Vortex solutions in bose-Einstein condensation under a trapping potential varying randomly in time

Anne De Bouard, Reika Fukuizumi, Romain Poncet, Björn Schmalfuß

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this paper is to perform a theoretical and numerical study on the dynamics of vortices in Bose-Einstein condensation in the case where the trapping potential varies randomly in time. We take a deterministic vortex solution as an initial condition for the stochastically fluctuated Gross-Pitaevskii equation, and we observe the influence of the stochastic perturbation on the evolution. We theoretically prove that up to times of the order of ε-2, the solution having the same symmetry properties as the vortex decomposes into the sum of a randomly modulated vortex solution and a small remainder, and we derive the equations for the modulation parameter. In addition, we show that the first order of the remainder, as ε goes to zero, converges to a Gaussian process. Finally, some numerical simulations on the dynamics of the vortex solution in the presence of noise are presented.

Original languageEnglish
Pages (from-to)2793-2817
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume20
Issue number9
DOIs
Publication statusPublished - 2015 Nov 1

Keywords

  • Collective coordinates approach
  • Harmonic potential
  • Nonlinear Schrödinger equation
  • Stochastic partial differential equations
  • Vortices
  • White noise

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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