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

TL;DR

This paper systematically derives the distribution of eigenfrequencies for ground state oscillations in a Bose-Einstein condensate within the Thomas-Fermi limit across 1D, 2D, and 3D cases, connecting theory, numerics, and symmetry.

Contribution

It provides a comprehensive derivation of eigenfrequency distributions in the Thomas-Fermi limit for BECs, extending previous work to multiple dimensions and linking with symmetry-based predictions.

Findings

Eigenfrequency distributions are derived for 1D, 2D, and 3D cases.

Connections established with prior theoretical and numerical results.

Invariant frequencies are explained through symmetry principles.

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.