Damping of phonons in Bose gas at low temperatures

TL;DR

This paper investigates how phonons in a homogeneous Bose gas are damped at low temperatures by computing the imaginary part of their excitation spectrum using perturbation theory and two analytical approaches.

Contribution

It provides a detailed calculation of phonon damping in Bose gases at low temperatures, employing novel perturbative methods and resonance analysis.

Findings

Computed the imaginary part of the phononic spectrum at low temperatures

Identified resonance phenomena near zero energy

Applied two complementary analytical approaches

Abstract

We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions interacting with a small potential with a positive Fourier transform. We compute the imaginary part of the phononic excitation spectrum in the lowest order of perturbation theory in thermodynamic limit at low temperatures and low momentum. Our analysis is based on perturbation theory of the standard Liouvillean. We use two approaches: the first, motivated by the standard representation of operator algebras, examines resonances near zero; the second analyzes the 2-point correlation function in the energy-momentum space.