Antiresonance and Localization in Quantum Dynamics

Дата и время публикации : 1996-08-13T14:47:31Z

Авторы публикации и институты :
I. Dana
E. Eisenberg
N. Shnerb

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: To appear in Physical Review E. 51 pre-print pages + 9 postscript figures
Первичная категория: cond-mat

Все категории : cond-mat, chao-dyn, nlin.CD, quant-ph

Краткий обзор статьи: The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential localization generally occurs for $eta$ (a scaled $hbar$) in the infinitesimal vicinity of QAR points $eta_0$. The localization length $xi_0$ is determined from the analytical properties of the kicking potential. This “QAR-localization" is associated in some cases with an integrable limit of the corresponding classical systems. The MKR dynamical problem is mapped into pseudorandom tight-binding models, exhibiting dynamical localization (DL). By considering exactly-solvable cases, numerical evidence is given that QAR-localization is an excellent approximation to DL sufficiently close to QAR. The transition from QAR-localization to DL in a semiclassical regime, as $eta$ is varied, is studied. It is shown that this transition takes place via a gradual reduction of the influence of the analyticity of the potential on the analyticity of the eigenstates, as the level of chaos is increased.

Category: Physics