Path-integral approach to the thermodynamics of bosons with memory: Partition function and specific heat

TL;DR

This paper develops a path-integral method to analyze the thermodynamics of bosons with memory effects, deriving a recurrence relation for the partition function and applying it to compute the specific heat of an open quantum bosonic system.

Contribution

It introduces a generalized path-integral approach for bosonic systems with memory kernels, extending previous models and enabling calculation of thermodynamic properties.

Findings

Derived a recurrence relation for the partition function of bosons with memory

Applied the method to compute the specific heat of an open quantum bosonic system

Demonstrated the approach's generalization over existing treatments

Abstract

For a system of bosons that interact through a class of general memory kernels, a recurrence relation for the partition function is derived within the path-integral formalism. This approach provides a generalization to previously known treatments in the literature of harmonically coupled systems of identical particles. As an example the result is applied to the specific heat of a simplified model of an open quantum system of bosons, harmonically coupled to a reservoir of distinguishable fictitious masses.