Hydrodynamic excitations of Bose condensates in anisotropic traps

TL;DR

This paper studies the collective excitations of Bose-Einstein condensates in anisotropic traps, revealing an additional conserved quantity and analyzing the chaotic nature of quasi-particle dynamics.

Contribution

It introduces a new conserved quantity and provides a method to analyze excitations in anisotropic traps using matrix diagonalization.

Findings

Identification of an additional conserved quantity

Wave equation separation in elliptic coordinates

Chaotic quasi-particle dynamics at certain energies

Abstract

The collective excitations of Bose condensates in anisotropic axially symmetric harmonic traps are investigated in the hydrodynamic and Thomas-Fermi limit. We identify an additional conserved quantity, besides the axial angular momentum and the total energy, and separate the wave equation in elliptic coordinates. The solution is reduced to the algebraic problem of diagonalizing finite dimensional matrices. The classical quasi-particle dynamics in the local density approximation for energies of the order of the chemical potential is shown to be chaotic.