Quasiparticle decay in a one-dimensional Bose-Fermi mixture

TL;DR

This paper investigates the decay mechanisms of quasiparticles in a one-dimensional Bose-Fermi mixture, revealing how decay rates depend on momentum, mass ratios, and interaction parameters, with special cases where decay vanishes.

Contribution

The study provides a microscopic theory analysis of quasiparticle decay in 1D Bose-Fermi mixtures, including detailed scaling laws and conditions for decay suppression.

Findings

Decay rate scales as q^3 for low-momentum quasiparticles when q < k_F

Decay rate scales as q^2 for high-momentum quasiparticles when q > k_F

Decay rate vanishes in the integrable model case.

Abstract

In a one-dimensional weakly interacting Bose-Fermi mixture one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main scattering process which leads to their decay is the backscattering of a Bogoliubov quasiparticle off the Fermi sea, where a particle-hole pair is excited. For a low-momentum quasiparticle (phonon) of momentum $q$, we find that the decay rate scales as $q^3$ provided $q$ is smaller than the Fermi momentum $k_F$, while in the opposite case the decay behaves as $q^2$. If the ratio of the masses of fermions and bosons equals to the ratio of the boson-fermion and the boson-boson interaction strengths, the decay rate changes dramatically. It scales as $q^7$ for $q<k_F$ while we find $q^6$ scaling at $q>k_F$. For a high momentum Bogoliubov quasiparticle, we find a constant decay rate for $q<k_F$, while it scales as $1/q$ for $q>k_F$. We also find an analytic expression for the decay rate in the crossover region between low and high momenta. The decay rate is a continuous, but nonanalytic function of the momentum at $q=k_F$. In the special case when the parameters of our system correspond to the integrable model, we observe that the decay rate vanishes.