相关论文: On the normalization of the partition function of …
The N-particle partition function of a one-dimensional $\delta$-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as…
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
One-dimensional repulsive delta-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle…
We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an…
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…
We propose a simple estimator that allows to calculate the absolute value of a system's partition function from a finite sampling of its canonical ensemble. The estimator utilizes a volume correction term to compensate the effect that the…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
We present the thermodynamic Bethe ansatz as a way to factorize the partition function of a 2d field theory, in particular, a conformal field theory and we compare it with another approach to factorization due to K. Schoutens which consists…
The eigenfunctions and eigenvalues of the master-equation for zero range process on a ring are found exactly via the Bethe ansatz. The rates of particle exit from a site providing the Bethe ansatz applicability are shown to be expressed in…
In some previous articles, we defined several partitions of the total kinetic energy T of a system of N classical particles in the d-dimensional Euclidean space into components corresponding to various modes of motion. In the present paper,…
In this brief technical communication it is demonstrated how using Bethe ansatz technique the explicit expression for the two-point free energy distribution function in (1+1) directed polymers can be derived in rather simple way. Obtained…
A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…
The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the…
The partition function of a bosonic Riemann gas is given by the Riemann zeta function. We assume that the hamiltonian of this gas at a given temperature $\beta^{-1}$ has a random variable $\omega$ with a given probability distribution over…
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as…
One of the most common types of functions in mathematics, physics, and engineering is a sum of products, sometimes called a partition function. After "normalization," a sum of products has a natural graphical representation, called a normal…