相关论文: Partition functions and symmetric polynomials
The thermodynamical entropy of a system which consists of different kinds of ideal gases is known to be defined successfully in the case when the differences are described by classical or quantum theory. Since these theories are special…
It is shown that a similar functional form $S=a+b\ln N$ holds approximately for the information entropy S as function of the number of particles N for atoms, nuclei and atomic clusters (fermionic systems) and correlated boson-atoms in a…
In a previous work, both the constants of motion of a classical system and the symmetries of the corresponding quantum version have been computed with the help of factorizations. As their expressions were not polynomial, in this paper the…
We introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in finite lattice. We introduce the $L$-operator related with the $U_q(sl_2)$ $R$-matrix, and…
Andrews studied a function which appears in Ramanujan's identities. In Ramanujan's "Lost" Notebook, there are several formulas involving this function, but they are not as simple as the identities with other similar shape of functions.…
Some basic concepts concerning systems of identical particles are discussed in the framework of a realist interpretation, where the wave function is the quantum object and |psi(r)|^2 d^3r is the probability that the wave function causes an…
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
We study a family of identities regarding a divisibility property of the Kostant partition function which first appeared in a paper of Baldoni and Vergne. To prove the identities, Baldoni and Vergne used techniques of residues and called…
In this text we introduce and analyze families of symmetric functions arising as partition functions for colored fermionic vertex models associated with the quantized affine Lie superalgebra $U_q \big( \widehat{\mathfrak{sl}} (1 | n)…
We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender's…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
Folsom, Kent, and Ono used the theory of modular forms modulo $\ell$ to establish remarkable ``self-similarity'' properties of the partition function and give an overarching explanation of many partition congruences. We generalize their…
We extend the inner product from bosonic Fock space to a pairing between suitable antifunctionals on the symmetric algebra. Our account is illustrated by the (Gaussian) half-form pairing between positive polarizations in the form needed for…
Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the Quantum Isolated Horizon(QIH) with explanations of the underlying physical motivations. An extensive thermodynamic…
Dodgson polynomials appear in Schwinger parametric Feynman integrals and are closely related to the well known Kirchhoff (or first Symanzik) polynomial. In this article a new combinatorial interpretation and a generalisation of Dodgson…
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…