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arXiv:nlin/0410040

Tunneling of Bose-Einstein condensates and nonlinear models with separatrix crossings

A. P. Itin

Published Oct 20, 2004• 0 citations
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Abstract

This paper has been withdrawn by the author. Instead, more comprehensive and accurate works are placed in: 1) cond-mat/0610767: Universality in nonadiabatic behaviour of classical actions in nonlinear models with separatrix crossings, to appear in Phys.Rev.E; and 2) nlin/0611007: Change in the adiabatic invariant in a nonlinear two-mode model of Feshbach resonance passage, to appear in Physica D

DOI
10.48550/arxiv.nlin/0410040

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This paper has been withdrawn by the author. Instead, more comprehensive and accurate works are placed in: 1) cond-mat/0610767: Universality in nonadiabatic behaviour of classical actions in nonlinear models with separatrix crossings, to appear in Phys.Rev.E; and 2) nlin/0611007: Change in the adiabatic invariant in a nonlinear two-mode model of Feshbach resonance passage, to appear in Physica D
We discuss the dynamics of approximate adiabatic invariants in several nonlinear models being related to the physics of Bose-Einstein condensates (BECs). We show that the nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunneling, and BEC tunneling oscillations in a double well can be considered within a unifying approach based on the theory of separatrix crossings. The separatrix crossing theory was applied previously to some problems of classical mechanics, plasma physics, and hydrodynamics, but has not been used in the rapidly growing BEC-related field yet. We derive explicit formulas for the change in the action in several models. Extensive numerical calculations support the theory and demonstrate its universal character. We also discovered a nonlinear phenomenon in the NLZ model which we propose to call separated adiabatic tunneling.