Quasi-energy spectral series and the Aharonov-Anandan phase for the nonlocal Gross--Pitaevsky equation

2006/12/05 by A. L. Lisok, Lisok, A. L., A. Yu. Trifonov +4
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0612017

17 pages

openalex publication_date 2006/12/05 · arxiv created 2007/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the nonlocal T-periodic Gross-Pitaevsky operator, formal solutions of the Floquet problem asymptotic in small parameter ℏ, ℏ→0, up to O(ℏ^3/2) have been constructed. The quasi-energy spectral series found correspond to the closed phase trajectories of the Hamilton-Ehrenfest system which are stable in the linear approximation. The monodromy operator of this equation has been constructed to within O(ℏ^3/2) in the class of trajectory-concentrated functions. The Aharonov-Anandan phases have been calculated for the quasi-energy states.

Related

• Semiclassical symmetry of the Gross-Pitaevskii equation with quadratic nonlocal Hamiltonian
• Floquet theory and stability for Hamiltonian partial differential equations
• Near invariance of quasi-energy spectrum of Floquet Hamiltonians
• Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential
• A Floquet Operator with Pure Point Spectrum and Energy Instability