Long-range s-wave interactions in Bose-Einstein Condensates: An exact correspondence between truncated free energy and dynamics

TL;DR

This paper establishes an exact correspondence between the corrected free energy functional and the dynamics in Bose-Einstein Condensates with non-local s-wave interactions, enabling advanced perturbative studies beyond traditional models.

Contribution

It proves an exact link between free energy corrections and dynamics in BECs with non-local interactions, extending analysis beyond the Fermi pseudopotential.

Findings

Exact correspondence between free energy and dynamics for non-local interactions

Allows perturbative analysis beyond traditional models

Provides a framework for studying higher-order corrections

Abstract

We consider the Gross-Pitaevskii(GP) model of a Bose-Einstein Condensate(BEC) with non-local s-wave interactions. The non-locality is represented by corrections to the local GP equation. Due to such corrections to the GP equation, there arise corrections to the free energy functional as well. We present here a proof of the exact correspondence between the free energy and the dynamics for typical terms appearing while considering corrections to the GP equation at any order. This non-trivial correspondence can be used to study BECs perturbatively while going beyond the Fermi pseudopotential.