학술논문
Perturbative analysis of dynamical localization.
Document Type
Journal
Author
Barata, J. C. A. (BR-SPL-P) AMS Author Profile; Cortez, D. A. (BR-SPL-P) AMS Author Profile
Source
Subject
81 Quantum theory -- 81Q General mathematical topics and methods in quantum theory
81Q15Perturbation theories for operators and differential equations
81Q15
Language
English
Abstract
Summary: ``In this paper we present a mathematical investigation ofthe phenomenon of dynamical localization in a class ofquasi-periodically and periodically time-dependent two-levelsystems. Our results are based on a sort of `renormalization'procedure, which is developed here in a systematic way in order toadapt it to the case of dynamical localization. In the quasi-periodiccase this procedure leads to a formal perturbative expansion free ofsecular terms. In the periodic case a convergent perturbative solutionis obtained and, in particular, a convergent perturbative expansionfor the secular frequency is presented. The case of ac-dc fields isdiscussed in some detail, leading to the conclusion that thephenomenon of dynamical localization is not exact in that situation.''