Path-integral approach to the thermodynamics of bosons with memory: Density and correlation functions

TL;DR

This paper develops a path-integral method to analyze the thermodynamics of bosonic systems with memory effects, deriving key density and correlation functions for quadratic models with general memory kernels.

Contribution

It introduces a novel path-integral framework for bosons with memory interactions, enabling calculation of density and correlation functions in complex systems.

Findings

Derived explicit expressions for density and correlation functions

Analyzed condensate fraction and pair correlations in trapped bosons

Applied the formalism to systems with harmonic coupling to external masses

Abstract

Expanding upon previous work, using the path-integral formalism we derive expressions for the one-particle reduced density matrix and the two-point correlation function for a quadratic system of bosons that interact through a general class of memory kernels. The results are applied to study the density, condensate fraction and pair correlation function of trapped bosons harmonically coupled to external distinguishable masses.