P.G. Kevrekidis and D.E. Pelinovsky

Distribution of eigenfrequencies for oscillations of the ground state in the Thomas-Fermi limit

Physical Review A 81, 023627 (5 pages) (2010)

Abstract:
In this work, we present a systematic derivation of the distribution of eigenfrequencies for oscillations of the ground state of a repulsive Bose-Einstein condensate in the semi-classical (Thomas-Fermi) limit. Our calculations are performed in 1-, 2- and 3-dimensional settings. Connections with the earlier work of Stringari, with numerical computations, and with theoretical expectations for invariant frequencies based on symmetry principles are also given.

Keywords:
Gross-Pitaevskii equation, ground states, stability and eigenfrequencies, semi-classical limit, Thomas-Fermi approximation