Phonon decay in one-dimensional atomic Bose quasicondensates via Beliaev-Landau damping

In a one-dimensional Bose gas, there is no nontrivial scattering channel involving three Bogoliubov quasiparticles that conserves both energy and momentum. Nevertheless, we show that such three-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.