Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross-Pitaevskii Equation

Autor:	Tzou, Justin C., Kevrekidis, Panayotis G., Kolokolnikov, Theodore, Carretero-Gonzalez, Ricardo
Rok vydání:	2015
Předmět:	Condensed Matter - Quantum Gases Nonlinear Sciences - Pattern Formation and Solitons 35Q55 76M23 76A25
Druh dokumentu:	Working Paper
Popis:	For a dissipative variant of the two-dimensional Gross-Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas-Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one-dimensional amplitude equation that describes the slow evolution of the envelope of the initial instability. We show that the mechanism responsible for initiating vortex formation is a modulational instability of the amplitude equation. We also illustrate the role of dissipation in the symmetry breaking process. All analyses are confirmed by detailed numerical computations. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1509.02998 Zobrazit plný text záznamu View this record from Arxiv