We consider the asymptotics of the partition function of the extended Gross-Witten-Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partition function can be written as a Toepl...
详细信息
We consider the asymptotics of the partition function of the extended Gross-Witten-Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partition function can be written as a Toeplitz determinant with entries expressed in terms of the modified Bessel functions of the first kind and furnishes a tau$\tau$-function sequence of the Painlev & eacute;III '$\text{III}<^>{\prime }$ equation. We derive the asymptotic expansions of the Toeplitz determinant up to and including the constant terms as the size of the determinant tends to infinity. The constant terms therein are expressed in terms of the Riemann zeta-function and the Barnes G$G$-function. A third-order phase transition in the leading terms of the asymptotic expansions is also observed.
In this paper, we consider a certain class of inequalities for the partition function of the following form: Pi(T)(i=1) p(n+s(i)) >= Pi(T)(i=1) p(n+r(i)) which we call multiplicative inequalities. Given a multiplic...
详细信息
In this paper, we consider a certain class of inequalities for the partition function of the following form: Pi(T)(i=1) p(n+s(i)) >= Pi(T)(i=1) p(n+r(i)) which we call multiplicative inequalities. Given a multiplicative inequality with the condition that Sigma(T)(i=1) s(i)(m) not equal Sigma(T)(i=1) r(i)(m) for at least one m >= 1, we shall construct a unified framework so as to decide whether such a inequality holds or not. As a consequence, we will see that study of such inequalities has manifold applications. For example, one can retrieve log-concavity property, strong log-concavity, and the multiplicative inequality for p(n) considered by Bessenrodt and Ono, to name a few. Furthermore, we obtain an asymptotic expansion for the finite difference of the logarithm of p(n), denoted by (-1)(r-1)Delta(r) logp(n), which generalizes a result by Chen, Wang, and Xie. (c) 2023 Elsevier Inc. All rights reserved.
We present a comprehensive and elaborate study of W LVI (K-like W-55(+)) by using multi-configuration Dirac-Fock method (MCDF). We have included relativistic corrections, QED (quantum electrodynamics) and Breit correc...
详细信息
We present a comprehensive and elaborate study of W LVI (K-like W-55(+)) by using multi-configuration Dirac-Fock method (MCDF). We have included relativistic corrections, QED (quantum electrodynamics) and Breit corrections in our computation. We have reported energy levels and radiative data for multipole transitions (i.e., electric dipole (E1), electric quadrupole (E2), magnetic dipole (Ml), and magnetic quadrupole (M2)) within the lowest 142 fine-structure levels and predicted soft X-ray transition (SXR) and extreme ultraviolet transitions (EUV) from higher excited states to the ground state. We have compared our calculated data with energy levels compiled by NIST and other available results in the literature and the small discrepancies found with them are discussed. Because only a few of the lowest levels are available in the literature, for checking excitation energies of higher excited states we have performed the same calculations with the distorted wave method. Furthermore, we have also provided relative population for the first five excited states, with both the partition function and thermodynamic quantities for W LVI and studied their variations with temperature. We believe that our reported new atomic data of W LVI may be useful in identification and analysis of spectral lines from various astrophysical and fusion plasma sources and may also be beneficial in plasma modeling.
作者：
Chen, Shi-ChaoHenan Univ
Sch Math & Stat Inst Contemporary Math Kaifeng 475004 Peoples R China
A folklore conjecture on the partition function asserts that the density of odd values of p(n) is 1/2. In general, for a positive integer t, let p(t)(n) be the t-multipartition function and delta(t) be the density of ...
详细信息
A folklore conjecture on the partition function asserts that the density of odd values of p(n) is 1/2. In general, for a positive integer t, let p(t)(n) be the t-multipartition function and delta(t) be the density of the odd values of p(t)(n). It is widely believed that delta(t) exists. Given an odd integer a and an integer b depending on a and t, Judge and Zanello framed an infinite family of conjectural congruence relations on p(t)(an +b) (mod 2) which establishes a striking connection between delta(a) and delta(1). As a special case t = 1, it implies that delta(1) > 0 if (3, a) = 1 and delta(a) > 0. This conjecture was proved for several values of a by Judge, Keith and Zanello. In this paper we prove that the conjecture is true for a = l(alpha) is a prime power with l >= 5 and a = 3. (C) 2021 Elsevier Inc. All rights reserved.
We study the partition function of the Ising model on a graph with the help of quantum computing. The Boltzmann factor is modeled on a quantum computer as a trace of some evolution operator with effective Hamiltonian ...
详细信息
We study the partition function of the Ising model on a graph with the help of quantum computing. The Boltzmann factor is modeled on a quantum computer as a trace of some evolution operator with effective Hamiltonian over ancilla spins (qubits) corresponding to graph links. We propose two methods for this which are based on effective Hamiltonian with three-spin interaction and on two-spin interaction. The limit of small temperatures allows us to find the ground state of the system that is related to the discrete combinatorial optimization problem. The partition function of the Ising model for two-spin clusters is calculated on IBM's quantum computer. The possibility of finding ground state is also demonstrated for two-spin clusters.
Intending to describe the dark matter (DM) of dwarf galaxies, we concentrate on one model of the slowly rotating and gravitating Bose-Einstein condensate (BEC). For a deeper understanding of its properties, we calcula...
详细信息
Intending to describe the dark matter (DM) of dwarf galaxies, we concentrate on one model of the slowly rotating and gravitating Bose-Einstein condensate (BEC). For a deeper understanding of its properties, we calculate the partition function and compare the characteristics derived from it with the results based on the solution of Gross-Pitaevskii equation (GPE). In our approach, which uses Green's functions of spatial evolution operators, we formulate in a unified way the boundary conditions, important for applying the Thomas-Fermi approximation. Taking this into account, we revise some of the results obtained earlier. We also derive the spatial particle distribution, similar to the model with rotation, by using the deformation of commutation relations for a macroscopic wave function and modifying the GPE. It is shown that such an approach leads to the entropy inhomogeneity and makes the distribution dependent on temperature.
For any positive integer k >= 1, let p(1/k)(n) be the number of solutions of the equation n = [k root a(1)] + ... + [k root a(d)] with integers a(1) >= ... >= a(d) >= 1, where [t] is the integral part of r...
详细信息
For any positive integer k >= 1, let p(1/k)(n) be the number of solutions of the equation n = [k root a(1)] + ... + [k root a(d)] with integers a(1) >= ... >= a(d) >= 1, where [t] is the integral part of real number t. Recently, Luca and Ralaivaosaona gave an asymptotic formula for p(1/2)(n). In this paper, we give an asymptotic development of p(1/k)(n) for all k >= 1. Moreover, we prove that the number of such partitions is even (respectively, odd) infinitely often.
Higher-order approximation based on Taylor expansion over the saddle point is employed to approach the partition function of a hot nucleus in the presence of the like-particle pairing correlations. Analytical expressi...
详细信息
Higher-order approximation based on Taylor expansion over the saddle point is employed to approach the partition function of a hot nucleus in the presence of the like-particle pairing correlations. Analytical expressions have been derived for the correction terms of different thermodynamic quantities such as energy, entropy and heat capacity. Furthermore, the theory has been applied to the schematic and realistic models. It is found that the correction terms are temperature-dependent functions and are more deeply sensitive to the pairing gap in the vicinity of the critical temperature.
Statistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics. However, these...
详细信息
Statistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics. However, these two representations are usually regarded as separate tools for network analysis, without exploiting the potential synergies between them. In this paper, we establish a link between the Ihara Zeta function from algebraic graph theory and the partition function from statistical mechanics, and exploit this relationship to obtain a deeper structural characterisation of network structure. Specifically, the relationship allows us to explore the connection between the microscopic structure and the macroscopic characterisation of a network. We derive thermodynamic quantities describing the network, such as entropy, and show how these are related to the frequencies of prime cycles of various lengths. In particular, the n-th order partial derivative of the Ihara Zeta function can be used to compute the number of prime cycles in a network, which in turn is related to the partition function of Bose-Einstein statistics. The corresponding derived entropy allows us to explore a phase transition in the network structure with critical points at high and low-temperature limits. Numerical experiments and empirical data are presented to evaluate the qualitative and quantitative performance of the resulting structural network characterisations.
We analyze Ising/Curie-Weiss models on the Erdos-Renyi graph with N vertices and edge probability p = p(N) that were introduced by Bovier and Gayrard (J. Stat. Phys. 72 (3-4) (1993) 643-664) and investigated in (J. St...
详细信息
We analyze Ising/Curie-Weiss models on the Erdos-Renyi graph with N vertices and edge probability p = p(N) that were introduced by Bovier and Gayrard (J. Stat. Phys. 72 (3-4) (1993) 643-664) and investigated in (J. Stat. Phys. 177 (1) (2019) 78-94) and (Kabluchko, Lowe and Schubert (2019)). We prove Central Limit Theorems for the partition function of the model and - at other decay regimes of p(N) - for the logarithmic partition function. We find critical regimes for p(N) at which the behavior of the fluctuations of the partition function changes.
暂无评论