Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitevskii Breather

TL;DR

This paper investigates quantum fluctuations in the relative velocity of solitons within a Bose-Einstein condensate breather, using quantum Monte Carlo simulations and analytical Bogoliubov approximation, with results showing good agreement.

Contribution

It introduces a combined approach of quantum Monte Carlo and analytical methods to study quantum fluctuations in soliton dynamics within a trapped Bose-Einstein condensate.

Findings

Quantum fluctuations are effectively monitored via two-body correlation functions.

Quantum Monte Carlo results agree well with Bogoliubov approximation predictions.

The study enhances understanding of quantum effects in soliton interactions.

Abstract

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored,indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculations, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.