Collective excitations of a Bose-condensed gas: Fate of second sound in the crossover regime between hydrodynamic and collisionless regimes

TL;DR

This paper develops a moment method to analyze collective excitations, including second and first sound, in a Bose-Einstein condensate across the crossover from hydrodynamic to collisionless regimes, revealing mode coupling effects.

Contribution

The study introduces a moment method applied to the Zaremba-Nikuni-Griffin equation, enabling detailed analysis of collective modes in BECs across different regimes, including the crossover.

Findings

Second sound loses density response weight in the crossover regime.

First sound exhibits a broad peak structure in the crossover.

The moment method results agree with Landau two-fluid equations even outside the hydrodynamic regime.

Abstract

We develop the moment method for Bose-Einstein condensates (BECs) at finite temperatures that enable us to study collective sound modes from the hydrodynamic to the collisionless regime. In particular, we investigate collective excitations in a weakly interacting dilute Bose gas by applying the moment method to the Zaremba-Nikuni-Griffin equation, which is the coupled equation of the Boltzmann equation with the generalized Gross-Pitaevskii equation. Utilizing the moment method, collective excitations in the crossover regime between the hydrodynamic and collisionless regimes are investigated in detail. In the crossover regime, the second sound mode loses the weight of the density response function because of the significant coupling with incoherent modes, whereas the first sound shows a distinct but broad peak structure. We compare the result obtained by the moment method with that of the Landau two-fluid equations and show that the collective mode predicted by the Landau two-fluid equations well coincides with the result from the moment method even far from the hydrodynamic regime, whereas clear distinction also emerges in the relatively higher momentum regime.