Quasi-particle excitations and dynamical structure function of trapped Bose-condensates in the WKB approximation

TL;DR

This paper uses the WKB approximation to analyze quasi-particle excitations in trapped Bose-condensates, deriving energy spectra and structure functions relevant for experimental observations.

Contribution

It introduces a WKB-based method to solve Bogoliubov equations for trapped Bose-condensates, providing a new approach to calculate excitation energies and structure functions.

Findings

Discrete quasi-particle energies determined

Dynamic structure function peaks calculated

Method applicable to experimental light-scattering data

Abstract

The Bogoliubov equations of the quasi-particle excitations in a weakly interacting trapped Bose-condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasi-particle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasi-particle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function which can be observed by off-resonance inelastic light-scattering.