Related papers: The partition function of the unit interval
The main aim of this paper is twofold: (1) Suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions --- a way of writing an…
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…
Estimates of some integrals related to variations of smooth functions are presented.
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.…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
From first principles, the author gathers a few general rules that need to be abided by in the calculation of the internal partition functions (IPFs) of individual molecules. These rules are violated in many schemes in the literature where…
We set up some weighted norm inequalities for fractional oscillatory integral operators. As applications, the corresponding results for commutators formed by $BMO(\mathbb{R}^{n})$ functions and the operators are established.
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
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…
By using Jet Calculus as a consistent framework to describe multiparton dynamics we explain the peculiar evolution equation of fracture functions by means of the recently introduced extended fracture functions.
Using the new variational approach proposed recently for a systematic improvement of the locally harmonic Feynman-Kleinert approximation to path integrals we calculate the partition function of the anharmonic oscillator for all temperatures…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
In this note we obtain a formula for the sectional curvature on an arbitrary two-dimensional smooth manifold $M$ equipped with a Lorentzian metric $g$.
We construct a pathwise calculus for functionals of integer-valued measures and use it to derive an martingale representation formula with respect to a large class of integer-valued random measures. Using these results, we extend the…
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…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
We shed doubt on a commonly used manipulation in computing the partition function for a matrix valued operator together with its attendant invocation of the multiplicative anomaly.