Decay of excitations in interacting one-dimensional Bose gases
Zoran Ristivojevic (CPhT, Ecole Polytechnique, Palaiseau)
Excitation spectrum in weakly-interacting systems of bosons have the Bogoliubov form. In three dimensions, those excitations are unstable due to residual weak interactions. The resulting process is known as Beliaev decay [1,2] and has been experimentally observed [3]. The related problem of decay of excitations in one-dimensional Bose gases is a fundamental long-standing problem. In this talk I will present its solution [4]. As a result of the conservation laws in one dimension, at zero temperature the leading mechanism of decay of a quasiparticle excitation is its disintegration into three others. We find that a phonon excitation has a decay rate proportional to the seventh power of momentum. In the integrable case of contact interaction between the bosons, the decay rate vanishes. Our theory is based on studying the anharmonic effects produced by the leading integrability breaking perturbations to the Lieb-Liniger model. It is not limited to the decay of lowest momentum phonon excitations and can describe full crossover as momentum increases and the excitation spectrum approaches its quadratic form.
[1] S. T. Beliaev, Sov. Phys. JETP 7, 299 (1958).
[2] L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2 (Pergamon Press, Oxford, 1980).
[3] N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, Phys. Rev. Lett. 89, 220401 (2002).
[4] Z. Ristivojevic and K. A. Matveev, arxiv:1312.5322 (2013).