Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: Application to the classical-like dynamics of quantum accelerator modes

2003/10/31 by R. Bach, Radka Bach, K. Burnett +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #nlin.CD #physics.atom-ph #physics.gen-ph

paper · pdf · doi:10.1103/physreva.71.033417

published as Phys. Rev. A 71, 033417 (2005) · 20 pages, 4 figures. Very substantially revised and expanded version

arxiv created 2004/12/14 · openalex publication_date 2005/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining solutions, which are stable when constrained to remain pure-state Gaussian wave packets, and then propagating them using a cumulant-based formalism. Using this methodology, we study the relative longevity, under different parameter regimes, of quantum accelerator modes. Within this attractively simple formalism, we are able to obtain good qualitative agreement with exact wave-function dynamics.

Citations

• Quantum resonances and decoherence for -kicked atoms
• Gravity-Sensitive Quantum Dynamics in Cold Atoms
• Classical Scaling Theory of Quantum Resonances

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