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 language | English |
|---|---|
| Pages (from-to) | 2793-2817 |
| Number of pages | 25 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 20 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 1 Nov 2015 |
Keywords
- Collective coordinates approach
- Harmonic potential
- Nonlinear Schrödinger equation
- Stochastic partial differential equations
- Vortices
- White noise