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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 …
Dark-Bright Solitons And Vortices In Bose-Einstein Condensates, Dong Yan
Dark-Bright Solitons And Vortices In Bose-Einstein Condensates, Dong Yan
Doctoral Dissertations
This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrodinger equation, the so-called Gross-Pitaevskii (GP) equation, which is a mean-field description of BECs. The systematic analysis begins by considering the dark-bright (DB)-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component BECs. The interaction between two DB solitons in a homogeneous condensate and at the presence of the trap are both considered. Our analytical approximation relies in a Hamiltonian perturbation theory, which leads to an equation of motion of the centers of DB-soliton interacting pairs. Employing this equation, we demonstrate the …
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.
Collisionally Inhomogeneous Bose-Einstein Condensates In Double-Well Potentials, C Wang, Pg Kevrekidis, N Whitaker, Dj Frantzeskakis, S Middelkamp, P Schmelcher
Collisionally Inhomogeneous Bose-Einstein Condensates In Double-Well Potentials, C Wang, Pg Kevrekidis, N Whitaker, Dj Frantzeskakis, S Middelkamp, P Schmelcher
Mathematics and Statistics Department Faculty Publication Series
In this work, we consider quasi-one-dimensional Bose–Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double-well potentials. In particular, we study a setup in which such a “collisionally inhomogeneous” BEC has the same (attractive–attractive or repulsive–repulsive) or different (attractive–repulsive) types of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the non-interacting (linear) limit into their nonlinear counterparts. The collisional inhomogeneity produces a saddle–node bifurcation scenario between two additional solution branches; as the inhomogeneity becomes stronger, the turning point of the saddle–node tends to infinity and eventually only …