Effective Action and Field Equation for BEC from Weak to Strong Couplings

TL;DR

This paper develops an effective action framework for Bose-Einstein condensates that extends from weak to strong coupling regimes, revealing a transition from Schrödinger to fractional dynamics with Levy walk behavior.

Contribution

It introduces a double-fractional generalization of the Schrödinger equation to describe strong coupling effects in BECs, extending beyond the traditional Gross-Pitaevskii approach.

Findings

Effective action captures strong coupling physics.

Particle trajectories follow Levy walks in the strong coupling limit.

Generalization bridges weak and strong interaction regimes.

Abstract

While free and weakly interacting nonrelativistic particles are described by a Gross-Pitaevskii equation, which is a nonlinear self-interacting Schr\"odinger equation, the phenomena in the strong- coupling limit are governed by an effective action that is extremized by a double-fractional generalization of this equation. Its particle orbits perform L\`evy walks rather than Gaussian random walks.