Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation
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 symmetrybreaking, 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.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 San Diego State Univ., San Diego, CA (United States)
 Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Dalhousie Univ., Halifax, Nova Scotia (Canada)
 Publication Date:
 Report Number(s):
 LAUR1429088
Journal ID: ISSN 01672789; PII: S0167278915002596
 Grant/Contract Number:
 DMS1312856; IRSES605096; FA95501210332; 2010239; RGPIN33798; RGPAS/461907; AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Physica. D, Nonlinear Phenomena
 Additional Journal Information:
 Journal Volume: 317; Journal Issue: C; Journal ID: ISSN 01672789
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING; Vortex nucleation; nonlinear Schrodinger equation; GrossPitaevskii equation; BoseEinstein condensates
 OSTI Identifier:
 1259962
 Alternate Identifier(s):
 OSTI ID: 1359740
CarreteroGonzález, R., Kevrekidis, P. G., and Kolokolnikov, T.. Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation. United States: N. p.,
Web. doi:10.1016/j.physd.2015.11.009.
CarreteroGonzález, R., Kevrekidis, P. G., & Kolokolnikov, T.. Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation. United States. doi:10.1016/j.physd.2015.11.009.
CarreteroGonzález, R., Kevrekidis, P. G., and Kolokolnikov, T.. 2016.
"Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation". United States.
doi:10.1016/j.physd.2015.11.009. https://www.osti.gov/servlets/purl/1259962.
@article{osti_1259962,
title = {Vortex nucleation in a dissipative variant of the nonlinear Schrödinger equation under rotation},
author = {CarreteroGonzález, R. and Kevrekidis, P. G. and Kolokolnikov, T.},
abstractNote = {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 μ2/3. 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 symmetrybreaking, 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.},
doi = {10.1016/j.physd.2015.11.009},
journal = {Physica. D, Nonlinear Phenomena},
number = C,
volume = 317,
place = {United States},
year = {2016},
month = {3}
}