Generating function for quantum depletion of Bose-Einstein condensates

TL;DR

This paper derives an explicit asymptotic formula for the generating function of quantum depletion in a Bose gas at zero temperature, providing insights into the number of particles outside the condensate.

Contribution

It introduces a new explicit asymptotic formula for the generating function of quantum depletion in Bose-Einstein condensates.

Findings

Derived an explicit asymptotic formula for the generating function.

Proved an upper bound for the tails of quantum depletion.

Enhanced understanding of particle distribution outside the condensate.

Abstract

We consider a Bose gas on the unit torus at zero temperature in the Gross-Pitaevskii regime, known to perform Bose-Einstein condensation: a macroscopic fraction of the bosons occupy the same quantum state, called condensate. We study the Bose gas' quantum depletion, that is the number of bosons outside the condensate, and derive an explicit asymptotic formula of its generating function. Moreover, we prove an upper bound for the tails of the quantum depletion.