Variational Approach to the Dynamics of Bose-Einstein Condensates.I --Variational Ansatz and Quantum Dynamics--

TL;DR

This paper develops a variational approach incorporating quantum fluctuations to analyze the dynamics of Bose-Einstein condensates, addressing divergence issues in the perturbation series.

Contribution

It introduces a Gaussian variational method that accounts for quantum fluctuations and carefully handles divergences from pair-wise scattering in BEC dynamics.

Findings

Divergences in perturbation series are effectively removed.

Quantum fluctuations are incorporated into the variational framework.

The method improves understanding of BEC dynamics beyond mean-field approximation.

Abstract

Variational method is applied to describe Bose-Einstein condensates (BEC) interacting via a pseudo-potential, taking into account quantum fluctuations around the mean field by the Gaussian approximation. Contributions from the pair-wise scattering by the singular potential should be removed carefully to avoid double countings in the perturbation series in terms of original bare interaction. We show that this procedure removes all dangerous terms which contain divergences.