Related papers: Partition function for general multi-level systems
A general formula for the grand canonical partition function for a para Fermi system of any order and of any number of levels is derived.
New formulas are given for the grand partition function of paraboson systems of order p with n orbitals and parafermion systems of order p with m orbitals. These formulas allow the computation of statistical and thermodynamic functions for…
Starting from determinants at finite temperature obeying an intermediate boundary condition between the periodic (bosonic) and antiperiodic (fermionic) cases, we find results which can be mapped onto the ones obtained from anyons for the…
In this paper we propose a Hamiltonian of the n-level system by making use of generalized Pauli matrices.
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…
We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then reobtained as particular cases as ours. The technique we employ is a non-relativistic…
A general formula for the canonical partition function for a system obeying any statistics based on the permutation group is derived. The formula expresses the canonical partition function in terms of sums of Schur functions. The only…
In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.
We present a method to approximate partition functions of quantum systems using mixed-state quantum computation. For positive semi-definite Hamiltonians, our method has expected running-time that is almost linear in $(M/(\epsilon_{\rm…
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…
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 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…
For the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems an improvement with respect to previous formulations is presented. By including anharmonicities and employing a variational…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total…
We compare different analytical and numerical methods for studying the partitions of a finite system into fragments. We propose a new numerical method of exploring the partition space by generating the Markov chains of partitions based on…
We perform the calculation of the partition function of the Poisson-sigma model on the world sheet with the topology of a two-dimensional disc. Considering the special case of a linear Poisson structure we recover the partition function of…
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…
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…
We present two algorithms, one quantum and one classical, for estimating partition functions of quantum spin Hamiltonians. The former is a DQC1 (Deterministic quantum computation with one clean qubit) algorithm, and the first such for…