TY - JOUR

T1 - Frequency Dependence of Quantum Localization in a Periodically Driven System

AU - Machida, Manabu

AU - Saito, Keiji

AU - Miyashita, Seiji

PY - 2002/10

Y1 - 2002/10

N2 - 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 Landau-Zener 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 Landau-Zener picture works for the local transition processes between levels.

AB - 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 Landau-Zener 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 Landau-Zener picture works for the local transition processes between levels.

KW - Quantum chaos

KW - Quantum dynamics

KW - Quantum localization

KW - Random matrix

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U2 - 10.1143/JPSJ.71.2427

DO - 10.1143/JPSJ.71.2427

M3 - Article

AN - SCOPUS:0036972180

VL - 71

SP - 2427

EP - 2433

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 10

ER -