic origin, and the relations to the moments of inertia have been systematically analyzed. The phenomenon of signature separation in odd-odd nuclei, induced by time-odd mean fields, has been analyzed in detail.

Multifractality and quantum diffusion from self-consistent theory of localization

Energy Technology Data Exchange (ETDEWEB)

Suslov, I. M., E-mail: suslov@kapitza.ras.ru [Kapitza Institute for Physical Problems (Russian Federation)

2015-11-15

Multifractal properties of wave functions in a disordered system can be derived from self-consistent theory of localization by Vollhardt and Wölfle. A diagrammatic interpretation of results allows to obtain all scaling relations used in numerical experiments. The arguments are given that the one-loop Wegner result for a space dimension d = 2 + ϵ is exact, so the multifractal spectrum is strictly parabolical. The σ-models are shown to be deficient at the four-loop level and the possible reasons of that are discussed. The extremely slow convergence to the thermodynamic limit is demonstrated. The open question on the relation between multifractality and a spatial dispersion of the diffusion coefficient D(ω, q) is resolved in the compromise manner due to ambiguity of the D(ω, q) definition. Comparison is made with the extensive numerical material.

A systematic study of even-even nuclei in the nuclear chart by the relativistic mean field theory

Energy Technology Data Exchange (ETDEWEB)

Sumiyoshi, K.; Hirata, D.; Tanihata, I.; Sugahara, Y.; Toki, H. [Institute of Physical and Chemical Research, Wako, Saitama (Japan)

1997-03-01

We study systematically the properties of nuclei in the whole mass range up to the drip lines by the relativistic mean field (RMF) theory with deformations as a microscopic framework to provide the data of nuclear structure in the nuclear chart. The RMF theory is a phenomenological many-body framework, in which the self-consistent equations for nucleons and mesons are solved with arbitrary deformation, and has a potential ability to provide all the essential information of nuclear structure such as masses, radii and deformations together with single particle states and wave functions from the effective lagrangian containing nuclear interaction. As a first step toward the whole project, we study the ground state properties of even-even nuclei ranging from Z=8 to Z=120 up to the proton and neutron drip lines in the RMF theory. We adopt the parameter set TMA, which has been determined by the experimental masses and charge radii in a wide mass range, for the effective lagrangian of the RMF theory. We take into account the axially symmetric deformation using the constrained method on the quadrupole moment. We provide the properties of all even-even nuclei with all the possible ground state deformations extracted from the deformation energy curves by the constrained calculations. By studying the calculated ground state properties systematically, we aim to explore the general trend of masses, radii and deformations in the whole region of the nuclear chart. We discuss the agreement with experimental data and the predictions such as magicness and triaxial deformations beyond the experimental frontier. (author)

Self-consistent T-matrix theory of superconductivity

Czech Academy of Sciences Publication Activity Database

Šopík, B.; Lipavský, Pavel; Männel, M.; Morawetz, K.; Matlock, P.

2011-01-01

Roč. 84, č. 9 (2011), 094529/1-094529/13 ISSN 1098-0121 R&D Projects: GA ČR GAP204/10/0212; GA ČR(CZ) GAP204/11/0015 Institutional research plan: CEZ:AV0Z10100521 Keywords : superconductivity * T-matrix * superconducting gap * restricted self-consistency Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.691, year: 2011

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique

Science.gov (United States)

Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut

2017-07-01

The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

Consistent momentum space regularization/renormalization of supersymmetric quantum field theories: the three-loop β-function for the Wess-Zumino model

International Nuclear Information System (INIS)

Carneiro, David; Sampaio, Marcos; Nemes, Maria Carolina; Scarpelli, Antonio Paulo Baeta

2003-01-01

We compute the three loop β function of the Wess-Zumino model to motivate implicit regularization (IR) as a consistent and practical momentum-space framework to study supersymmetric quantum field theories. In this framework which works essentially in the physical dimension of the theory we show that ultraviolet are clearly disentangled from infrared divergences. We obtain consistent results which motivate the method as a good choice to study supersymmetry anomalies in quantum field theories. (author)

Investigation of the thermo-mechanical behavior of neutron-irradiated Fe-Cr alloys by self-consistent plasticity theory

Energy Technology Data Exchange (ETDEWEB)

Xiao, Xiazi [State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871 (China); CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, BIC-ESAT, Peking University, Beijing 100871 (China); Terentyev, Dmitry [Structural Material Group, Institute of Nuclear Materials Science, SCK CEN, Mol (Belgium); Yu, Long [State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871 (China); Bakaev, A. [Structural Material Group, Institute of Nuclear Materials Science, SCK CEN, Mol (Belgium); Jin, Zhaohui [School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Duan, Huiling, E-mail: hlduan@pku.edu.cn [State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871 (China); CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, BIC-ESAT, Peking University, Beijing 100871 (China)

2016-08-15

The thermo-mechanical behavior of non-irradiated (at 223 K, 302 K and 573 K) and neutron irradiated (at 573 K) Fe-2.5Cr, Fe-5Cr and Fe-9Cr alloys is studied by a self-consistent plasticity theory, which consists of constitutive equations describing the contribution of radiation defects at grain level, and the elastic-viscoplastic self-consistent method to obtain polycrystalline behaviors. Attention is paid to two types of radiation-induced defects: interstitial dislocation loops and solute rich clusters, which are believed to be the main sources of hardening in Fe-Cr alloys at medium irradiation doses. Both the hardening mechanism and microstructural evolution are investigated by using available experimental data on microstructures, and implementing hardening rules derived from atomistic data. Good agreement with experimental data is achieved for both the yield stress and strain hardening of non-irradiated and irradiated Fe-Cr alloys by treating dislocation loops as strong thermally activated obstacles and solute rich clusters as weak shearable ones. - Highlights: • A self-consistent plasticity theory is proposed for irradiated Fe-Cr alloys. • Both the irradiation-induced hardening and plastic flow evolution are studied. • Dislocation loops and solute rich clusters are considered as the main defects. • Numerical results of the proposed model match with corresponding experimental data.

Self-consistent analysis of radial electric field and fast ion losses in CHS Torsatron/Heliotron

International Nuclear Information System (INIS)

Sanuki, H.; Itoh, K.; Itoh, S.

1992-09-01

A self-consistent analysis is developed to determine the radial electric field and loss cone boundary in Torsatron/Heliotron plasmas under the influence of non-classical ion losses such as the loss cone loss ans charge exchange loss of fast ions with neutrals. Analysis is applied to the NBI heated plasmas in the Compact Helical System (CHS) device. Comparison is made between theoretical results and experimental observations. The increased ion particle losses caused by the orbit loss and charge exchange loss with neutrals make the radial electric field more negative than the value of purely neoclassical calculation. The partition of the injection energy among the shine through, direct orbit loss, change exchange loss and bulk heating is evaluated by using the self-consistent electric field profile. On-going experiments in the CHS device are briefly introduced. (author)

Neutron stars in relativistic mean field theory with isovector scalar meson

International Nuclear Information System (INIS)

Kubis, S.; Kutschera, M.; Stachniewicz, S.

1996-12-01

We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)]. A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼ 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the δ-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing δmeson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab

Neutron stars in relativistic mean field theory with isovector scalar meson

International Nuclear Information System (INIS)

Kubis, S.; Kutschera, M.; Stachniewicz, S.

1998-01-01

We study the equation of state (EOS) of β-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson (a 0 (980)). A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼30 MeV. We find that the quantity most sensitive to the δ-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the δ-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger δ-meson coupling. (author)

Neutron stars in relativistic mean field theory with isovector scalar meson

Energy Technology Data Exchange (ETDEWEB)

Kubis, S.; Kutschera, M.; Stachniewicz, S. [Institute of Nuclear Physics, Cracow (Poland)

1996-12-01

We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)]. A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s} {approx} 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the {delta}-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing {delta}meson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab.

Self-consistent Bulge/Disk/Halo Galaxy Dynamical Modeling Using Integral Field Kinematics

Science.gov (United States)

Taranu, D. S.; Obreschkow, D.; Dubinski, J. J.; Fogarty, L. M. R.; van de Sande, J.; Catinella, B.; Cortese, L.; Moffett, A.; Robotham, A. S. G.; Allen, J. T.; Bland-Hawthorn, J.; Bryant, J. J.; Colless, M.; Croom, S. M.; D'Eugenio, F.; Davies, R. L.; Drinkwater, M. J.; Driver, S. P.; Goodwin, M.; Konstantopoulos, I. S.; Lawrence, J. S.; López-Sánchez, Á. R.; Lorente, N. P. F.; Medling, A. M.; Mould, J. R.; Owers, M. S.; Power, C.; Richards, S. N.; Tonini, C.

2017-11-01

We introduce a method for modeling disk galaxies designed to take full advantage of data from integral field spectroscopy (IFS). The method fits equilibrium models to simultaneously reproduce the surface brightness, rotation, and velocity dispersion profiles of a galaxy. The models are fully self-consistent 6D distribution functions for a galaxy with a Sérsic profile stellar bulge, exponential disk, and parametric dark-matter halo, generated by an updated version of GalactICS. By creating realistic flux-weighted maps of the kinematic moments (flux, mean velocity, and dispersion), we simultaneously fit photometric and spectroscopic data using both maximum-likelihood and Bayesian (MCMC) techniques. We apply the method to a GAMA spiral galaxy (G79635) with kinematics from the SAMI Galaxy Survey and deep g- and r-band photometry from the VST-KiDS survey, comparing parameter constraints with those from traditional 2D bulge-disk decomposition. Our method returns broadly consistent results for shared parameters while constraining the mass-to-light ratios of stellar components and reproducing the H I-inferred circular velocity well beyond the limits of the SAMI data. Although the method is tailored for fitting integral field kinematic data, it can use other dynamical constraints like central fiber dispersions and H I circular velocities, and is well-suited for modeling galaxies with a combination of deep imaging and H I and/or optical spectra (resolved or otherwise). Our implementation (MagRite) is computationally efficient and can generate well-resolved models and kinematic maps in under a minute on modern processors.

Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density

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Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.

1988-01-01

The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.

The influence of thermodynamic self-consistency on the phase behaviour of symmetric binary mixtures

CERN Document Server

Scholl-Paschinger, E; Kahl, G

2004-01-01

We have investigated the phase behaviour of a symmetric binary mixture with particles interacting via hard-core Yukawa potentials. To calculate the thermodynamic properties we have used the mean spherical approximation (MSA), a conventional liquid state theory, and the closely related self-consistent Ornstein-Zernike approximation which is defined via an MSA-type closure relation, requiring, in addition, thermodynamic self-consistency between the compressibility and the energy-route. We investigate on a quantitative level the effect of the self-consistency requirement on the phase diagram and on the critical behaviour and confirm the existence of three archetypes of phase diagram, which originate from the competition between the first order liquid/vapour transition and the second order demixing transition.

Excited-state potential-energy surfaces of metal-adsorbed organic molecules from linear expansion Δ-self-consistent field density-functional theory (ΔSCF-DFT).

Science.gov (United States)

Maurer, Reinhard J; Reuter, Karsten

2013-07-07

Accurate and efficient simulation of excited state properties is an important and much aspired cornerstone in the study of adsorbate dynamics on metal surfaces. To this end, the recently proposed linear expansion Δ-self-consistent field method by Gavnholt et al. [Phys. Rev. B 78, 075441 (2008)] presents an efficient alternative to time consuming quasi-particle calculations. In this method, the standard Kohn-Sham equations of density-functional theory are solved with the constraint of a non-equilibrium occupation in a region of Hilbert-space resembling gas-phase orbitals of the adsorbate. In this work, we discuss the applicability of this method for the excited-state dynamics of metal-surface mounted organic adsorbates, specifically in the context of molecular switching. We present necessary advancements to allow for a consistent quality description of excited-state potential-energy surfaces (PESs), and illustrate the concept with the application to Azobenzene adsorbed on Ag(111) and Au(111) surfaces. We find that the explicit inclusion of substrate electronic states modifies the topologies of intra-molecular excited-state PESs of the molecule due to image charge and hybridization effects. While the molecule in gas phase shows a clear energetic separation of resonances that induce isomerization and backreaction, the surface-adsorbed molecule does not. The concomitant possibly simultaneous induction of both processes would lead to a significantly reduced switching efficiency of such a mechanism.

Dynamical self-arrest in symmetric and asymmetric diblock copolymer melts using a replica approach within a local theory.

Science.gov (United States)

Wu, Sangwook

2009-03-01

We investigate dynamical self-arrest in a diblock copolymer melt using a replica approach within a self-consistent local method based on dynamical mean-field theory (DMFT). The local replica approach effectively predicts (chiN)_{A} for dynamical self-arrest in a block copolymer melt for symmetric and asymmetric cases. We discuss the competition of the cubic and quartic interactions in the Landau free energy for a block copolymer melt in stabilizing a glassy state depending on the chain length. Our local replica theory provides a universal value for the dynamical self-arrest in block copolymer melts with (chiN)_{A} approximately 10.5+64N;{-3/10} for the symmetric case.

Consistent Quantum Theory

Science.gov (United States)

Griffiths, Robert B.

2001-11-01

Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantum mechanics

Unitary field theories

International Nuclear Information System (INIS)

Bergmann, P.G.

1980-01-01

A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion

Neutron stars in relativistic mean field theory with isovector scalar meson

Energy Technology Data Exchange (ETDEWEB)

Kubis, S.; Kutschera, M.; Stachniewicz, S. [H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)

1998-03-01

We study the equation of state (EOS) of {beta}-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson (a{sub 0}(980)). A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s}{approx}30 MeV. We find that the quantity most sensitive to the {delta}-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the {delta}-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger {delta}-meson coupling. (author) 8 refs, 6 figs, 2 tabs

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Science.gov (United States)

Rohringer, G.; Hafermann, H.; Toschi, A.; Katanin, A. A.; Antipov, A. E.; Katsnelson, M. I.; Lichtenstein, A. I.; Rubtsov, A. N.; Held, K.

2018-04-01

Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.

Enriching Elementary Quantum Mechanics with the Computer: Self-Consistent Field Problems in One Dimension

Science.gov (United States)

Bolemon, Jay S.; Etzold, David J.

1974-01-01

Discusses the use of a small computer to solve self-consistent field problems of one-dimensional systems of two or more interacting particles in an elementary quantum mechanics course. Indicates that the calculation can serve as a useful introduction to the iterative technique. (CC)

The mean field theory in EM procedures for blind Markov random field image restoration.

Science.gov (United States)

Zhang, J

1993-01-01

A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.

General fluid theories, variational principles and self-organization

International Nuclear Information System (INIS)

Mahajan, S.M.

2002-01-01

This paper reports two distinct but related advances: (1) The development and application of fluid theories that transcend conventional magnetohydrodynamics (MHD), in particular, theories that are valid in the long-mean-free-path limit and in which pressure anisotropy, heat flow, and arbitrarily strong sheared flows are treated consistently. (2) The discovery of new pressure-confining plasma configurations that are self-organized relaxed states. (author)

Pathological behavior of the open-shell restricted self-consistent-field equations

International Nuclear Information System (INIS)

Moscardo, F.; Alvarez-Collado, J.R.

1979-01-01

The possible solutions of open-shell restricted self-consistent-field equations for a doublet are studied for Li and Na atoms, according to the values of the parameters implied in those equations. A similar behavior, characterized by the presence of several variational solutions is observed in both atoms. Some of these solutions can be assigned to excited configurations. Excitation energies are in good agreement with experimental data. Doublet stability for the solutions obtained has been studied, discussing the saddle-point character present in those solutions associated to excited configurations

Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

Directory of Open Access Journals (Sweden)

Matt Challacombe

2014-03-01

Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.

Pathological behavior of the open-shell restricted self-consistent-field equations

Energy Technology Data Exchange (ETDEWEB)

Moscardo, F.; Alvarez-Collado, J.R.

1979-02-01

The possible solutions of open-shell restricted self-consistent-field equations for a doublet are studied for Li and Na atoms, according to the values of the parameters implied in those equations. A similar behavior, characterized by the presence of several variational solutions is observed in both atoms. Some of these solutions can be assigned to excited configurations. Excitation energies are in good agreement with experimental data. Doublet stability for the solutions obtained has been studied, discussing the saddle-point character present in those solutions associated to excited configurations.

Non-topological solitons in field theories with kinetic self-coupling

International Nuclear Information System (INIS)

Diaz-Alonso, Joaquin; Rubiera-Garcia, Diego

2007-01-01

We investigate some fundamental features of a class of non-linear relativistic Lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which are finite-energy and stable. We determine general conditions for the existence and stability of these non-topological soliton solutions. In particular, we perform a linear stability analysis that goes beyond the usual Derrick-like criteria. On the basis of these considerations we obtain a complete characterization of the soliton-supporting members of the aforementioned class of non-linear field theories. We then classify the family of soliton-supporting theories according to the central and asymptotic behaviors of the soliton field, and provide illustrative explicit examples of models belonging to each of the corresponding sub-families. In the present work we restrict most of our considerations to one and many-components scalar models. We show that in these cases the finite-energy static spherically symmetric solutions are stable against charge-preserving perturbations, provided that the vacuum energy of the model vanishes and the energy density is positive definite. We also discuss briefly the extension of the present approach to models involving other types of fields, but a detailed study of this more general scenario will be addressed in a separate publication

Classical field theory

CERN Document Server

Franklin, Joel

2017-01-01

Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...

Short-range correlations in an extended time-dependent mean-field theory

International Nuclear Information System (INIS)

Madler, P.

1982-01-01

A generalization is performed of the time-dependent mean-field theory by an explicit inclusion of strong short-range correlations on a level of microscopic reversibility relating them to realistic nucleon-nucleon forces. Invoking a least action principle for correlated trial wave functions, equations of motion for the correlation functions and the single-particle model wave function are derived in lowest order of the FAHT cluster expansion. Higher order effects as well as long-range correlations are consider only to the extent to which they contribute to the mean field via a readjusted phenomenological effective two-body interaction. The corresponding correlated stationary problem is investigated and appropriate initial conditions to describe a heavy ion reaction are proposed. The singleparticle density matrix is evaluated

Field theory and strings

International Nuclear Information System (INIS)

Bonara, L.; Cotta-Ramusino, P.; Rinaldi, M.

1987-01-01

It is well-known that type I and heterotic superstring theories have a zero mass spectrum which correspond to the field content of N=1 supergravity theory coupled to supersymmetric Yang-Mills theory in 10-D. The authors study the field theory ''per se'', in the hope that simple consistency requirements will determine the theory completely once one knows the field content inherited from string theory. The simplest consistency requirements are: N=1 supersymmetry; and absence of chiral anomalies. This is what the authors discuss in this paper here leaving undetermined the question of the range of validity of the resulting field theory. As is known, a model of N=1 supergravity (SUGRA) coupled to supersymmetric Yang-Mills (SYM) theory was known in the form given by Chapline and Manton. The coupling of SUGRA to SYM was determined by the definition of the ''field strength'' 3-form H in this paper

Non-Gaussian path integration in self-interacting scalar field theories

International Nuclear Information System (INIS)

Kaya, Ali

2004-01-01

In self-interacting scalar field theories kinetic expansion is an alternative way of calculating the generating functional for Green's functions where the zeroth order non-Gaussian path integral becomes diagonal in x-space and reduces to the product of an ordinary integral at each point which can be evaluated exactly. We discuss how to deal with such functional integrals and propose a new perturbative expansion scheme which combines the elements of the kinetic expansion with the usual perturbation theory techniques. It is then shown that, when the cutoff dependences of the bare parameters in the potential are chosen to have a well defined non-Gaussian path integral without the kinetic term, the theory becomes trivial in the continuum limit

Multiscale methods framework: self-consistent coupling of molecular theory of solvation with quantum chemistry, molecular simulations, and dissipative particle dynamics.

Science.gov (United States)

Kovalenko, Andriy; Gusarov, Sergey

2018-01-31

In this work, we will address different aspects of self-consistent field coupling of computational chemistry methods at different time and length scales in modern materials and biomolecular science. Multiscale methods framework yields dramatically improved accuracy, efficiency, and applicability by coupling models and methods on different scales. This field benefits many areas of research and applications by providing fundamental understanding and predictions. It could also play a particular role in commercialization by guiding new developments and by allowing quick evaluation of prospective research projects. We employ molecular theory of solvation which allows us to accurately introduce the effect of the environment on complex nano-, macro-, and biomolecular systems. The uniqueness of this method is that it can be naturally coupled with the whole range of computational chemistry approaches, including QM, MM, and coarse graining.

Towards a fully self-consistent inversion combining historical and paleomagnetic data for geomagnetic field reconstructions

Science.gov (United States)

Arneitz, P.; Leonhardt, R.; Fabian, K.; Egli, R.

2017-12-01

Historical and paleomagnetic data are the two main sources of information about the long-term geomagnetic field evolution. Historical observations extend to the late Middle Ages, and prior to the 19th century, they consisted mainly of pure declination measurements from navigation and orientation logs. Field reconstructions going back further in time rely solely on magnetization acquired by rocks, sediments, and archaeological artefacts. The combined dataset is characterized by a strongly inhomogeneous spatio-temporal distribution and highly variable data reliability and quality. Therefore, an adequate weighting of the data that correctly accounts for data density, type, and realistic error estimates represents the major challenge for an inversion approach. Until now, there has not been a fully self-consistent geomagnetic model that correctly recovers the variation of the geomagnetic dipole together with the higher-order spherical harmonics. Here we present a new geomagnetic field model for the last 4 kyrs based on historical, archeomagnetic and volcanic records. The iterative Bayesian inversion approach targets the implementation of reliable error treatment, which allows different record types to be combined in a fully self-consistent way. Modelling results will be presented along with a thorough analysis of model limitations, validity and sensitivity.

Self-Consistent Theory of Shot Noise Suppression in Ballistic Conductors

Science.gov (United States)

Bulashenko, O. M.; Rubí, J. M.; Kochelap, V. A.

Shot-noise measurements become a fundamental tool to probe carrier interactions in mesoscopic systems [1]. A matter of particular interest is the significance of Coulomb interaction which may keep nearby electrons more regularly spaced rather than strictly at random and lead to the noise reduction. That effect occurs in different physical situations. Among them are charge-limited ballistic transport, resonant tunneling, single-electron tunneling, etc. In this communication we address the problem of Coulomb correlations in ballistic conductors under the space-charge-limited transport conditions, and present for the first time a semiclassical self-consistent theory of shot noise in these conductors by solving analytically the kinetic equation coupled self-consistently with a Poisson equation. Basing upon this theory, exact results for current noise in a two-terminal ballistic conductor under the action of long-range Coulomb correlations has been derived. The noise reduction factor (in respect to the uncorrelated value) is obtained in a closed analytical form for a full range of biases ranging from thermal to shot-noise limits which describe perfectly the results of the Monte Carlo simulations for a nondegenerate electron gas [2]. The magnitude of the noise reduction exceeds 0.01, which is of interest from the point of view of possible applications. Using these analytical results one may estimate a relative contribution to the noise from different groups of carriers (in energy space and/or real space) and to investigate in great detail the correlations between different groups of carriers. This leads us to suggest an electron energy spectroscopy experiment to probe the Coulomb correlations in ballistic conductors. Indeed, while the injected carriers are uncorrelated, those in the volume of the conductor are strongly correlated, as follows from the derived formulas for the fluctuation of the distribution function. Those correlations may be observed experimentally by

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

Energy Technology Data Exchange (ETDEWEB)

Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)

2015-03-07

In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations.

Science.gov (United States)

Kelly, Aaron; Brackbill, Nora; Markland, Thomas E

2015-03-07

In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

Magnetized Anisotropic Dark Energy Models in Barber’s Second Self-Creation Theory

Directory of Open Access Journals (Sweden)

D. D. Pawar

2014-01-01

Full Text Available The present paper deals with Bianchi type IX cosmological model with magnetized anisotropic dark energy by using Barber’s self-creation theory. The energy momentum tensor consists of anisotropic fluid with EoS parameter ω and a uniform magnetic field of energy density ρB. In order to obtain the exact solution we have assumed that dark energy components and the components of magnetic field interact minimally and obey the law of conservation of energy momentum tensors. We have also used the special law of variation for the mean generalized Hubble parameter and power law relation between scalar field and scale factor. Some physical and kinematical properties of the models have been discussed.

Mean-field approach to unconventional superconductivity

International Nuclear Information System (INIS)

Sacks, William; Mauger, Alain; Noat, Yves

2014-01-01

Highlights: • A model Hamiltonian for unconventional superconductivity (SC) is proposed. • The pseudogap (PG) state is described in terms of pair fluctuations. • SC coherence is restored by a new pair–pair interaction, which counteracts fluctuations. • Given the temperature dependence of the parameters, the SC to PG transition is examined. • The theory fits the ‘peak–dip–hump’ features of cuprate and pnictide excitation spectra. - Abstract: We propose a model that connects the quasiparticle spectral function of high-T c superconductors to the condensation energy. Given the evidence for pair correlations above T c , we consider a coarse-grain Hamiltonian of fluctuating pairs describing the incoherent pseudogap (PG) state, together with a novel pair–pair interaction term that restores long-range superconducting (SC) coherence below T c . A mean-field solution then leads to a self-consistent gap equation containing the new pair–pair coupling. The corresponding spectral function A(k,E) reveals the characteristic peak–dip–hump features of cuprates, now observed on iron pnictides (LiFeAs). The continuous transition from SC to PG states is discussed

Versatility of field theory motivated nuclear effective Lagrangian approach

International Nuclear Information System (INIS)

Arumugam, P.; Sharma, B.K.; Sahu, P.K.; Patra, S.K.; Sil, Tapas; Centelles, M.; Vinas, X.

2004-01-01

We analyze the results for infinite nuclear and neutron matter using the standard relativistic mean field model and its recent effective field theory motivated generalization. For the first time, we show quantitatively that the inclusion in the effective theory of vector meson self-interactions and scalar-vector cross-interactions explains naturally the recent experimental observations of the softness of the nuclear equation of state, without losing the advantages of the standard relativistic model for finite nuclei

A self consistent study of the phase transition in the scalar electroweak theory at finite temperature

International Nuclear Information System (INIS)

Kerres, U.; Mack, G.; Palma, G.

1994-12-01

We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two-step method. It combines i) dimensional reduction to a 3-dimensional lattice theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations. (orig.)

A self consistent study of the phase transition in the scalar electroweak theory at finite temperature

International Nuclear Information System (INIS)

Kerres, U.

1995-01-01

We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two-step method. It combines i) dimensional reduction to a 3-dimensional lattice theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations. ((orig.))

Two-particle irreducible effective actions versus resummation: Analytic properties and self-consistency

Directory of Open Access Journals (Sweden)

Michael Brown

2015-11-01

Full Text Available Approximations based on two-particle irreducible (2PI effective actions (also known as Φ-derivable, Cornwall–Jackiw–Tomboulis or Luttinger–Ward functionals depending on context have been widely used in condensed matter and non-equilibrium quantum/statistical field theory because this formalism gives a robust, self-consistent, non-perturbative and systematically improvable approach which avoids problems with secular time evolution. The strengths of 2PI approximations are often described in terms of a selective resummation of Feynman diagrams to infinite order. However, the Feynman diagram series is asymptotic and summation is at best a dangerous procedure. Here we show that, at least in the context of a toy model where exact results are available, the true strength of 2PI approximations derives from their self-consistency rather than any resummation. This self-consistency allows truncated 2PI approximations to capture the branch points of physical amplitudes where adjustments of coupling constants can trigger an instability of the vacuum. This, in effect, turns Dyson's argument for the failure of perturbation theory on its head. As a result we find that 2PI approximations perform better than Padé approximation and are competitive with Borel–Padé resummation. Finally, we introduce a hybrid 2PI–Padé method.

Topological recursion for Gaussian means and cohomological field theories

Science.gov (United States)

Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.

2015-12-01

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.

Multiagent model and mean field theory of complex auction dynamics

Science.gov (United States)

Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng

2015-09-01

Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.

Multiagent model and mean field theory of complex auction dynamics

International Nuclear Information System (INIS)

Chen, Qinghua; Wang, Yougui; Huang, Zi-Gang; Lai, Ying-Cheng

2015-01-01

Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena. (paper)

Alfven-wave particle interaction in finite-dimensional self-consistent field model

International Nuclear Information System (INIS)

Padhye, N.; Horton, W.

1998-01-01

A low-dimensional Hamiltonian model is derived for the acceleration of ions in finite amplitude Alfven waves in a finite pressure plasma sheet. The reduced low-dimensional wave-particle Hamiltonian is useful for describing the reaction of the accelerated ions on the wave amplitudes and phases through the self-consistent fields within the envelope approximation. As an example, the authors show for a single Alfven wave in the central plasma sheet of the Earth's geotail, modeled by the linear pinch geometry called the Harris sheet, the time variation of the wave amplitude during the acceleration of fast protons

Astrophysical data analysis with information field theory

International Nuclear Information System (INIS)

Enßlin, Torsten

2014-01-01

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented

Astrophysical data analysis with information field theory

Science.gov (United States)

Enßlin, Torsten

2014-12-01

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

Astrophysical data analysis with information field theory

Energy Technology Data Exchange (ETDEWEB)

Enßlin, Torsten, E-mail: ensslin@mpa-garching.mpg.de [Max Planck Institut für Astrophysik, Karl-Schwarzschild-Straße 1, D-85748 Garching, Germany and Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, D-80539 München (Germany)

2014-12-05

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

Functional approach to a time-dependent self-consistent field theory

International Nuclear Information System (INIS)

Reinhardt, H.

1979-01-01

The time-dependent Hartree-Fock approximation is formulated within the path integral approach. It is shown that by a suitable choice of the collective field the classical equation of motion of the collective field coincides with the time-dependent Hartree (TDH) equation. The consideration is restricted to the TDH equation, since the exchange terms do not appear in the functional approach on the same footing as the direct terms

Sine-Gordon mean field theory of a Coulomb gas

Energy Technology Data Exchange (ETDEWEB)

Diehl, Alexandre; Barbosa, Marcia C.; Levin, Yan

1997-12-31

Full text. The Coulomb gas provides a paradigm for the study of various models of critical phenomena. In particular, it is well known that the two dimensional (2 D). Coulomb gas can be directly used to study the superfluidity transition in {sup 4} He films, arrays of Josephson junctions, roughening transition, etc. Not withstanding its versatility, our full understanding of the most basic model of Coulomb gas, namely an ensemble of hard spheres carrying either positive or negative charges at their center, is still lacking. It is now well accepted that at low density the two dimensional plasma of equal number of positive and negative particles undergoes a Kosterlitz-Thouless (KT) metal insulator transition. This transition is of an infinite order and is characterized by a diverging Debye screening length. As the density of particles increases, the validity of the KT theory becomes questionable and the possibility of the KT transition being replaced by some kind of first order discontinuity has been speculated for a long time. In this work sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean-field free energy is constructed and the corresponding phase diagrams in two and three dimensions are obtained. When analyzed in terms of chemical potential, the sine-Gordon theory predicts the phase diagram topologically identical to the Monte Carlo simulations and a recently developed Debye-Huckel-Bjerrum theory. In 2D, we find that the infinite-order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole insulating phase is mapped onto zero density. (author)

Self-interacting, boson, quantum field theory, and the thermodynamic limit in d dimensions

International Nuclear Information System (INIS)

Baker, G.A. Jr.

1975-01-01

By use of a finite volume, lattice approximation, an approximation to the analytic continuation of a polynomial, self-interacting boson quantum field theory from Minkowski space to Euclidean space was set up. The infinite volume limit for various boundary conditions is shown to exist and to be asymptotic to the perturbation expansion in the coupling constant g at g = 0. For g: phi 4 : d theory mass renormalizability is proved and it is shown how, by use of Nelson's reconstruction theorem, the corresponding Minkowski space quantum field theory can be obtained. It is discussed, at least for d greater than or equal to 4, how statistical mechanical techniques, used to analyze the Ising model in the critical region just above the critical temperature, can be used to compute the properties of quantum field theory. (U.S.)

Self-Consistent Study of Conjugated Aromatic Molecular Transistors

International Nuclear Information System (INIS)

Jing, Wang; Yun-Ye, Liang; Hao, Chen; Peng, Wang; Note, R.; Mizuseki, H.; Kawazoe, Y.

2010-01-01

We study the current through conjugated aromatic molecular transistors modulated by a transverse field. The self-consistent calculation is realized with density function theory through the standard quantum chemistry software Gaussian03 and the non-equilibrium Green's function formalism. The calculated I – V curves controlled by the transverse field present the characteristics of different organic molecular transistors, the transverse field effect of which is improved by the substitutions of nitrogen atoms or fluorine atoms. On the other hand, the asymmetry of molecular configurations to the axis connecting two sulfur atoms is in favor of realizing the transverse field modulation. Suitably designed conjugated aromatic molecular transistors possess different I – V characteristics, some of them are similar to those of metal-oxide-semiconductor field-effect transistors (MOSFET). Some of the calculated molecular devices may work as elements in graphene electronics. Our results present the richness and flexibility of molecular transistors, which describe the colorful prospect of next generation devices. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

The self-consistent dynamic pole tide in global oceans

Science.gov (United States)

Dickman, S. R.

1985-01-01

The dynamic pole tide is characterized in a self-consistent manner by means of introducing a single nondifferential matrix equation compatible with the Liouville equation, modelling the ocean as global and of uniform depth. The deviations of the theory from the realistic ocean, associated with the nonglobality of the latter, are also given consideration, with an inference that in realistic oceans long-period modes of resonances would be increasingly likely to exist. The analysis of the nature of the pole tide and its effects on the Chandler wobble indicate that departures of the pole tide from the equilibrium may indeed be minimal.

Gaming practices in everyday life. An analytical operationalization of field theory by means of practice theory

Directory of Open Access Journals (Sweden)

Claus Toft-Nielsen

2015-05-01

Full Text Available This article investigates digital game play (gaming as a specific media field (Bourdieu, 1984, p. 72, in which especially gaming capital (Consalvo, 2007 functions as a theoretical lens. We aim to analyse the specific practices that constitute and are constituted in and around gaming. This multitude of practices is theoretically qualified by the second generation of practice theorists, including (Bruchler & Postill, 2010; Reckwitz, 2002; Schatzki, 2008; Warde, 2005. The empirical data are drawn from qualitative studies of gamers and gaming practices (focus groups as well as participant observations, and function as exemplary cases that illustrate our theoretical arguments. Our purpose is to analytically operationalize field theory, by means of practice theory, to enhance our understanding of digital games as new media and the specific contexts and media practices herein.

Gaming practices in everyday life. An analytical operationalization of field theory by means of practice theory

DEFF Research Database (Denmark)

Toft-Nielsen, Claus; Krogager, Stinne Gunder Strøm

2015-01-01

This article investigates digital game play (gaming) as a specific media field (Bourdieu, 1984, p. 72), in which especially gaming capital (Consalvo, 2007) functions as a theoretical lens. We aim to analyse the specific practices that constitute and are constituted in and around gaming....... This multitude of practices is theoretically qualified by the second generation of practice theorists, including (Bruchler & Postill, 2010; Reckwitz, 2002; Schatzki, 2008; Warde, 2005). The empirical data are drawn from qualitative studies of gamers and gaming practices (focus groups as well as participant...... observations), and function as exemplary cases that illustrate our theoretical arguments. Our purpose is to analytically operationalize field theory, by means of practice theory, to enhance our understanding of digital games as new media and the specific contexts and media practices herein....

Mean-field theory of meta-learning

International Nuclear Information System (INIS)

Plewczynski, Dariusz

2009-01-01

We discuss here the mean-field theory for a cellular automata model of meta-learning. Meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents that acquire and process incoming information using various types, or different versions, of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share the opposite classification outcome can be observed in the system. Therefore, the probability of selecting a proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are built from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents

The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time

International Nuclear Information System (INIS)

Marek-Crnjac, L.

2006-01-01

In the present work we show the connections between the topology of four-manifolds, conformal field theory, the mathematical probability theory and Cantorian space-time. In all these different mathematical fields, we find as the main connection the appearance of the golden mean

Self-consistent asset pricing models

Science.gov (United States)

Malevergne, Y.; Sornette, D.

2007-08-01

We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alphas and betas of the factor model are unobservable. Self-consistency leads to renormalized betas with zero effective alphas, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value αi at the origin between an asset i's return and the proxy's return. Self-consistency also introduces “orthogonality” and “normality” conditions linking the betas, alphas (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from January 1990 to February 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the self-consistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the

An impurity solver for nonequilibrium dynamical mean field theory based on hierarchical quantum master equations

Energy Technology Data Exchange (ETDEWEB)

Haertle, Rainer [Institut fuer Theoretische Physik, Georg-August-Universitaet Goettingen, Goettingen (Germany); Millis, Andrew J. [Department of Physics, Columbia University, New York (United States)

2016-07-01

We present a new impurity solver for real-time and nonequilibrium dynamical mean field theory applications, based on the recently developed hierarchical quantum master equation approach. Our method employs a hybridization expansion of the time evolution operator, including an advanced, systematic truncation scheme. Convergence to exact results for not too low temperatures has been demonstrated by a direct comparison to quantum Monte Carlo simulations. The approach is time-local, which gives us access to slow dynamics such as, e.g., in the presence of magnetic fields or exchange interactions and to nonequilibrium steady states. Here, we present first results of this new scheme for the description of strongly correlated materials in the framework of dynamical mean field theory, including benchmark and new results for the Hubbard and periodic Anderson model.

Systematic homogenization and self-consistent flux and pin power reconstruction for nodal diffusion methods. 1: Diffusion equation-based theory

International Nuclear Information System (INIS)

Zhang, H.; Rizwan-uddin; Dorning, J.J.

1995-01-01

A diffusion equation-based systematic homogenization theory and a self-consistent dehomogenization theory for fuel assemblies have been developed for use with coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is based on a multiple-scales asymptotic expansion carried out through second order in a small parameter, the ratio of the average diffusion length to the reactor characteristic dimension. By starting from the neutron diffusion equation for a three-dimensional heterogeneous medium and introducing two spatial scales, the development systematically yields an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections and assembly-surface-flux discontinuity factors. The rector eigenvalue 1/k eff is shown to be obtained to the second order in the small parameter, and the heterogeneous diffusion theory flux is shown to be obtained to leading order in that parameter. The latter of these two results provides a natural procedure for the reconstruction of the local fluxes and the determination of pin powers, even though homogenized assemblies are used in the global nodal diffusion calculation

Self-Consistent Model of Magnetospheric Electric Field, Ring Current, Plasmasphere, and Electromagnetic Ion Cyclotron Waves: Initial Results

Science.gov (United States)

Gamayunov, K. V.; Khazanov, G. V.; Liemohn, M. W.; Fok, M.-C.; Ridley, A. J.

2009-01-01

Further development of our self-consistent model of interacting ring current (RC) ions and electromagnetic ion cyclotron (EMIC) waves is presented. This model incorporates large scale magnetosphere-ionosphere coupling and treats self-consistently not only EMIC waves and RC ions, but also the magnetospheric electric field, RC, and plasmasphere. Initial simulations indicate that the region beyond geostationary orbit should be included in the simulation of the magnetosphere-ionosphere coupling. Additionally, a self-consistent description, based on first principles, of the ionospheric conductance is required. These initial simulations further show that in order to model the EMIC wave distribution and wave spectral properties accurately, the plasmasphere should also be simulated self-consistently, since its fine structure requires as much care as that of the RC. Finally, an effect of the finite time needed to reestablish a new potential pattern throughout the ionosphere and to communicate between the ionosphere and the equatorial magnetosphere cannot be ignored.

Multiconfigurational self-consistent field calculations of nuclear shieldings using London atomic orbitals

DEFF Research Database (Denmark)

Ruud, Kenneth; Helgaker, Trygve; Kobayashi, Rika

1994-01-01

to corresponding individual gauges for localized orbitals (IGLO) results. The London results show better basis set convergence than IGLO, especially for heavier atoms. It is shown that the choice of active space is crucial for determination of accurate nuclear shielding constants.......Nuclear shielding calculations are presented for multiconfigurational self-consistent field wave functions using London atomic orbitals (gauge invariant atomic orbitals). Calculations of nuclear shieldings for eight molecules (H2O, H2S, CH4, N2, CO, HF, F2, and SO2) are presented and compared...

Introduction to gauge field theory

International Nuclear Information System (INIS)

Bailin, D.; Love, A.

1986-01-01

This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications

A multi-species exchange model for fully fluctuating polymer field theory simulations.

Science.gov (United States)

Düchs, Dominik; Delaney, Kris T; Fredrickson, Glenn H

2014-11-07

Field-theoretic models have been used extensively to study the phase behavior of inhomogeneous polymer melts and solutions, both in self-consistent mean-field calculations and in numerical simulations of the full theory capturing composition fluctuations. The models commonly used can be grouped into two categories, namely, species models and exchange models. Species models involve integrations of functionals that explicitly depend on fields originating both from species density operators and their conjugate chemical potential fields. In contrast, exchange models retain only linear combinations of the chemical potential fields. In the two-component case, development of exchange models has been instrumental in enabling stable complex Langevin (CL) simulations of the full complex-valued theory. No comparable stable CL approach has yet been established for field theories of the species type. Here, we introduce an extension of the exchange model to an arbitrary number of components, namely, the multi-species exchange (MSE) model, which greatly expands the classes of soft material systems that can be accessed by the complex Langevin simulation technique. We demonstrate the stability and accuracy of the MSE-CL sampling approach using numerical simulations of triblock and tetrablock terpolymer melts, and tetrablock quaterpolymer melts. This method should enable studies of a wide range of fluctuation phenomena in multiblock/multi-species polymer blends and composites.

Structural aspects of quantum field theory and noncommutative geometry

CERN Document Server

Grensing, Gerhard

2013-01-01

This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...

Mean-field approximation minimizes relative entropy

International Nuclear Information System (INIS)

Bilbro, G.L.; Snyder, W.E.; Mann, R.C.

1991-01-01

The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach

Final theory spiral-field-model. Basic ideas for a compatible physics and a consistent nature science

International Nuclear Information System (INIS)

Hartje, U.A.J.

2005-01-01

This script contains theses for an universal 'Spiral-Field-Theory' that are capable to dissolve problems in parallel from different areas which are far from each other. Starting point is the stuck principle discussion about the relationships between the Classic Physics and the Quantum Physics. Aim is the clarification of questions which remained open. In 1925 Max Planck had formulated as follows: 'The research of physics can not rest, so long not has been together-welded: on the one hand the mechanics and the electrodynamics with on the other hand the lesson of the stationary one and the radiating heat to a sole unitary theory'. The Spiral-Field-Model develops a supporting structure from General Field into which they will class the secure knowledge from experiments and well-proved theories. The most important thing of this new Final Theory is the detailed generating of all nature courses of phenomena exclusively from radiation and that in the direct meaning of the word. In the final effect the two great disciplines of the physics which are drifted from each other, become bonded together to a super ordinate theoretical building of the nature sciences. (orig.)

Unified field theory with Einsteinian photons and heavy bosons as field quants

Energy Technology Data Exchange (ETDEWEB)

Treder, H J

1975-08-01

After discussing previously the classical electrodynamics which corresponds to the quantum electrodynamics with two sorts of photons (photons with zero rest mass and nonvanishing rest mass), the general field theory of a vector field A/sup v/ with two sorts if field quanta is given. It is shown that the postulate for the ''unity of the four-current'' determining the physical contents of this theory makes it possible to regard it as a classical ansatz of a unified theory of the electromagnetic and the weak interactions. From the ''unity of the currents'' results that the electrons are delta-like point-particles with a finite self-potential and finite field masses M = epsilon/sup 2//2 kc/sup -2/. The Compton wave-length of the heavy photons k/sup -1/ = h/mc has the meaning of an ''elementary length'' of the electromagnetic interactions and the rest mass m = khc/sup -1/ of these bosons is of the order of a baryon mass. (auth)

On the binding of calcium by micelles composed of carboxy-modified pluronics measured by means of differential potentiometric titration and modeled with a self-consistent-field theory.

Science.gov (United States)

Lauw, Y; Leermakers, F A M; Cohen Stuart, M A; Pinheiro, J P; Custers, J P A; van den Broeke, L J P; Keurentjes, J T F

2006-12-19

We perform differential potentiometric titration measurements for the binding of Ca2+ ions to micelles composed of the carboxylic acid end-standing Pluronic P85 block copolymer (i.e., CAE-85 (COOH-(EO)26-(PO)39-(EO)26-COOH)). Two different ion-selective electrodes (ISEs) are used to detect the free calcium concentration; the first ISE is an indicator electrode, and the second is a reference electrode. The titration is done by adding the block copolymers to a known solution of Ca2+ at neutral pH and high enough temperature (above the critical micellization temperature CMT) and various amount of added monovalent salt. By measuring the difference in the electromotive force between the two ISEs, the amount of Ca2+ that is bound by the micelles is calculated. This is then used to determine the binding constant of Ca2+ with the micelles, which is a missing parameter needed to perform molecular realistic self-consistent-field (SCF) calculations. It turns out that the micelles from block copolymer CAE-85 bind Ca2+ ions both electrostatically and specifically. The specific binding between Ca2+ and carboxylic groups in the corona of the micelles is modeled through the reaction equilibrium -COOCa+ -COO- + Ca2+ with pKCa = 1.7 +/- 0.06.

Pionic atoms, the relativistic mean-field theory and the pion-nucleon scattering lenghts

International Nuclear Information System (INIS)

Goudsmit, P.F.A.; Leisi, H.J.; Matsinos, E.

1991-01-01

Analysing pionic-atom data of isoscalar nuclei within the relativistic mean-field (RMF) theory, we determine the pseudoscalar πNN mixing parameter x=0.24±0.06 (syst.) and the strength of the nuclear scalar meson field for pions, S π =-34±14 (syst.) MeV. We show that these values are compatible with the elementary π-N interaction. Our RMF model provides a solution to the long-standing problem of the s-wave repulsion. (orig.)

Calculation of Self-consistent Radial Electric Field in Presence of Convective Electron Transport in a Stellarator

International Nuclear Information System (INIS)

Kernbichler, W.; Heyn, M.F.; Kasilov, S.V.

2003-01-01

Convective transport of supra-thermal electrons can play a significant role in the energy balance of stellarators in case of high power electron cyclotron heating. Here, together with neoclassical thermal particle fluxes also the supra-thermal electron flux should be taken into account in the flux ambipolarity condition, which defines the self-consistent radial electric field. Since neoclassical particle fluxes are non-linear functions of the radial electric field, one needs an iterative procedure to solve the ambipolarity condition, where the supra-thermal electron flux has to be calculated for each iteration. A conventional Monte-Carlo method used earlier for evaluation of supra-thermal electron fluxes is rather slow for performing the iterations in reasonable computer time. In the present report, the Stochastic Mapping Technique (SMT), which is more effective than the conventional Monte Carlo method, is used instead. Here, the problem with a local monoenergetic supra-thermal particle source is considered and the effect of supra-thermal electron fluxes on both, the self-consistent radial electric field and the formation of different roots of the ambipolarity condition are studied

Advances in dynamic and mean field games theory, applications, and numerical methods

CERN Document Server

Viscolani, Bruno

2017-01-01

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinar...

Gate-controlled current and inelastic electron tunneling spectrum of benzene: a self-consistent study.

Science.gov (United States)

Liang, Y Y; Chen, H; Mizuseki, H; Kawazoe, Y

2011-04-14

We use density functional theory based nonequilibrium Green's function to self-consistently study the current through the 1,4-benzenedithiol (BDT). The elastic and inelastic tunneling properties through this Au-BDT-Au molecular junction are simulated, respectively. For the elastic tunneling case, it is found that the current through the tilted molecule can be modulated effectively by the external gate field, which is perpendicular to the phenyl ring. The gate voltage amplification comes from the modulation of the interaction between the electrodes and the molecules in the junctions. For the inelastic case, the electron tunneling scattered by the molecular vibrational modes is considered within the self-consistent Born approximation scheme, and the inelastic electron tunneling spectrum is calculated.

Linking lipid architecture to bilayer structure and mechanics using self-consistent field modelling

Energy Technology Data Exchange (ETDEWEB)

Pera, H.; Kleijn, J. M.; Leermakers, F. A. M., E-mail: Frans.leermakers@wur.nl [Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6307 HB Wageningen (Netherlands)

2014-02-14

To understand how lipid architecture determines the lipid bilayer structure and its mechanics, we implement a molecularly detailed model that uses the self-consistent field theory. This numerical model accurately predicts parameters such as Helfrichs mean and Gaussian bending modulus k{sub c} and k{sup ¯} and the preferred monolayer curvature J{sub 0}{sup m}, and also delivers structural membrane properties like the core thickness, and head group position and orientation. We studied how these mechanical parameters vary with system variations, such as lipid tail length, membrane composition, and those parameters that control the lipid tail and head group solvent quality. For the membrane composition, negatively charged phosphatidylglycerol (PG) or zwitterionic, phosphatidylcholine (PC), and -ethanolamine (PE) lipids were used. In line with experimental findings, we find that the values of k{sub c} and the area compression modulus k{sub A} are always positive. They respond similarly to parameters that affect the core thickness, but differently to parameters that affect the head group properties. We found that the trends for k{sup ¯} and J{sub 0}{sup m} can be rationalised by the concept of Israelachivili's surfactant packing parameter, and that both k{sup ¯} and J{sub 0}{sup m} change sign with relevant parameter changes. Although typically k{sup ¯}<0, membranes can form stable cubic phases when the Gaussian bending modulus becomes positive, which occurs with membranes composed of PC lipids with long tails. Similarly, negative monolayer curvatures appear when a small head group such as PE is combined with long lipid tails, which hints towards the stability of inverse hexagonal phases at the cost of the bilayer topology. To prevent the destabilisation of bilayers, PG lipids can be mixed into these PC or PE lipid membranes. Progressive loading of bilayers with PG lipids lead to highly charged membranes, resulting in J{sub 0}{sup m}≫0, especially at low ionic

Covariant Noncommutative Field Theory

Energy Technology Data Exchange (ETDEWEB)

Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)

2008-07-02

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.

Covariant Noncommutative Field Theory

International Nuclear Information System (INIS)

Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

2008-01-01

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced

Self energies of the electron and photon in the unified space field theory

International Nuclear Information System (INIS)

Duong Van Phi, Nguyen Mong Giao.

1981-01-01

Self energies of the electron and photon are calculated in the second approximation of perturbation theory. The formalism of the field theory of interaction in the unified 8-dimensional space is used. The calculations are free of divergence the unitary condition is fulfilled. It is shown that the ''naked'' and physical masses of a free electron are identical. A similar result is obtained for a free photon. Some other effects are discussed [ru

A mean field approach to the Ising chain in a transverse magnetic field

Science.gov (United States)

Osácar, C.; Pacheco, A. F.

2017-07-01

We evaluate a mean field method to describe the properties of the ground state of the Ising chain in a transverse magnetic field. Specifically, a method of the Bethe-Peierls type is used by solving spin blocks with a self-consistency condition at the borders. The computations include the critical point for the phase transition, exponent of magnetisation and energy density. All results are obtained using basic quantum mechanics at an undergraduate level. The advantages and the limitations of the approach are emphasised.

Studies in quantum field theory

International Nuclear Information System (INIS)

Bender, C.M.; Mandula, J.E.; Shrauner, J.E.

1982-01-01

Washington University is currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large orders; quark condensation in QCD; chiral symmetry breaking; the l/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD

Superheavy nuclei in the relativistic mean-field theory

International Nuclear Information System (INIS)

Lalazissis, G.A.; Ring, P.; Gambhir, Y.K.

1996-01-01

We have carried out a study of superheavy nuclei in the framework of the relativistic mean-field theory. Relativistic Hartree-Bogoliubov (RHB) calculations have been performed for nuclei with large proton and neutron numbers. A finite-range pairing force of Gogny type has been used in the RHB calculations. The ground-state properties of very heavy nuclei with atomic numbers Z=100-114 and neutron numbers N=154-190 have been obtained. The results show that in addition to N=184 the neutron numbers N=160 and N=166 exhibit an extra stability as compared to their neighbors. For the case of protons the atomic number Z=106 is shown to demonstrate a closed-shell behavior in the region of well deformed nuclei about N=160. The proton number Z=114 also indicates a shell closure. Indications for a doubly magic character at Z=106 and N=160 are observed. Implications of shell closures on a possible synthesis of superheavy nuclei are discussed. (orig.)

Studies of self-consistent field structure in a quasi-optical gyrotron

International Nuclear Information System (INIS)

Antonsen, T.M. Jr.

1993-04-01

The presence of an electron beam in a quasi-optical gyrotron cavity alters the structure of the fields from that of the empty cavity. A computer code has been written which calculates this alteration for either an electron beam or a thin dielectric tube placed in the cavity. Experiments measuring the quality factor of such a cavity performed for the case of a dielectric tube and the results agree with the predictions of the code. Simulations of the case of an electron beam indicate that self-consistent effects can be made small in that almost all the power leaves the cavity in a symmetric gaussian-like mode provided the resonator parameters are chosen carefully. (author) 6 figs., 1 tab., 13 refs

Noether charges for self-interacting quantum field theories in curved spacetimes with a Killing-vector

International Nuclear Information System (INIS)

Hollands, S.

2001-01-01

We consider a self-interacting, perturbative Klein-Gordon quantum field in a curved spacetime admitting a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether charge which arises, in a certain sense, as a surface integral over the time-component of some interacting Noether current-density associated with the Killing field. The proof of this involves the demonstration of a corresponding set of Ward identities. Our work is based on the perturbative construction by Brunetti and Fredenhagen (Commun. Math. Phys. 208 (2000) 623-661) of self-interacting quantum field theories in general globally hyperbolic spacetimes. (orig.)

Can Malin's gravitational-field equations be modified to obtain a viable theory of gravity to obtain a viable theory of gravity to obtain a viable theory of gravity

International Nuclear Information System (INIS)

Smalley, L.L.; Prestage, J.

1976-01-01

Malin's gravitational theory, which was recently shown by Lindblom and Nester to be incorrect, is modified by means of a recently proposed method for obtaining viable gravitational theories. The resulting self-consistent theory, which is in effect a Rastall-type modification of the Einstein theory, exhibits nonconservation of momentum, yet agrees with all experimental limits known to date within the PPN framework

Virtual-site correlation mean field approach to criticality in spin systems

International Nuclear Information System (INIS)

Sen, Aditi; Sen, Ujjwal

2013-01-01

We propose a virtual-site correlation mean field theory for dealing with interacting many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the virtual-site correlation mean field theory deals with single- as well as two-body ones, and involves a virtual site for every interaction term in the Hamiltonian. We generalize the theory to a cluster virtual-site correlation mean field, that works with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are generally much better in the proposed theories as compared to the corresponding ones in mean field theories

Quantum field theory on brane backgrounds

International Nuclear Information System (INIS)

Flachi, A.

2001-11-01

The development of higher dimensional quantum field theories is reviewed from the older Kaluza-Klein theory to the new brane models, emphasising their relevance in modern particle physics. The issue of spontaneous symmetry breaking in the Randall-Sundrum model is considered. The role of the coupling between bulk fields and the curvature is investigated and a model in favour of bulk symmetry breaking is presented. The lowest order quantum corrections arising from a quantized scalar field in the Randall-Sundrum spacetime are computed. A careful discussion of the boundary conditions as well as the renormalization is provided. The massless case is also discussed and a proof of the vanishing of the conformal anomaly in this model is given. An analysis of the self-consistency is presented and the radius stabilization problem studied. It is shown that quantum effects may provide a stabilization of the radius, nevertheless, when the hierarchy problem is simultaneously solved, fine tuning of the brane tensions is necessary. The previous results are extended in order to include the contribution to the one-loop effective action from fermions. The boundary conditions are discussed and their relation with gauge invariance accurately examined. The possibility of breaking the gauge symmetries by using Wilson-loops is investigated. The analysis of the self- consistency is extended when the contribution of fermions is included, and it is shown that also in this case it is not possible to stabilize the radius and simultaneously solving the hierarchy problem, unless the brane tensions are fine tuned to a high degree. (author)

Bootstrapping gravity: A consistent approach to energy-momentum self-coupling

International Nuclear Information System (INIS)

Butcher, Luke M.; Hobson, Michael; Lasenby, Anthony

2009-01-01

It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity of this idea has recently been brought into doubt [T. Padmanabhan, Int. J. Mod. Phys. D 17, 367 (2008).]. Motivated by this, we present a graviton action for which energy-momentum self-coupling is indeed consistent with the Einstein field equations. The Hilbert energy-momentum tensor for this graviton is calculated explicitly and shown to supply the correct second-order term in the field equations; in contrast, the Fierz-Pauli action fails to supply the correct term. A formalism for perturbative expansions of metric-based gravitational theories is then developed, and these techniques employed to demonstrate that our graviton action is a starting point for a straightforward energy-momentum self-coupling procedure that, order by order, generates the Einstein-Hilbert action (up to a classically irrelevant surface term). The perturbative formalism is extended to include matter and a cosmological constant, and interactions between perturbations of a free matter field and the gravitational field are studied in a vacuum background. Finally, the effect of a nonvacuum background is examined, and the graviton is found to develop a nonvanishing 'mass-term' in the action.

Renormalization of self-consistent Schwinger-Dyson equations at finite temperature

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2002-01-01

We show that Dyson resummation schemes based on Baym's Φ-derivable approximations can be renormalized with counter term structures solely defined on the vacuum level. First applications to the self-consistent solution of the sunset self-energy in φ 4 -theory are presented. (orig.)

Hamiltonian Anomalies from Extended Field Theories

Science.gov (United States)

Monnier, Samuel

2015-09-01

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

Self-consistency and coherent effects in nonlinear resonances

International Nuclear Information System (INIS)

Hofmann, I.; Franchetti, G.; Qiang, J.; Ryne, R. D.

2003-01-01

The influence of space charge on emittance growth is studied in simulations of a coasting beam exposed to a strong octupolar perturbation in an otherwise linear lattice, and under stationary parameters. We explore the importance of self-consistency by comparing results with a non-self-consistent model, where the space charge electric field is kept 'frozen-in' to its initial values. For Gaussian distribution functions we find that the 'frozen-in' model results in a good approximation of the self-consistent model, hence coherent response is practically absent and the emittance growth is self-limiting due to space charge de-tuning. For KV or waterbag distributions, instead, strong coherent response is found, which we explain in terms of absence of Landau damping

Simple Theory for the Dynamics of Mean-Field-Like Models of Glass-Forming Fluids

Science.gov (United States)

Szamel, Grzegorz

2017-10-01

We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The theory predicts an ergodicity-breaking transition that is identical to the so-called dynamic transition predicted within the replica approach. Thus, it can provide the missing dynamic component of the random first order transition framework. In the large-dimensional limit the theory reproduces the result of a recent exact calculation of Maimbourg et al. [Phys. Rev. Lett. 116, 015902 (2016), 10.1103/PhysRevLett.116.015902]. Our approach provides an alternative, physically motivated derivation of this result.

Atomically flat superconducting nanofilms: multiband properties and mean-field theory

Science.gov (United States)

Shanenko, A. A.; Aguiar, J. Albino; Vagov, A.; Croitoru, M. D.; Milošević, M. V.

2015-05-01

Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.

Atomically flat superconducting nanofilms: multiband properties and mean-field theory

International Nuclear Information System (INIS)

Shanenko, A A; Aguiar, J Albino; Vagov, A; Croitoru, M D; Milošević, M V

2015-01-01

Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D–2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin–Wagner–Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri–Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg–Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields. (paper)

Modeling of the 3RS tau protein with self-consistent field method and Monte Carlo simulation

NARCIS (Netherlands)

Leermakers, F.A.M.; Jho, Y.S.; Zhulina, E.B.

2010-01-01

Using a model with amino acid resolution of the 196 aa N-terminus of the 3RS tau protein, we performed both a Monte Carlo study and a complementary self-consistent field (SCF) analysis to obtain detailed information on conformational properties of these moieties near a charged plane (mimicking the

Hidden Fermi liquid, scattering rate saturation, and Nernst effect: a dynamical mean-field theory perspective.

Science.gov (United States)

Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel

2013-07-19

We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale T(FL). Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale T(sat). We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above T(FL), in particular the linear-in-T resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements.

Mean field theory of EM algorithm for Bayesian grey scale image restoration

International Nuclear Information System (INIS)

Inoue, Jun-ichi; Tanaka, Kazuyuki

2003-01-01

The EM algorithm for the Bayesian grey scale image restoration is investigated in the framework of the mean field theory. Our model system is identical to the infinite range random field Q-Ising model. The maximum marginal likelihood method is applied to the determination of hyper-parameters. We calculate both the data-averaged mean square error between the original image and its maximizer of posterior marginal estimate, and the data-averaged marginal likelihood function exactly. After evaluating the hyper-parameter dependence of the data-averaged marginal likelihood function, we derive the EM algorithm which updates the hyper-parameters to obtain the maximum likelihood estimate analytically. The time evolutions of the hyper-parameters and so-called Q function are obtained. The relation between the speed of convergence of the hyper-parameters and the shape of the Q function is explained from the viewpoint of dynamics

Shapes and dynamics from the time-dependent mean field

International Nuclear Information System (INIS)

Stevenson, P.D.; Goddard, P.M.; Rios, A.

2015-01-01

Explaining observed properties in terms of underlying shape degrees of freedom is a well-established prism with which to understand atomic nuclei. Self-consistent mean-field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time-dependent extension of the mean-field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of 28 Si in the first case, and 240 Pu in the latter case

Field theory reformulated without self-energy parts: the dressing operator

International Nuclear Information System (INIS)

Haan, M. de

2004-01-01

The reformulation of field theory for avoiding self-energy parts in the dynamical evolution has been applied successfully in the framework of the Lee model [Ann. Phys. 311 (2004) 314], enabling a kinetic extension of the description. The basic ingredient is the recognition of these self-energy parts [Trends Stat. Phys. 3 (2000) 115]. The original reversible description is embedded in the new one and appears now as a restricted class of initial conditions [Progr. Theor. Phys. 109 (2003) 881]. This program is realized here in the reduced formalism for a scalar field, interacting with a two-level atom, beyond the usual rotating wave approximation. The kinetic evolution operator, previously surmised [Physica A 171 (1991) 159], is here derived from first principles, justifying the usual practice in optics where the common use of the so-called pole approximation [Atoms in Electromagnetic Fields, 1994, 119] should no longer be viewed as an approximation but as an alternative description in the appropriate formalism. That model illustrates how some dressing of the atomic levels (and vertices), through an appropriate operator, finds its place naturally into the new formalism since the bare and dressed ground states do no longer coincide. Moreover, finite velocity for field propagation is now possible in all cases, without the presence of precursors for multiple detections

Coagulation kinetics beyond mean field theory using an optimised Poisson representation

Energy Technology Data Exchange (ETDEWEB)

Burnett, James [Department of Mathematics, UCL, Gower Street, London WC1E 6BT (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT (United Kingdom)

2015-05-21

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

Self-consistent collective coordinate method for large amplitude collective motions

International Nuclear Information System (INIS)

Sakata, F.; Hashimoto, Y.; Marumori, T.; Une, T.

1982-01-01

A recent development of the self-consistent collective coordinate method is described. The self-consistent collective coordinate method was proposed on the basis of the fundamental principle called the invariance principle of the Schroedinger equation. If this is formulated within a framework of the time dependent Hartree Fock (TDHF) theory, a classical version of the theory is obtained. A quantum version of the theory is deduced by formulating it within a framework of the unitary transformation method with auxiliary bosons. In this report, the discussion is concentrated on a relation between the classical theory and the quantum theory, and an applicability of the classical theory. The aim of the classical theory is to extract a maximally decoupled collective subspace out of a huge dimensional 1p - 1h parameter space introduced by the TDHF theory. An intimate similarity between the classical theory and a full quantum boson expansion method (BEM) was clarified. Discussion was concentrated to a simple Lipkin model. Then a relation between the BEM and the unitary transformation method with auxiliary bosons was discussed. It became clear that the quantum version of the theory had a strong relation to the BEM, and that the BEM was nothing but a quantum analogue of the present classical theory. The present theory was compared with the full TDHF calculation by using a simple model. (Kato, T.)

A relativistic self-consistent model for studying enhancement of space charge limited field emission due to counter-streaming ions

International Nuclear Information System (INIS)

Lin, M. C.; Lu, P. S.; Chang, P. C.; Ragan-Kelley, B.; Verboncoeur, J. P.

2014-01-01

Recently, field emission has attracted increasing attention despite the practical limitation that field emitters operate below the Child-Langmuir space charge limit. By introducing counter-streaming ion flow to neutralize the electron charge density, the space charge limited field emission (SCLFE) current can be dramatically enhanced. In this work, we have developed a relativistic self-consistent model for studying the enhancement of SCLFE by a counter-streaming ion current. The maximum enhancement is found when the ion effect is saturated, as shown analytically. The solutions in non-relativistic, intermediate, and ultra-relativistic regimes are obtained and verified with 1-D particle-in-cell simulations. This self-consistent model is general and can also serve as a benchmark or comparison for verification of simulation codes, as well as extension to higher dimensions

Constant self-dual Abelian gauge fields and fermions in SU(2) gauge theory

International Nuclear Information System (INIS)

Kay, D.; Parthasarathy, R.; Viswanathan, K.S.

1983-01-01

Fermion one-loop corrections to the effective action in a self-dual Abelian background field are calculated for an SU(2) gauge theory. It is found that these corrections for massless fermions tend to destabilize the vacuum. The quantitative and qualitative features of such corrections for the case of massive fermions are discussed

Enhanced gauge symmetry and winding modes in double field theory

Energy Technology Data Exchange (ETDEWEB)

Aldazabal, G. [Centro Atómico Bariloche,8400 S.C. de Bariloche (Argentina); Instituto Balseiro (CNEA-UNC) and CONICET,8400 S.C. de Bariloche (Argentina); Graña, M. [Institut de Physique Théorique, CEA/ Saclay,91191 Gif-sur-Yvette Cedex (France); Iguri, S. [Instituto de Astronomía y Física del Espacio (CONICET-UBA), Universidad de Buenos Aires,1428 Buenos Aires (Argentina); Mayo, M. [Centro Atómico Bariloche,8400 S.C. de Bariloche (Argentina); Instituto Balseiro (CNEA-UNC) and CONICET,8400 S.C. de Bariloche (Argentina); Nuñez, C. [Instituto de Astronomía y Física del Espacio (CONICET-UBA), Universidad de Buenos Aires,1428 Buenos Aires (Argentina); Departamento de Física, FCEN, Universidad de Buenos Aires,C.C. 67 - Suc. 28, 1428 Buenos Aires (Argentina); Rosabal, J.A. [Departamento de Física, FCEN, Universidad de Buenos Aires,C.C. 67 - Suc. 28, 1428 Buenos Aires (Argentina)

2016-03-15

We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the U(1)×U(1) symmetry to SU(2)×SU(2). We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with ((O(d+3,d+3))/(O(d+3)×O(d+3))) structure, where d is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.

Pearl-necklace structures in core-shell molecular brushes: Experiments, Monte Carlo simulations and self-consistent field modeling

NARCIS (Netherlands)

Polotsky, A.; Charlaganov, M.; Xu, Y.P.; Leermakers, F.A.M.; Daoud, M.; Muller, A.H.E.; Dotera, T.; Borisov, O.V.

2008-01-01

We present theoretical arguments and experimental evidence for a longitudinal instability in core-shell cylindrical polymer brushes with a solvophobic inner (core) block and a solvophilic outer (shell) block in selective solvents. The two-gradient self-consistent field Scheutjens-Fleer (SCF-SF)

A new perturbative approximation applied to supersymmetric quantum field theory

International Nuclear Information System (INIS)

Bender, C.M.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.; Los Alamos National Lab.

1988-01-01

We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not known of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

Heavy-ion interactions in relativistic mean-field models

International Nuclear Information System (INIS)

Rashdan, M.

1996-01-01

The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model. (orig.)

Mean-field theory of photoinduced molecular reorientation in azobenzene liquid crystalline side-chain polymers

DEFF Research Database (Denmark)

Pedersen, T.G.; Johansen, P.M.

1997-01-01

. The theory provides an explanation for the high long-term stability of the photoinduced anisotropy as well as a theoretical prediction of the temporal behavior of photoinduced birefringence. The theoretical results agree favorably with measurements in the entire range of writing intensities used......A novel mean-field theory of photoinduced reorientation and optical anisotropy in liquid crystalline side-chain polymers is presented and compared with experiments, The reorientation mechanism is based on photoinduced trans cis isomerization and a multidomain model of the material is introduced...

Self-dual gauge theories

International Nuclear Information System (INIS)

Zet, G.

2002-01-01

The self-duality equations are important in gauge theories because they show the connection between gauge models with internal symmetry groups and gauge theory of gravity. They are differential equations of the first order and it is easier to investigate the solutions for different particular configurations of the gauge fields and of space-times.One of the most important property of the self-duality equations is that they imply the Yang-Mills field equations. In this paper we will prove this property for the general case of a gauge theory with compact Lie group of symmetry over a 4-dimensional space-time manifold. It is important to remark that there are 3m independent self-duality equations (of the first order) while the number of Yang-Mills equations is equal to 4m, where m is the dimension of the gauge group. Both of them have 4m unknown functions which are the gauge potentials A μ a (x), a = 1, 2, ....,m; μ = 0, 1, 2, 3. But, we have, in addition, m gauge conditions for A μ a (x), (for example Coulomb, Lorentz or axial gauge) which together with the selfduality equation constitute a system of 4m equations. The Bianchi identities for the self-dual stress tensor F μν a coincide with the Yang-Mills equations and do not imply therefore supplementary conditions. We use the axial gauge in order to obtain the self duality equations for a SU(2) gauge theory over a curved space-time. The compatibility between self-duality and Yang-Mills equations is studied and some classes of solutions are obtained. In fact, we will write the Einstein-Yang-Mills equations and we will analyse only the Yang-Mills sector. The Einstein equations can not be obtained of course from self-duality. They should be obtained if we would consider a gauge theory having P x SU(2) as symmetry group, where P is the Poincare group. More generally, a gauge theory of N-extended supersymmetry can be developed by imposing the self-duality condition. (author)

The self-consistent field model for Fermi systems with account of three-body interactions

Directory of Open Access Journals (Sweden)

Yu.M. Poluektov

2015-12-01

Full Text Available On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained. It is shown that the delta-like three-body interaction gives no contribution into the self-consistent field, and the description of three-body forces requires their nonlocality to be taken into account. The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces. The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature. Expansions of the effective mass and pressure in powers of density are obtained. It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass. The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction. The quasiparticle energy spectrum is calculated with account of three-body forces.

Dimension of ring polymers in bulk studied by Monte-Carlo simulation and self-consistent theory.

Science.gov (United States)

Suzuki, Jiro; Takano, Atsushi; Deguchi, Tetsuo; Matsushita, Yushu

2009-10-14

We studied equilibrium conformations of ring polymers in melt over the wide range of segment number N of up to 4096 with Monte-Carlo simulation and obtained N dependence of radius of gyration of chains R(g). The simulation model used is bond fluctuation model (BFM), where polymer segments bear excluded volume; however, the excluded volume effect vanishes at N-->infinity, and linear polymer can be regarded as an ideal chain. Simulation for ring polymers in melt was performed, and the nu value in the relationship R(g) proportional to N(nu) is decreased gradually with increasing N, and finally it reaches the limiting value, 1/3, in the range of N>or=1536, i.e., R(g) proportional to N(1/3). We confirmed that the simulation result is consistent with that of the self-consistent theory including the topological effect and the osmotic pressure of ring polymers. Moreover, the averaged chain conformation of ring polymers in equilibrium state was given in the BFM. In small N region, the segment density of each molecule near the center of mass of the molecule is decreased with increasing N. In large N region the decrease is suppressed, and the density is found to be kept constant without showing N dependence. This means that ring polymer molecules do not segregate from the other molecules even if ring polymers in melt have the relationship nu=1/3. Considerably smaller dimensions of ring polymers at high molecular weight are due to their inherent nature of having no chain ends, and hence they have less-entangled conformations.

Twistor-theoretic approach to topological field theories

International Nuclear Information System (INIS)

Ito, Kei.

1991-12-01

The two-dimensional topological field theory which describes a four-dimensional self-dual space-time (gravitational instanton) as a target space, which we constructed before, is shown to be deeply connected with Penrose's 'twistor theory'. The relations are presented in detail. Thus our theory offers a 'twistor theoretic' approach to topological field theories. (author)

On the consistency of classical and quantum supergravity theories

Energy Technology Data Exchange (ETDEWEB)

Hack, Thomas-Paul [II. Institute for Theoretical Physics, University of Hamburg (Germany); Makedonski, Mathias [Department of Mathematical Sciences, University of Copenhagen (Denmark); Schenkel, Alexander [Department of Stochastics, University of Wuppertal (Germany)

2012-07-01

It is known that pure N=1 supergravity in d=4 spacetime dimensions is consistent at a classical and quantum level, i.e. that in a particular gauge the field equations assume a hyperbolic form - ensuring causal propagation of the degrees of freedom - and that the associated canonical quantum field theory satisfies unitarity. It seems, however, that it is yet unclear whether these properties persist if one considers the more general and realistic case of N=1, d=4 supergravity theories including arbitrary matter fields. We partially clarify the issue by introducing novel hyperbolic gauges for the gravitino field and proving that they commute with the resulting equations of motion. Moreover, we review recent partial results on the unitarity of these general supergravity theories and suggest first steps towards a comprehensive unitarity proof.

The time-dependent relativistic mean-field theory and the random phase approximation

International Nuclear Information System (INIS)

Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang

2001-01-01

The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained

Relativistic mean field theory for deformed nuclei with pairing correlations

International Nuclear Information System (INIS)

Geng, Lisheng; Toki, Hiroshi; Sugimoto, Satoru; Meng, Jie

2003-01-01

We develop a relativistic mean field (RMF) description of deformed nuclei with pairing correlations in the BCS approximation. The treatment of the pairing correlations for nuclei whose Fermi surfaces are close to the threshold of unbound states needs special attention. With this in mind, we use a delta function interaction for the pairing interaction to pick up those states whose wave functions are concentrated in the nuclear region and employ the standard BCS approximation for the single-particle states obtained from the BMF theory with deformation. We apply the RMF + BCS method to the Zr isotopes and obtain a good description of the binding energies and the nuclear radii of nuclei from the proton drip line to the neutron drip line. (author)

Self-consistent equilibria in the pulsar magnetosphere

International Nuclear Information System (INIS)

Endean, V.G.

1976-01-01

For a 'collisionless' pulsar magnetosphere the self-consistent equilibrium particle distribution functions are functions of the constants of the motion ony. Reasons are given for concluding that to a good approximation they will be functions of the rotating frame Hamiltonian only. This is shown to result in a rigid rotation of the plasma, which therefore becomes trapped inside the velocity of light cylinder. The self-consistent field equations are derived, and a method of solving them is illustrated. The axial component of the magnetic field decays to zero at the plasma boundary. In practice, some streaming of particles into the wind zone may occur as a second-order effect. Acceleration of such particles to very high energies is expected when they approach the velocity of light cylinder, but they cannot be accelerated to very high energies near the star. (author)

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: Multi-center molecular Ornstein-Zernike self-consistent field approach

Science.gov (United States)

Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi

2015-07-01

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl- + CH3Cl → ClCH3 + Cl-) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: multi-center molecular Ornstein-Zernike self-consistent field approach.

Science.gov (United States)

Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi

2015-07-07

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

Correlations and self-consistency in pion scattering. II

International Nuclear Information System (INIS)

Johnson, M.B.; Keister, B.D.

1978-01-01

In an attempt to overcome certain difficulties of summing higher order processes in pion multiple scattering theories, a new, systematic expansion for the interaction of a pion in nuclear matter is derived within the context of the Foldy-Walecka theory, incorporating nucleon-nucleon correlations and an idea of self-consistency. The first two orders in the expansion are evaluated as a function of the nonlocality range; the expansion appears to be rapidly converging, in contrast to expansion schemes previously examined. (Auth.)

Quark self-energy beyond the mean field at finite temperature

International Nuclear Information System (INIS)

Zhuang, P.

1995-01-01

The Nambu--Jona-Lasinio model, an effective low-energy model of QCD, is extended to the next to the leading order in the 1/N c expansion at finite temperature and density. The contributions to the quark self-energy and the constituent quark mass from the meson dressing are considered in a perturbative approach about the mean field. In particular, the temperature dependence of the quark mass is shown numerically at zero chemical potential. The correction to the quark mass from the meson dressing amounts to 20% compared to the result of the leading order at low temperature, and rapidly approaches zero at high temperature

Implementation of the diagonalization-free algorithm in the self-consistent field procedure within the four-component relativistic scheme.

Science.gov (United States)

Hrdá, Marcela; Kulich, Tomáš; Repiský, Michal; Noga, Jozef; Malkina, Olga L; Malkin, Vladimir G

2014-09-05

A recently developed Thouless-expansion-based diagonalization-free approach for improving the efficiency of self-consistent field (SCF) methods (Noga and Šimunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four-component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four-component diagonalization-free SCF calculations on several heavy-metal complexes, the largest of which contains more than 80 atoms (about 6000 4-spinor basis functions). The diagonalization-free procedure is about twice as fast as the corresponding diagonalization. Copyright © 2014 Wiley Periodicals, Inc.

Quantum self-consistency of AdSxΣ brane models

International Nuclear Information System (INIS)

Flachi, Antonino; Pujolas, Oriol

2003-01-01

Continuing our previous work, we consider a class of higher dimensional brane models with the topology of AdS D 1 +1 xΣ, where Σ is a one-parameter compact manifold and two branes of codimension one are located at the orbifold fixed points. We consider a setup where such a solution arises from Einstein-Yang-Mills theory and evaluate the one-loop effective potential induced by gauge fields and by a generic bulk scalar field. We show that this type of brane model resolves the gauge hierarchy between the Planck and electroweak scales through redshift effects due to the warp factor a=e -πkr . The value of a is then fixed by minimizing the effective potential. We find that, as in the Randall-Sundrum case, the gauge field contribution to the effective potential stabilizes the hierarchy without fine-tuning as long as the Laplacian Δ Σ on Σ has a zero eigenvalue. Scalar fields can stabilize the hierarchy depending on the mass and the nonminimal coupling. We also address the quantum self-consistency of the solution, showing that the classical brane solution is not spoiled by quantum effects

Quantum field theory of fluids.

Science.gov (United States)

Gripaios, Ben; Sutherland, Dave

2015-02-20

The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.

WORKSHOP: Thermal field theory

Energy Technology Data Exchange (ETDEWEB)

Anon.

1989-04-15

The early history of the Universe is a crucial testing ground for theories of elementary particles. Speculative ideas about the constituents of matter and their interactions are reinforced if they are consistent with what we suppose happened near the beginning of time and discarded if they are not. The cosmological consequences of these theories are usually deduced using a general statistical approach called thermal field theory. Thus, 75 physicists from thirteen countries met in Cleveland, Ohio, last October for the first 'Workshop on Thermal Field Theories and their Applications'.

Mean-field Ensemble Kalman Filter

KAUST Repository

Law, Kody

2015-01-07

A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

On the scaling limits in the Euclidean (quantum) field theory

International Nuclear Information System (INIS)

Gielerak, R.

1983-01-01

The author studies the concept of scaling limits in the context of the constructive field theory. He finds that the domain of attraction of a free massless Euclidean scalar field in the two-dimensional space time contains almost all Euclidean self-interacting models of quantum fields so far constructed. The renormalized scaling limit of the Wick polynomials of several self-interacting Euclidean field theory models are shown to be the same as in the free field theory. (Auth.)

Orbifold constructions and the classification of self-dual c=24 conformal field theories

International Nuclear Information System (INIS)

Montague, P.S.

1994-01-01

We discuss questions arising from the work of Schellekens [A.N. Schellekens, Phys. Lett. B 277 (1992) 277; Meromorphic c=24 conformal field theories, CERN-TH.6478/92, 1992.] After introducing the concept of complementary representations, we examine Z 2 -orbifold constructions in general, and propose a technique for identifying the orbifold theory without knowledge of its explicit construction. This technique is then generalised to twists of order 3, 5 and 7, and we proceed to apply our considerations to the FKS constructions H (Λ) (Λ an even self-dual lattice) and the reflection-twisted orbifold theories and H ;(Λ), which together remain the only c=24 theories which have so far been proven to exist [L. Dolan, P. Goddard and P. Montague, Nucl. Phys. B 338 (1990) 529.] We also make, in the course of our arguments, some comments on the automorphism groups of the theories H (Λ) and and H ;(Λ), and of meromorphic theories in general, introducing the concept of deterministic theories. ((orig.))

Exotic dual of type II double field theory

Directory of Open Access Journals (Sweden)

Eric A. Bergshoeff

2017-04-01

Full Text Available We perform an exotic dualization of the Ramond–Ramond fields in type II double field theory, in which they are encoded in a Majorana–Weyl spinor of O(D,D. Starting from a first-order master action, the dual theory in terms of a tensor–spinor of O(D,D is determined. This tensor–spinor is subject to an exotic version of the (self-duality constraint needed for a democratic formulation. We show that in components, reducing O(D,D to GL(D, one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, such as the 4-form in type IIB string theory.

Dynamical mean-field theory and path integral renormalisation group calculations of strongly correlated electronic states

Energy Technology Data Exchange (ETDEWEB)

Heilmann, D.B.

2007-02-15

The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)

Dynamical mean-field theory and path integral renormalisation group calculations of strongly correlated electronic states

International Nuclear Information System (INIS)

Heilmann, D.B.

2007-02-01

The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)

Self-consistent potential variations in magnetic wells

International Nuclear Information System (INIS)

Kesner, J.; Knorr, G.; Nicholson, D.R.

1981-01-01

Self-consistent electrostatic potential variations are considered in a spatial region of weak magnetic field, as in the proposed tandem mirror thermal barriers (with no trapped ions). For some conditions, equivalent to ion distributions with a sufficiently high net drift speed along the magnetic field, the desired potential depressions are found. When the net drift speed is not high enough, potential depressions are found only in combination with strong electric fields on the boundaries of the system. These potential depressions are not directly related to the magnetic field depression. (author)

Nonequilibrium quantum field theories

International Nuclear Information System (INIS)

Niemi, A.J.

1988-01-01

Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena. (orig.)

Self-consistence equations for extended Feynman rules in quantum chromodynamics

International Nuclear Information System (INIS)

Wielenberg, A.

2005-01-01

In this thesis improved solutions for Green's functions are obtained. First the for this thesis essential techniques and concepts of QCD as euclidean field theory are presented. After a discussion of the foundations of the extended approach for the Feynman rules of QCD with a systematic approach for the 4-gluon vertex a modified renormalization scheme for the extended approach is developed. Thereafter the resummation of the Dyson-Schwinger equations (DSE) by the appropriately modified Bethe-Salpeter equation is discussed. Then the leading divergences for the 1-loop graphs of the resummed DSE are determined. Thereafter the equation-of-motion condensate is defined as result of an operator-product expansion. Then the self-consistency equations for the extended approaches are defined and numerically solved. (HSI)

Systems with N correlated fermions. Mean-field models for nuclear structures and other N-body systems

International Nuclear Information System (INIS)

Grasso, M.

2009-10-01

This document is a summary of the author's research activities whose common topic is the N-body problem. The first chapter introduces the N-body issue through models based on the mean-field theory and on the Hartree-Fock-Bogoliubov equations. The second chapter presents the understanding of exotic nuclei features within the mean-field approach. Exotic phenomena like nuclear bubble structure, pairing correlations and pairing violations, giant neutron halos, non-standard terms in the Skyrme interactions are reviewed. The chapter 3 is dedicated to some extensions of the RPA (random phase approximation). For instance the computation of the shell structure far from the stability valley requires a more accurate assessment of the energy of the individual states through the introduction of a particle-vibration coupling. Different RPA extensions are described: first the self-consistent extension enlarged beyond particle-hole configurations, then the boson-mapping-based extension in a 3-level Lipkin model and also the second random-phase approximation. The chapter 4 gathers some studies concerning ultra-cold gases of trapped atoms. These systems are the only structures that allow the study of the correlations associated to superfluidity in terms of interaction intensity, temperature or system size. The mean-field approach is adequate for these studies. The last chapter draws a perspective for the mean-field-based models, their limits are assessed and ways of improvement are proposed. (A.C.)

Renormalized plasma turbulence theory: A quasiparticle picture

International Nuclear Information System (INIS)

DuBois, D.F.

1981-01-01

A general renormalized statistical theory of Vlasov turbulence is given which proceeds directly from the Vlasov equation and does not assume prior knowledge of sophisticated field-theoretic techniques. Quasiparticles are the linear excitations of the turbulent system away from its instantaneous mean (ensemble-averaged) state or background; the properties of this background state ''dress'' or renormalize the quasiparticle responses. It is shown that all two-point responses (including the dielectric) and all two-point correlation functions can be completely described by the mean distribution function and three fundamental quantities. Two of these are the quasiparticle responses: the propagator and the potential source: which measure, respectively, the separate responses of the mean distribution function and the mean electrostatic potential to functional changes in an external phase-space source added to Vlasov's equation. The third quantity is the two-point correlation function of the incoherent part of the phase-space density which acts as a self-consistent source of quasiparticle and potential fluctuations. This theory explicitly takes into account the self-consistent nature of the electrostatic-field fluctuations which introduces new effects not found in the usual ''test-particle'' theories. Explicit equations for the fundamental quantities are derived in the direct interaction approximation. Special attention is paid to the two-point correlations and the relation to theories of phase-space granulation

Nuclear response beyond mean field theory

International Nuclear Information System (INIS)

Brand, M.G.E.; Allaart, K.; Dickhoff, W.H.

1990-01-01

An extension of the RPA equations is derived, with emphasis on the relation between the single-particle Green function and the polarization propagator. Including second order self-energy contributions the resulting particle-hole interaction includes the coupling to two-particle-two-hole (2p2h) states and the resulting response satisfies relevant conservation laws. This aspect of the theory is shown to be essential to obtain reliable and meaningful results for excitation strengths and to avoid ghost solutions. This method is applied to electromagnetic and charge exchange excitations in 48 Ca up to 100 MeV. A G-matrix interaction based on meson exchange is used which takes care of short-range correlations. The results compare favourably with measured excitation strengths and electromagnetic form factors both at low energy as well as in the giant resonance region. Remaining discrepancies point in the direction of further strength reduction due to short-range correlations as well as a possible stronger coupling to 2p2h states at low energy. (orig.)

Novel Approaches to Spectral Properties of Correlated Electron Materials: From Generalized Kohn-Sham Theory to Screened Exchange Dynamical Mean Field Theory

Science.gov (United States)

Delange, Pascal; Backes, Steffen; van Roekeghem, Ambroise; Pourovskii, Leonid; Jiang, Hong; Biermann, Silke

2018-04-01

The most intriguing properties of emergent materials are typically consequences of highly correlated quantum states of their electronic degrees of freedom. Describing those materials from first principles remains a challenge for modern condensed matter theory. Here, we review, apply and discuss novel approaches to spectral properties of correlated electron materials, assessing current day predictive capabilities of electronic structure calculations. In particular, we focus on the recent Screened Exchange Dynamical Mean-Field Theory scheme and its relation to generalized Kohn-Sham Theory. These concepts are illustrated on the transition metal pnictide BaCo2As2 and elemental zinc and cadmium.

Solvent effects in time-dependent self-consistent field methods. II. Variational formulations and analytical gradients

International Nuclear Information System (INIS)

Bjorgaard, J. A.; Velizhanin, K. A.; Tretiak, S.

2015-01-01

This study describes variational energy expressions and analytical excited state energy gradients for time-dependent self-consistent field methods with polarizable solvent effects. Linear response, vertical excitation, and state-specific solventmodels are examined. Enforcing a variational ground stateenergy expression in the state-specific model is found to reduce it to the vertical excitation model. Variational excited state energy expressions are then provided for the linear response and vertical excitation models and analytical gradients are formulated. Using semiempiricalmodel chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Lastly, analytical gradients are further tested by performing microcanonical excited state molecular dynamics with p-nitroaniline

Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

Science.gov (United States)

Tweney, Ryan D.

2011-07-01

James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: Multi-center molecular Ornstein–Zernike self-consistent field approach

International Nuclear Information System (INIS)

Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi

2015-01-01

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein–Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple S N 2 reaction (Cl − + CH 3 Cl → ClCH 3 + Cl − ) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF

Mean field dynamics of networks of delay-coupled noisy excitable units

Energy Technology Data Exchange (ETDEWEB)

Franović, Igor, E-mail: franovic@ipb.ac.rs [Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Todorović, Kristina; Burić, Nikola [Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade (Serbia); Vasović, Nebojša [Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, PO Box 162, Belgrade (Serbia)

2016-06-08

We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.

Superstring field theory equivalence: Ramond sector

International Nuclear Information System (INIS)

Kroyter, Michael

2009-01-01

We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.

Kaehler-Chern-Simons theory and symmetries of anti-self-dual gauge fields

International Nuclear Information System (INIS)

Nair, V.P.; Schiff, J.

1992-01-01

Kaehler-Chern-Simons theory, which was proposed as a generalization of ordinary Chern-Simons theory, is explored in more detail. The theory describes anti-self-dual instantons on a four-dimensional Kaehler manifold. The phase space is the space of gauge potentials, whose symplectic reduction by the constraints of anti-self-duality leads to the moduli space of instantons. We show that infinitesimal Baecklund transformations, previously related to 'hidden symmetries' of instantons, are canonical transformations generated by the anti-self-duality constraints. The quantum wave functions naturally lead to a generalized Wess-Zumino-Witten action, which in turn has associated chiral current algebras. The dimensional reduction of the anti-self-duality equations leading to integrable two-dimensional theories is briefly discussed in this framework. (orig.)

Subcritical saturation of the magnetorotational instability through mean magnetic field generation

Science.gov (United States)

Xie, Jin-Han; Julien, Keith; Knobloch, Edgar

2018-03-01

The magnetorotational instability is widely believed to be responsible for outward angular momentum transport in astrophysical accretion discs. The efficiency of this transport depends on the amplitude of this instability in the saturated state. We employ an asymptotic expansion based on an explicit, astrophysically motivated time-scale separation between the orbital period, Alfvén crossing time and viscous or resistive dissipation time-scales, originally proposed by Knobloch and Julien, to formulate a semi-analytical description of the saturated state in an incompressible disc. In our approach a Keplerian shear flow is maintained by the central mass but the instability saturates via the generation of a mean vertical magnetic field. The theory assumes that the time-averaged angular momentum flux and the radial magnetic flux are constant and determines both self-consistently. The results predict that, depending on parameters, steady saturation may be supercritical or subcritical, and in the latter case that the upper (lower) solution branch is always stable (unstable). The angular momentum flux is always outward, consistent with the presence of accretion, and for fixed wavenumber peaks in the subcritical regime. The limit of infinite Reynolds number at large but finite magnetic Reynolds number is also discussed.

Effective field theory for NN interactions

International Nuclear Information System (INIS)

Tran Duy Khuong; Vo Hanh Phuc

2003-01-01

The effective field theory of NN interactions is formulated and the power counting appropriate to this case is reviewed. It is more subtle than in most effective field theories since in the limit that the S-wave NN scattering lengths go to infinity. It is governed by nontrivial fixed point. The leading two body terms in the effective field theory for nucleon self interactions are scale invariant and invariant under Wigner SU(4) spin-isospin symmetry in this limit. Higher body terms with no derivatives (i.e. three and four body terms) are automatically invariant under Wigner symmetry. (author)

A simplified density matrix minimization for linear scaling self-consistent field theory

International Nuclear Information System (INIS)

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

Topological symmetry breaking of self-interacting fractional Klein-Gordon field theories on toroidal spacetime

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2008-01-01

Quartic self-interacting fractional Klein-Gordon scalar massive and massless field theories on toroidal spacetime are studied. The effective potential and topologically generated mass are determined using zeta-function regularization technique. Renormalization of these quantities are derived. Conditions for symmetry breaking are obtained analytically. Simulations are carried out to illustrate regions or values of compactified dimensions where symmetry-breaking mechanisms appear

Filling- and interaction-driven Mott transition. Quantum cluster calculations within self-energy-functional theory

International Nuclear Information System (INIS)

Balzer, Matthias

2008-01-01

The central goal of this thesis is the examination of strongly correlated electron systems on the basis of the two-dimensional Hubbard model. We analyze how the properties of the Mott insulator change upon doping and with interaction strength. The numerical evaluation is done using quantum cluster approximations, which allow for a thermodynamically consistent description of the ground state properties. The framework of self-energy-functional theory offers great flexibility for the construction of cluster approximations. A detailed analysis sheds light on the quality and the convergence properties of different cluster approximations within the self-energy-functional theory. We use the one-dimensional Hubbard model for these examinations and compare our results with the exact solution. In two dimensions the ground state of the particle-hole symmetric model at half-filling is an antiferromagnetic insulator, independent of the interaction strength. The inclusion of short-range spatial correlations by our cluster approach leads to a considerable improvement of the antiferromagnetic order parameter as compared to dynamical mean-field theory. In the paramagnetic phase we furthermore observe a metal-insulator transition as a function of the interaction strength, which qualitatively differs from the pure mean-field scenario. Starting from the antiferromagnetic Mott insulator a filling-controlled metal-insulator transition in a paramagnetic metallic phase can be observed. Depending on the cluster approximation used an antiferromagnetic metallic phase may occur at first. In addition to long-range antiferromagnetic order, we also considered superconductivity in our calculations. The superconducting order parameter as a function of doping is in good agreement with other numerical methods, as well as with experimental results. (orig.)

Self-determination theory and the welfare of employees

Directory of Open Access Journals (Sweden)

Ranđelović Kristina M.

2013-01-01

Full Text Available The objective of this article is to give an account of the psychological welfare of employees in the context of self-determination theory. SDT represents an approach to human motivation and personality that uses traditional empirical methods which make clear the importance of development of human innate abilities for personal development, integration and self-regulation. Self-determination theory emphasizes that welfare is an direct function with the satisfaction of basic psychological needs. According to the above mentioned theory self actualization (eudemonia represents the key aspect of psychological welfare. Namely, SDT aims to explain what it means to actualize oneself and how to schive that. The researches within self-determination theory are focused on the factors that allow or prevent psychological grouth, integrity and welfare. SDT is a theory with great prospect and it allows us not only to understand better the psychological processes in many aspects of use (sport, work, parenthood, education, etc. but also to direct programs and interventions that improve the circumstances in which people live. The theory has recently been applied in health-working psychology and few empirical findings have given support to its fundamental premises. SDT is a consistant theory that can be tested, it is applicable in almost all spheres of life (family, school system, health care, work, relationships among people ect. and it gives a broad spectrum of possible problems to research. It not only offers different social environments and his welfare, but the theory also offers directives how to improve the conditions in witch people live and work. The organizational context that allows the possibility to choose, make autonomous decisions, clear explanations of certain work assignments, as well as the appreciation of feelings and attitudes of the employees will bring about greater satisfaction of the innate needs for grouth. It is necessary, in our

Mean-field theory of anyons near Bose statistics

International Nuclear Information System (INIS)

McCabe, J.; MacKenzie, R.

1992-01-01

The validity of a mean-field approximation for a boson-based free anyon gas near Bose statistics is shown. The magnetic properties of the system is discussed in the approximation that the statistical magnetic field is uniform. It is proved that the anyon gas does not exhibit a Meissner effect in the domain of validity the approximation. (K.A.) 7 refs

Correlated effective field theory in transition metal compounds

International Nuclear Information System (INIS)

Mukhopadhyay, Subhasis; Chatterjee, Ibha

2004-01-01

Mean field theory is good enough to study the physical properties at higher temperatures and in higher dimensions. It explains the critical phenomena in a restricted sense. Near the critical temperatures, when fluctuations become important, it may not give the correct results. Similarly in low dimensions, the correlations become important and the mean field theory seems to be inadequate to explain the physical phenomena. At low-temperatures too, the quantum correlations become important and these effects are to be treated in an appropriate way. In 1974, Prof. M.E. Lines of Bell Laboratories, developed a theory which goes beyond the mean field theory and is known as the correlated effective field (CEF) theory. It takes into account the fluctuations in a semiempirical way. Lines and his collaborators used this theory to explain the short-range correlations and their anisotropy in the paramagnetic phase. Later Suzuki et al., Chatterjee and Desai, Mukhopadhyay and Chatterjee applied this theory to the magnetically ordered phase and a tremendous success of the theory has been found in real systems. The success of the CEF theory is discussed in this review. In order to highlight the success of this theory, earlier effective field theories and their improvements over mean field theories e.g., Bethe-Peierls-Weiss method, reaction field approximation, etc., are also discussed in this review for completeness. The beauty of the CEF theory is that it is mean field-like, but captures the essential physics of real systems to a great extent. However, this is a weak correlated theory and as a result is inappropriate for the metallic phase when strong correlations become important. In recent times, transition metal oxides become important due to the discovery of the high-temperature superconductivity and the colossal magnetoresistance phenomena. These oxides seem to be Mott insulators and undergo an insulator to metal transition by applying magnetic field, pressure and by changing

False memory production :effects of self-consistent false information and motivated cognition

OpenAIRE

Brown, Martha

1996-01-01

Remembrance of one's personal past and the development of false memories have recently received intense public scrutiny. Based upon self-schema (Markus, 1977) and selfverification (Swann, 1987) theories, two studies were conducted to investigate the hypothesis that a self-schema guides cognitive processing of self-relevant information and thereby influences the construction of a memory that includes false information, particularly more so if this information is self-schema consistent than ...

Self-consistent finite-temperature model of atom-laser coherence properties

International Nuclear Information System (INIS)

Fergusson, J.R.; Geddes, A.J.; Hutchinson, D.A.W.

2005-01-01

We present a mean-field model of a continuous-wave atom laser with Raman output coupling. The noncondensate is pumped at a fixed input rate which, in turn, pumps the condensate through a two-body scattering process obeying the Fermi golden rule. The gas is then coupled out by a Gaussian beam from the system, and the temperature and particle number are self-consistently evaluated against equilibrium constraints. We observe the dependence of the second-order coherence of the output upon the width of the output-coupling beam, and note that even in the presence of a highly coherent trapped gas, perfect coherence of the output matter wave is not guaranteed

Attractive versus repulsive interactions in the Bose-Einstein condensation dynamics of relativistic field theories

Science.gov (United States)

Berges, J.; Boguslavski, K.; Chatrchyan, A.; Jaeckel, J.

2017-10-01

We study the impact of attractive self-interactions on the nonequilibrium dynamics of relativistic quantum fields with large occupancies at low momenta. Our primary focus is on Bose-Einstein condensation and nonthermal fixed points in such systems. For a model system, we consider O (N ) -symmetric scalar field theories. We use classical-statistical real-time simulations as well as a systematic 1 /N expansion of the quantum (two-particle-irreducible) effective action to next-to-leading order. When the mean self-interactions are repulsive, condensation occurs as a consequence of a universal inverse particle cascade to the zero-momentum mode with self-similar scaling behavior. For attractive mean self-interactions, the inverse cascade is absent, and the particle annihilation rate is enhanced compared to the repulsive case, which counteracts the formation of coherent field configurations. For N ≥2 , the presence of a nonvanishing conserved charge can suppress number-changing processes and lead to the formation of stable localized charge clumps, i.e., Q balls.

Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling

DEFF Research Database (Denmark)

Opper, Manfred; Winther, Ole

2001-01-01

We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge...... of the distribution of couplings between the random variables is required, our method adapts to the concrete set of couplings. We show the significance of the approach in two ways: Our approach reproduces replica symmetric results for a wide class of toy models (assuming a nonglassy phase) with given disorder...... distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches....

Fermion boson metamorphosis in field theory

International Nuclear Information System (INIS)

Ha, Y.K.

1982-01-01

In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered

Lectures on matrix field theory

CERN Document Server

Ydri, Badis

2017-01-01

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.

Towards weakly constrained double field theory

Directory of Open Access Journals (Sweden)

Kanghoon Lee

2016-08-01

Full Text Available We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.

The consistent histories interpretation of quantum fields in curved spacetime

International Nuclear Information System (INIS)

Blencowe, M.

1991-01-01

As an initial attempt to address some of the foundation problems of quantum mechanics, the author formulates the consistent histories interpretation of quantum field theory on a globally hyperbolic curved space time. He then constructs quasiclassical histories for a free, massive scalar field. In the final part, he points out the shortcomings of the theory and conjecture that one must take into account the fact that gravity is quantized in order to overcome them

Modeling self-consistent multi-class dynamic traffic flow

Science.gov (United States)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

Exact self-consistent solutions to the interacting spinor and scalar field equations in Bianchi type-I space-time

International Nuclear Information System (INIS)

Alvarado, R.; Rybakov, Yu.P.; Shikin, G.N.; Saha, B.

1995-01-01

Self-consistent solutions to the system of spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time. The absence of initial singularity should be emphasized for some types of solutions and also the isotropic mode of space-time expansion in some special cases. 3 refs

Landau-like theory for universality of critical exponents in quasistationary states of isolated mean-field systems.

Science.gov (United States)

Ogawa, Shun; Yamaguchi, Yoshiyuki Y

2015-06-01

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two nonclassical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends the universality class of the nonclassical exponents to spatially periodic one-dimensional systems and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.

Electronic structure and core-level spectra of light actinide dioxides in the dynamical mean-field theory

Czech Academy of Sciences Publication Activity Database

Kolorenč, Jindřich; Shick, Alexander; Lichtenstein, A.I.

2015-01-01

Roč. 92, č. 8 (2015), "085125-1"-"085125-10" ISSN 1098-0121 R&D Projects: GA ČR GC15-05872J Institutional support: RVO:68378271 Keywords : electronic-structure calculations * dynamical mean-field theory * Mott insulators * actinides * oxides * photoemission Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.736, year: 2014

Constraints and Hamiltonian in light-front quantized field theory

International Nuclear Information System (INIS)

Srivastava, P.P.

1993-01-01

Self-consistent hamiltonian formulation of scalar theory on the null plane is constructed and quantized following the Dirac procedure. The theory contains also constraint equations which would give, if solved, to a nonlocal Hamiltonian. In contrast to the equal-time formulation we obtain a different description of the spontaneous symmetry breaking in the continuum and the symmetry generators are found to annihilate the light-front vacuum. Two examples are given where the procedure cannot be applied self-consistently. The corresponding theories are known to be ill-defined from the equal-time quantization. (author)

Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure

International Nuclear Information System (INIS)

Yang Xuhua; Sun Bao; Wang Bo; Sun Youxian

2010-01-01

Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper. (general)

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson–Boltzmann electrostatics

Science.gov (United States)

Sun, Hui; Wen, Jiayi; Zhao, Yanxiang; Li, Bo; McCammon, J. Andrew

2015-01-01

Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson–Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum–Chandler–Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods. PMID:26723595

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics.

Science.gov (United States)

Sun, Hui; Wen, Jiayi; Zhao, Yanxiang; Li, Bo; McCammon, J Andrew

2015-12-28

Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.

Soliton excitations in polyacetylene and relativistic field theory models

International Nuclear Information System (INIS)

Campbell, D.K.; Bishop, A.R.; Los Alamos Scientific Lab., NM

1982-01-01

A continuum model of a Peierls-dimerized chain, as described generally by Brazovskii and discussed for the case of polyacetylene by Takayama, Lin-Liu and Maki (TLM), is considered. The continuum (Bogliubov-de Gennes) equations arising in this model of interacting electrons and phonons are shown to be equivalent to the static, semiclassical equations for a solvable model field theory of self-coupled fermions - the N = 2 Gross-Neveu model. Based on this equivalence we note the existence of soliton defect states in polyacetylene that are additional to, and qualitatively different from, the amplitude kinks commonly discussed. The new solutions do not have the topological stability of kinks but are essentially conventional strong-coupling polarons in the dimerized chain. They carry spin (1/2) and charge (+- e). In addition, we discuss further areas in which known field theory results may apply to a Peierls-dimerized chain, including relations between phenomenological PHI 4 and continuuum electron-phonon models, and the structure of the fully quantum versus mean field theories. (orig.)

Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach

Science.gov (United States)

Martindale, James D.; Fu, Henry C.

2017-09-01

This study is motivated by a microfluidic device that imparts a magnetic torque on an array of bacterial flagella. Bacterial flagella can transform their helical geometry autonomously in response to properties of the background fluid, which provides an intriguing mechanism allowing their use as an engineered element for the regulation or transport of chemicals in microscale applications. The synchronization of flagellar phase has been widely studied in biological contexts, but here we examine the synchronization of flagellar tilt, which is necessary for effective pumping. We first examine the effects of helical geometry and tilt on the pumping flows generated by a single rotating flagellum. Next, we explore a mean-field model for an array of helical flagella to understand how collective tilt arises and influences pumping. The mean-field methodology allows us to take into account possible phase differences through a time-averaging procedure and to model an infinite array of flagella. We find array separation distances, magnetic field strengths, and rotation frequencies that produce nontrivial self-consistent pumping solutions. For individual flagella, pumping is reversed when helicity or rotation is reversed; in contrast, when collective effects are included, self-consistent tilted pumping solutions become untilted nonpumping solutions when helicity or rotation is reversed.

Multiplicative renormalizability and self-consistent treatments of the Schwinger-Dyson equations

International Nuclear Information System (INIS)

Brown, N.; Dorey, N.

1989-11-01

Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched quantum electrodynamics, (QED), checking the consistency of various approximations. In particular, we show that the much used 'ladder' approximation is self-consistent, provided that the coupling constant is renormalized in a particular way. We also propose another approximation which satisfies this self-consistency test, but requires that the coupling be unrenormalized, as should be the case in the full quenched approximation. This new approximation admits an exact solution, which also satisfies the renormalization group equation for the quenched approximation. (author)

Unified field theory

International Nuclear Information System (INIS)

Vollendorf, F.

1976-01-01

A theory is developed in which the gravitational as well as the electromagnetic field is described in a purely geometrical manner. In the case of a static central symmetric field Newton's law of gravitation and Schwarzschild's line element are derived by means of an action principle. The same principle leads to Fermat's law which defines the world lines of photons. (orig.) [de