Alexander Itin, Shinichi Watanabe
(University of Electro-Communications)
Title
Nonlinear dynamics of Bose-Einstein condensates:
nonlinear two-level model with slowly changing parameters
and dynamical stabilization of matter-wave breathers.
Abstract
We consider two problems related to nonlinear dynamics of
Bose-Einstein condensates (BEC). The problem of dynamical
stabilization of BEC by rapidly oscillating scattering
length has been studied before by several methods:
Gaussian variational approximation, the method of moments,
method of modulated Townes soliton, and the direct
averaging of the Gross-Pitaevskii equation. We reconsider
these methods and find serious discrepancy between the
numerically obtained stabilized solution and that assumed
by the theoretical methods. Interesting new features of
stabilized solutions are revealed.
Secondly, we consider nonlinear two-level model with slowly
changing parameters. This problem arise in such systems as
BEC in two asymmetric wells coupled by tunelling,
BEC in an accelerating optical lattice etc. The equations
of motion form a particular example of a Hamiltonian system
with separatrix crossings for which there is a rigorous
averaging technique developed by A.I. Neishtadt . It was
applied previously to several problems in plasma physics,
hydrodynamics, classical mechanics. We apply it to the
nonlinear two-level problem with slowly changing parameters
in the context of BEC dynamics. Nonadiabatic quantum
dynamics can be described in terms of jumps of
corresponding classical action variables for which
general formulas exist.