Quasi-Homogeneous Dynamical Structure Factor for Atomic-Trap Bose Condensates

TL;DR

This paper extends the Thomas-Fermi model to describe the dynamical behavior of trapped Bose-Einstein condensates, providing a simple analytical expression for the dynamical structure factor that enhances understanding of scattering properties.

Contribution

It introduces a quasi-homogeneous approximation for the dynamical behavior of trapped Bose-Einstein condensates, extending the static Thomas-Fermi model to include dynamical properties.

Findings

Derived a simple analytical expression for $S(q, \, \omega)$

Provides insights into scattering properties of BECs

Enhances understanding of condensate dynamics in traps

Abstract

The essence of the Thomas-Fermi model is the assumption that the local behavior of a many-body system can be approximated by that of a homogeneous system. In this paper, we present the natural extension of the static Thomas-Fermi treatment of dilute Bose condensates, by describing the dynamical behavior of the condensate in the same quasi-homogeneous approximation. In particular, we calculate the dynamical structure factor $S(q, \omega)$ of a low-temperature condensate, confined in a harmonic oscillator trap. The result is a remarkably simple analytical function, which, with the proper interpretation, gives a powerful and insightful description of the scattering properties of the BEC-system.