Evaluation of the Permutational Structure of the Canonical Ensemble Partition Function

TL;DR

This paper introduces a novel permutational sampling method for quantum gases using path integrals, employing group theory operators to construct Markov chains, demonstrated through a four-particle harmonic trap example.

Contribution

It presents a new approach leveraging group theory operators for permutational sampling in quantum gases within the path integral framework.

Findings

Successful test calculation with four particles in a harmonic trap

Demonstrated feasibility of the method for quantum gas simulations

Potential for improved sampling efficiency in quantum statistical mechanics

Abstract

Proposed is an alternative method for permutational sampling in quantum gases using the path integral formulation of statistical mechanics. It is shown that in principle we are able to use two operators which enable us to construct a Markov chain through a graph of the irreducible representation of the symmetric group. As an illustration of this method, a test calculation of four particles in a harmonic trap is performed.