Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time
| Autor: | Romain Poncet, Reika Fukuizumi, Anne de Bouard |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Condensed Matter::Quantum Gases
Physics Applied Mathematics Mathematical analysis Perturbation (astronomy) law.invention Vortex Stochastic partial differential equation symbols.namesake law Quantum mechanics symbols Discrete Mathematics and Combinatorics Initial value problem Remainder Gaussian process Nonlinear Schrödinger equation Bose–Einstein condensate |
| Zdroj: | Discrete and Continuous Dynamical Systems - Series B. 20:2793-2817 |
| ISSN: | 1531-3492 |
| DOI: | 10.3934/dcdsb.2015.20.2793 |
| Popis: | 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 $\epsilon^{-2}$, 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 $\epsilon$ 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. |
| Databáze: | OpenAIRE |
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