The Experts below are selected from a list of 147 Experts worldwide ranked by ideXlab platform
O A Dobush - One of the best experts on this subject based on the ideXlab platform.
-
representation of the Grand Partition Function of the cell model the state equation in the mean field approximation
Journal of Molecular Liquids, 2016Co-Authors: M P Kozlovskii, O A DobushAbstract:Abstract The method to calculate the Grand Partition Function of a particle system, in which constituents interact with each other via potential, that include repulsive and attractive components, is proposed. The cell model, which was introduced to describe critical phenomena and phase transitions, is used to provide calculations. The exact procedure of integration over particle coordinates and summation over number of particles is proposed. As a result, an evident expression for the Grand Partition Function of the fluid cell model is obtained in the form of multiple integral over collective variables. As it can be seen directly from the structure of the transition Jacobian, the present multiparticle model appeared to be different from the Ising model, which is widely used to describe fluid systems. The state equation, which is valid for wide temperature ranges both above and below the critical one, is derived in mean-field approximation. The pressure calculated for the cell model at temperatures above the critical one is found to be continuously increasing Function of temperature and density. The isotherms of pressure as a Function of density have horizontal parts at temperatures below the critical one.
Kazumi Okuyama - One of the best experts on this subject based on the ideXlab platform.
-
Orientifolding of the ABJ Fermi gas
Journal of High Energy Physics, 2016Co-Authors: Kazumi OkuyamaAbstract:The Grand Partition Functions of ABJ theory can be factorized into even and odd parts under the reflection of fermion coordinate in the Fermi gas approach. In some cases, the even/odd part of ABJ Grand Partition Function is equal to that of N = 5 O n × U S p n ′ $$ \mathcal{N}=5\;\mathrm{O}(n)\times \mathrm{U}\mathrm{S}\mathrm{p}\left({n}^{\prime}\right) $$ theory, hence it is natural to think of the even/odd projection of Grand Partition Function as an orientifolding of ABJ Fermi gas system. By a systematic WKB analysis, we determine the coefficients in the perturbative part of Grand potential of such orientifold ABJ theory. We also find the exact form of the first few “half-instanton” corrections coming from the twisted sector of the reflection of fermion coordinate. For the Chern-Simons level k = 2 , 4 , 8 we find closed form expressions of the Grand Partition Functions of orientifold ABJ theory, and for k = 2 , 4 we prove the Functional relations among the Grand Partition Functions conjectured in arXiv:1410.7658 .
-
Exact results on the ABJM Fermi gas
Journal of High Energy Physics, 2012Co-Authors: Yasuyuki Hatsuda, Sanefumi Moriyama, Kazumi OkuyamaAbstract:We study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop a method to compute the Grand Partition Function of the ABJM theory, and compute exactly the Partition Function Z(N) up to N = 9 with the Chern-Simons level k = 1. We find that the eigenvalue problem of this quantum mechanical system is reduced to the diagonalization of a certain Hankel matrix. In reducing the number of integrations by commuting coordinates and momenta, we find an exact relation concerning the Grand Partition Function, which is interesting on its own right and very helpful for determining the Partition Function. We also study the TBA-type integral equations that allow us to compute the Grand Partition Function numerically. Surprisingly, all of our exact Partition Functions are written in terms of polynomials of π −1 with rational coefficients.
Masatoshi Yamamura - One of the best experts on this subject based on the ideXlab platform.
-
Even-Odd Effect on the Thermal Equilibrium State of the Pairing Model. I Comparison between Canonical and Grand Canonical Ensembles
Progress of Theoretical Physics, 2002Co-Authors: Atsushi Kuriyama, Joao Da Providencia, Yasuhiko Tsue, Masatoshi YamamuraAbstract:To facilitate the study of thermal properties of the pairing model, an approach based on the Grandcanonical ensemble is numerically comparedwith one basedon the canonical ensemble. At low temperature in the phase of pair condensation, their difference becomes significant, in particular with regard to the behavior depending on whether the total number of fermions is even or odd. We separate the Grand canonical ensemble into two pieces: one containing systems with even numbers of particles andone containing systems with odd numbers of particles. The Grand Partition Functions defined on such Grand canonical ensembles faithfully reproduce the even-odd effect. In a previous series of papers, 1),2) we applied the method of a mixed state representation 3) to the description of the thermal properties of the pairing model.In Ref.1), we showed that this method yields a mean field approximation when the system is in the thermal equilibrium state.We numerically studied the validity of this method by comparing it with the results obtained from an exact numerical evaluation of the Grand Partition Function given in Ref.2). As concerns the temperature dependence of physical quantities, such as the internal energy, the free energy, the occupation number of each level, and so on, our results agree well with those obtained using the exact evaluation of the Grand Partition Function, except in the neighborhood of the transition temperature.The number dependence of such quantities also agrees well, with an exception.This exception regards the entropy in the phase of pair condensation, for which the result from the mean field approximation does not have appreciable number dependence, while that from the exact evaluation of the Grand Partition Function exhibits typical behavior depending on whether the total number of fermions is even or odd.Hereafter, we call this characteristic the even-odd effect.This even-odd effect is however smeared out in the mean field approximation.This implies that an approach employing mean field approximation cannot be applied to the description of properties that explicitly depend on the parity of the fermion number, i.e., whether it is even or odd number. At low temperature, the properties of the thermal equilibrium state are mainly specified by the dynamical ground state, whose seniority number is approximately 0
-
Even-Odd Effect on the Thermal Equilibrium State of the Pairing Model. II Mean Field Approximation and Renormalized Distribution
Progress of Theoretical Physics, 2002Co-Authors: Atsushi Kuriyama, Joao Da Providencia, Yasuhiko Tsue, Masatoshi YamamuraAbstract:We define a mean field approximation of the modified Grand Partition Function of the pairing model, which has been defined on the modified Grand canonical ensemble with even or odd particle number. Using numerical evaluations, it is shown that this approximation reproduces the even-odd effect exhibited in the case of the modified Grand Partition Function at low temperature very well in a qualitative sense. The expectation values of one-body operators can be expressedsimply in terms of those obtainedwith the conventional mean field approximation when a Fermi-type distribution is replaced by a renormalized distribution. Although Wick’s theorm does not hold in this case, the dominant parts of the expectation values of two-body operators are also given using those obtained by the conventional mean fieldapproximation with the replacement mentionedabove.
-
pairing model and mixed state representation ii Grand Partition Function and its mean field approximation
Progress of Theoretical Physics, 2002Co-Authors: Atsushi Kuriyama, Joao Da Providencia, Yasuhiko Tsue, Masatoshi YamamuraAbstract:In order to compare the approach of the mixed state representation of the pairing model with the exact evaluation of the Grand Partition Function, we introduce the fermion space of a Grand canonical ensemble. For the definition of the Grand Partition Function, we adopt a quasi-spin space and evaluate its multiplicity. Then we show how to derive the mixed state representation, which yields results that are approximately the same as those of the thermal Hartree-Fock-Bogoliubov theory for the thermal equilibrium state, from the Grand Partition Function under the mean field approximation. We compare numerical results of the mean field approximation with those obtained from the exact evaluation of the Grand Partition Function. We find that the mean field approximation gives good results. However, we find a distinctive difference between the two sets of results in the condensed phase.
M P Kozlovskii - One of the best experts on this subject based on the ideXlab platform.
-
representation of the Grand Partition Function of the cell model the state equation in the mean field approximation
Journal of Molecular Liquids, 2016Co-Authors: M P Kozlovskii, O A DobushAbstract:Abstract The method to calculate the Grand Partition Function of a particle system, in which constituents interact with each other via potential, that include repulsive and attractive components, is proposed. The cell model, which was introduced to describe critical phenomena and phase transitions, is used to provide calculations. The exact procedure of integration over particle coordinates and summation over number of particles is proposed. As a result, an evident expression for the Grand Partition Function of the fluid cell model is obtained in the form of multiple integral over collective variables. As it can be seen directly from the structure of the transition Jacobian, the present multiparticle model appeared to be different from the Ising model, which is widely used to describe fluid systems. The state equation, which is valid for wide temperature ranges both above and below the critical one, is derived in mean-field approximation. The pressure calculated for the cell model at temperatures above the critical one is found to be continuously increasing Function of temperature and density. The isotherms of pressure as a Function of density have horizontal parts at temperatures below the critical one.
Atsushi Kuriyama - One of the best experts on this subject based on the ideXlab platform.
-
Even-Odd Effect on the Thermal Equilibrium State of the Pairing Model. I Comparison between Canonical and Grand Canonical Ensembles
Progress of Theoretical Physics, 2002Co-Authors: Atsushi Kuriyama, Joao Da Providencia, Yasuhiko Tsue, Masatoshi YamamuraAbstract:To facilitate the study of thermal properties of the pairing model, an approach based on the Grandcanonical ensemble is numerically comparedwith one basedon the canonical ensemble. At low temperature in the phase of pair condensation, their difference becomes significant, in particular with regard to the behavior depending on whether the total number of fermions is even or odd. We separate the Grand canonical ensemble into two pieces: one containing systems with even numbers of particles andone containing systems with odd numbers of particles. The Grand Partition Functions defined on such Grand canonical ensembles faithfully reproduce the even-odd effect. In a previous series of papers, 1),2) we applied the method of a mixed state representation 3) to the description of the thermal properties of the pairing model.In Ref.1), we showed that this method yields a mean field approximation when the system is in the thermal equilibrium state.We numerically studied the validity of this method by comparing it with the results obtained from an exact numerical evaluation of the Grand Partition Function given in Ref.2). As concerns the temperature dependence of physical quantities, such as the internal energy, the free energy, the occupation number of each level, and so on, our results agree well with those obtained using the exact evaluation of the Grand Partition Function, except in the neighborhood of the transition temperature.The number dependence of such quantities also agrees well, with an exception.This exception regards the entropy in the phase of pair condensation, for which the result from the mean field approximation does not have appreciable number dependence, while that from the exact evaluation of the Grand Partition Function exhibits typical behavior depending on whether the total number of fermions is even or odd.Hereafter, we call this characteristic the even-odd effect.This even-odd effect is however smeared out in the mean field approximation.This implies that an approach employing mean field approximation cannot be applied to the description of properties that explicitly depend on the parity of the fermion number, i.e., whether it is even or odd number. At low temperature, the properties of the thermal equilibrium state are mainly specified by the dynamical ground state, whose seniority number is approximately 0
-
Even-Odd Effect on the Thermal Equilibrium State of the Pairing Model. II Mean Field Approximation and Renormalized Distribution
Progress of Theoretical Physics, 2002Co-Authors: Atsushi Kuriyama, Joao Da Providencia, Yasuhiko Tsue, Masatoshi YamamuraAbstract:We define a mean field approximation of the modified Grand Partition Function of the pairing model, which has been defined on the modified Grand canonical ensemble with even or odd particle number. Using numerical evaluations, it is shown that this approximation reproduces the even-odd effect exhibited in the case of the modified Grand Partition Function at low temperature very well in a qualitative sense. The expectation values of one-body operators can be expressedsimply in terms of those obtainedwith the conventional mean field approximation when a Fermi-type distribution is replaced by a renormalized distribution. Although Wick’s theorm does not hold in this case, the dominant parts of the expectation values of two-body operators are also given using those obtained by the conventional mean fieldapproximation with the replacement mentionedabove.
-
pairing model and mixed state representation ii Grand Partition Function and its mean field approximation
Progress of Theoretical Physics, 2002Co-Authors: Atsushi Kuriyama, Joao Da Providencia, Yasuhiko Tsue, Masatoshi YamamuraAbstract:In order to compare the approach of the mixed state representation of the pairing model with the exact evaluation of the Grand Partition Function, we introduce the fermion space of a Grand canonical ensemble. For the definition of the Grand Partition Function, we adopt a quasi-spin space and evaluate its multiplicity. Then we show how to derive the mixed state representation, which yields results that are approximately the same as those of the thermal Hartree-Fock-Bogoliubov theory for the thermal equilibrium state, from the Grand Partition Function under the mean field approximation. We compare numerical results of the mean field approximation with those obtained from the exact evaluation of the Grand Partition Function. We find that the mean field approximation gives good results. However, we find a distinctive difference between the two sets of results in the condensed phase.
