Frequency Dependence of Quantum Localization in a Periodically Driven System
Abstract
We study the quantum localization phenomena for a random matrix model belonging to the Gaussian orthogonal ensemble (GOE). An oscillating external field is applied on the system. After the transient time evolution, energy is saturated to various values depending on the frequencies. We investigate the frequency dependence of the saturated energy. This dependence cannot be explained by a naive picture of successive independent LandauZener transitions at avoided level crossing points. The effect of quantum interference is essential. We define the number of Floquet states which have large overlap with the initial state, and calculate its frequency dependence. The number of Floquet states shows approximately linear dependence on the frequency, when the frequency is small. Comparing the localization length in Floquet states and that in energy states from the viewpoint of the Anderson localization, we conclude that the LandauZener picture works for the local transition processes between levels.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 October 2002
 DOI:
 10.1143/JPSJ.71.2427
 arXiv:
 arXiv:nlin/0207038
 Bibcode:
 2002JPSJ...71.2427M
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 12 pages and 6 figures