Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

Abstract

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg 1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.

13 pages, no figures

References in corpus (12)

• Theory of Bose-Einstein condensation in trapped gases
• Holonomic Quantum Computation
• Geometric quantum computation with NMR
• Collapse arrest and soliton stabilization in nonlocal nonlinear media
• Dynamics and Berry phase of two-species Bose-Einstein condensates
• Geometric phases of mesoscopic spin in Bose-Einstein condensates
• Chaotic properties of quantum many-body systems in the thermodynamic limit
• The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation
• Long Range Scattering and Modified Wave Operators for some Hartree Type Equations II
• Singular instability of exact stationary solutions of the nonlocal Gross-Pitaevskii equation
• The evolution operator of the Hartree-type equation with a quadratic potential
• Vortices in nonlocal Gross-Pitaevskii equation

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