# Multi-mode description of an interacting Bose-Einstein condensate

Source: [Multi-mode description of an interacting Bose-Einstein condensate](<https://www.sota2.com/research/paper/68fa31a71e209131ce880bac>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T18:59:16.653Z

Authors: K. Goral, M. Gajda, K. Rzazewski

Published: 2000-11-09T17:30:58.000Z

## Abstract

We study the equilibrium dynamics of a weakly interacting Bose-Einstein condensate trapped in a box. In our approach we use a semiclassical approximation similar to the description of a multi-mode laser. In dynamical equations derived from a full N-body quantum Hamiltonian we substitute all creation (and annihilation) operators (of a particle in a given box state) by appropriate c-number amplitudes. The set of nonlinear equations obtained in this way is solved numerically. We show that on the time scale of a few miliseconds the system exhibits relaxation - reaches an equilibrium with populations of different eigenstates fluctuating around their mean values.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0011165>)

[PDF](<https://arxiv.org/pdf/cond-mat/0011165.pdf>)