25pYE-3 Nonlinear dynamics of trapped Bose-Einstein condensates and nonlinear systems with separatrix crossings

Yeong E. Kim, Alexander L. Zubarev

A. P. Itin, Shinichi Watanabe

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.

Chuanwei Zhang

A. P. Itin

This paper has been withdrawn by the author.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

Grant Leonard Salmond

Qi Zhang, Peter Hänggi A, Jiangbin Gong

A two-mode Bose-Einstein condensate coupled by a high-frequency modulation field is found to display rich features. An effective stationary Hamiltonian approach reveals the emergence of additional degenerate eigenstates as well as additional topological structures of the spectrum. Possible applications, such as the suppression of nonlinear Landau-Zener tunneling, are discussed. An interesting phenomenon, which we call ``deterministic symmetry-breaking trapping'' associated with separatrix crossing, is also found in an adiabatic process.