Related papers: Generalized partition functions, interpolating sta…
We discuss some aspects of a new noncombinatorial fermionic approach to the two-dimensional dimer problem in statistical mechanics based on the integration over anticommuting Grassmann variables and factorization ideas for dimer density…
We derive the partition function of the one-body and two-body systems of classical noncommutative harmonic oscillator in two dimensions. Then, we employ the path integral approach to the quantum noncommutative harmonic oscillator and derive…
The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the cross-over length, beyond which asymptotic scaling laws apply, depends on…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic…
We show that Haldanes new definition of statistics, when generalised to infinite dimensional Hilbert spaces, is equal to the high temperature limit of the second virial coefficient. We thus show that this exclusion statistics parameter, g ,…
We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…
Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers-Ramanujan identities, the Gollnitz-Gordon identities, Euler's odd=distinct theorem, and the Andrews-Gordon…
We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein,…
Voros coefficients of the generalized hypergeometric differential equations with a large parameter are defined and their explicit forms are given for the origin and for the infinity. It is shown that they are Borel summable in some…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
The second virial coefficient for the Mie potential is evaluated using the method of brackets. This method converts a definite integral into a series in the parameters of the problem, in this case this is the temperature $T$. The results…
In statistical mechanics, for a system with fixed number of particles, e.g., a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the…
For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and…
The main purpose of this paper is the study of the action that produces Poisson-gradient systems and their multiple periodical solutions. The Section 1 establishes the basic tools. The section 2 underlines conditions in which the action…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
Two improvements with respect to previous formulations are presented for the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems. By including anharmonicities and employing a variational…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…
In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider applications of a recent Lieb-Thirring…