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Full-Text Articles in Physical Sciences and Mathematics
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Weakly Nonlinear Analysis Of Vortex Formation In A Dissipative Variant Of The Gross-Pitaevskii Equation, J. C. Tzou, P. G. Kevrekidis, T. Kolokolnikov, R. Carretero-González
Mathematics and Statistics Department Faculty Publication Series
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 …
Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, T Kapitula, Kjh Law, Pg Kevrekidis
Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, T Kapitula, Kjh Law, Pg Kevrekidis
Panos Kevrekidis
In this paper we consider the existence and spectral stability of excited states in two-species Bose–Einstein condensates in the case of a pancake magnetic trap. Each new excited state found in this paper is to leading order a linear combination of two one-species dipoles, each of which is a spectrally stable excited state for one-species condensates. The analysis is done via a Lyapunov–Schmidt reduction and is valid in the limit of weak nonlinear interactions. Some conclusions, however, can be made at this limit which remain true even when the interactions are large.