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Publication 09-CNA-17

Spectral Stability of Vortices in Two-Dimensional Bose-Einstein Condensates via the Evans Function and Krein Signature

Richard Kollár
Department of Applied Mathematics and Statistics
Faculty of Mathematics, Physics and Informatics
Comenius University
Mlynská dolina
842 48 Bratislava, Slovakia

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Abstract:We investigate spectral stability of vortex solutions of the Gross-Pitaevskii equation, a mean-field approximation for Bose-Einstein condensates (BEC) in an effectively two-dimensional axisymmetric harmonic trap. We study eigenvalues of the linearization both rigorously and through computation of the Evans function, a sensitive and robust technique whose use we justify mathematically. Computational effort is significantly reduced through use of the Krein signature of purely imaginary eigenvalues. In agreement with previous studies in the physical literature we find a singly-quantized vortex spectrally stable while the stability of multi-quantized vortices depends on the diluteness of the condensate, with alternating intervals of stability and instability.

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