Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation

Journal Article · Tue Mar 01 00:00:00 EST 2016 · Physica. D, Nonlinear Phenomena

DOI:https://doi.org/10.1016/j.physd.2015.11.009· OSTI ID:1259962

Carretero-González, R. ^[1]; Kevrekidis, P. G. ^[2]; Kolokolnikov, T. ^[3]

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1. San Diego State Univ., San Diego, CA (United States)
2. Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
3. Dalhousie Univ., Halifax, Nova Scotia (Canada)

In this work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential μ of the system, increasing proportionally to μ^2/3. The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We show how these unstable modes typically nucleate a large number of vortices in the periphery of the atomic cloud. However, through a pattern selection mechanism, prompted by symmetry-breaking, only few isolated vortices are pulled in sequentially from the periphery towards the bulk of the cloud resulting in highly symmetric stable vortex configurations with far fewer vortices than the original unstable mode. We conclude that these results may be of relevance to the experimentally tractable realm of finite temperature atomic condensates.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: DMS-1312856; IRSES-605096; FA9550-12-10332; 2010239; RGPIN-33798; RGPAS/461907; AC52-06NA25396
• OSTI ID: 1259962
• Alternate ID(s): OSTI ID: 1359740
• Report Number(s): LA-UR-14-29088; PII: S0167278915002596
• Journal Information: Physica. D, Nonlinear Phenomena, Vol. 317, Issue C; ISSN 0167-2789
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
97 MATHEMATICS AND COMPUTING
Vortex nucleation
nonlinear Schrodinger equation
Gross-Pitaevskii equation
Bose-Einstein condensates