Thermalization of dipole oscillations in confined systems by rare collisions

Maxim Khodas, Alex Levchenko

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Abstract

We study the relaxation of the center of mass or dipole oscillations in the system of interacting fermions confined spatially. With the confinement frequency ω fixed, the particles were considered to freely move along one (quasi-1D) or two (quasi-2D) spatial dimensions. We have focused on the regime of rare collisions, such that the inelastic collision rate 1/τin ω. The dipole oscillation relaxation rate 1/τ is obtained at three different levels: by direct perturbation theory, solving the integral Bethe-Salpeter equation, and applying the memory function formalism. As long as anharmonicity is weak, 1/τ 1/τin, the three methods are shown to give identical results. In the quasi-2D case, 1/τ ≠0 at zero temperature. In quasi-1D system, 1/τ T3 if the Fermi energy EF lies below the critical value EF<3ω /4. Otherwise, unless the system is close to integrability, the rate 1/τ has a temperature dependence similar to that in quasi-2D. In all cases, the relaxation results from the excitation of particle-hole pairs propagating along unconfined directions resulting in the relationship 1/τ 1/τin, with the inelastic rate 1/τin≠0 as the phase-space opens up at finite energy of excitation ω. While 1/τ τin in the hydrodynamic regime, ω 1/τin, in the regime of rare collisions, ω 1/τin, we obtain the opposite trend 1/τ 1/τin.

Original languageAmerican English
Article number064303
JournalPhysical Review B
Volume98
Issue number6
DOIs
StatePublished - 13 Aug 2018

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© 2018 American Physical Society.

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