Decay of Bogoliubov excitations in one-dimensional Bose gases

TL;DR

This paper develops a microscopic theory to analyze the decay mechanisms of Bogoliubov quasiparticles in one-dimensional Bose gases, revealing how decay rates vary with energy and momentum, and exploring effects of integrability-breaking perturbations.

Contribution

The paper introduces a systematic microscopic approach to study quasiparticle decay in 1D Bose gases, including the effects of integrability-breaking interactions.

Findings

Low-energy quasiparticles decay rate scales with the seventh power of momentum.

High-energy quasiparticles decay rate is momentum-independent.

Integrable models show no quasiparticle decay, while perturbations enable finite decay.

Abstract

We study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossover region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. We account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range.