Dipole Oscillations in Bose - Fermi Mixture in the Time-Dependent Grosspitaevskii and Vlasov equations

TL;DR

This paper investigates dipole oscillations in Bose-Fermi mixtures using a dynamical approach based on the time-dependent Gross-Pitaevskii and Vlasov equations, revealing complex behaviors not captured by traditional methods.

Contribution

It introduces a dynamical time-dependent framework to study collective oscillations in Bose-Fermi mixtures, highlighting differences from conventional approximation methods.

Findings

Fermion oscillations exhibit beats and damping.

Bose gas oscillates monotonously.

Fermion dipole oscillation cannot be simplified to center-of-mass motion.

Abstract

We study the dipole collective oscillations in the bose-fermi mixture using a dynamical time-dependent approach, which are formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. We find big difference in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the random-phase approximation and the sum-rule approach. While the bose gas oscillates monotonously, the fermion oscillation shows a beat and a damping. When the amplitude is not minimal, the dipole oscillation of the fermi gas cannot be described with a simple center-of-mass motion.