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 of the phenomenon of dynamical localization in a class of quasi-periodically and periodically time-dependent two-level systems. Our results are based on a sort of `renormalization' procedure, which is developed here in a systematic way in order to adapt it to the case of dynamical localization. In the quasi-periodic case this procedure leads to a formal perturbative expansion free of secular terms. In the periodic case a convergent perturbative solution is obtained and, in particular, a convergent perturbative expansion for the secular frequency is presented. The case of ac-dc fields is discussed in some detail, leading to the conclusion that the phenomenon of dynamical localization is not exact in that situation.''