Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

TL;DR

This paper derives an integral equation for inhomogeneous condensed bosons that generalizes the Gross-Pitaevskii differential equation, avoiding restrictive assumptions like the Thomas-Fermi approximation.

Contribution

It introduces a less restrictive integral equation for inhomogeneous bosons, extending the Gross-Pitaevskii framework beyond previous differential equation approaches.

Findings

Derivation of an integral equation for inhomogeneous bosons

Avoids assumptions like Thomas-Fermi approximation

Generalizes the Gross-Pitaevskii equation

Abstract

We give here the derivation of a Gross-Pitaevskii--type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided.