Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations

TL;DR

This paper introduces a novel approach to studying equilibrium quantum properties of interacting bosons by expressing Matsubara Green's functions as classical averages over stochastic differential equations, enabling non-perturbative numerical simulations.

Contribution

It presents a new method linking quantum Green's functions to classical stochastic processes, allowing direct numerical analysis of interacting boson systems in thermal equilibrium.

Findings

Derived an analytic characteristic function for a thermal state.

Discussed a Higgs-type phase transition in the model.

Validated the approach with an anharmonic oscillator example.

Abstract

Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. An analytic expression for the characteristic function in a thermal state is derived and a Higgs-type phase transition discussed, which occurs when the oscillator frequency becomes negative.