Phonon decay in 1D atomic Bose quasicondensates via Beliaev-Landau damping

TL;DR

This paper investigates phonon decay in 1D atomic Bose quasicondensates, revealing that Beliaev-Landau damping via three-wave mixing processes explains decay and influences phonon growth, with results supported by simulations.

Contribution

It demonstrates that Beliaev-Landau damping accounts for phonon decay in 1D Bose gases through three-wave mixing processes, providing an analytic decay rate and comparison with simulations.

Findings

Exponential decay of phonon occupation numbers observed.

Analytic decay rate derived and validated against simulations.

Damping processes slow down phonon growth during parametric oscillation.

Abstract

In a 1D Bose gas, there is no non-trivial scattering channel involving three Bogoliubov quasiparticles that conserves both energy and momentum. Nevertheless, we show that such 3-wave mixing processes (Beliaev and Landau damping) account for their decay via interactions with thermal fluctuations. Within an appropriate time window where the Fermi Golden Rule is expected to apply, the occupation number of the initially occupied mode decays exponentially and the rate takes a simple analytic form. The result is shown to compare favorably with simulations based on the Truncated Wigner Approximation. It is also shown that the same processes slow down the exponential growth of phonons induced by a parametric oscillation.