Kinetic theory and dynamic structure factor of a condensate in the random phase approximation

TL;DR

This paper develops a microscopic kinetic theory for a dilute Bose condensate within the generalized random phase approximation, satisfying key physical laws and properties, and uses it to predict the dynamic structure factor at finite temperature and relative motion.

Contribution

It introduces a kinetic theory framework that incorporates superfluidity and conservation laws within the GRPA, enabling calculation of the dynamic structure factor for Bose condensates.

Findings

Predicts the dynamic structure factor spectrum at finite temperature.

Validates the GRPA by comparing with experimental data.

Shows no collisions between condensed and normal atoms in stable conditions.

Abstract

We present the microscopic kinetic theory of a homogeneous dilute Bose condensed gas in the generalized random phase approximation (GRPA), which satisfies the following requirements: 1) the mass, momentum and energy conservation laws; 2) the H-theorem; 3) the superfluidity property and 4) the recovery of the Bogoliubov theory at zero temperature \cite{condenson}. In this approach, the condensate influences the binary collisional process between the two normal atoms, in the sense that their interaction force results from the mediation of a Bogoliubov collective excitation traveling throughout the condensate. Furthermore, as long as the Bose gas is stable, no collision happens between condensed and normal atoms. In this paper, we show how the kinetic theory in the GRPA allows to calculate the dynamic structure factor at finite temperature and when the normal and superfluid are in a relative motion. The obtained spectrum for this factor provides a prediction which, compared to the experimental results, allows to validate the GRPA. PACS numbers:03.75.Hh, 03.75.Kk, 05.30.-d