Quantum Localization in Open Chaotic Systems

Abstract

We study a quasi-Floquet state of a $\delta$-kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths $\xi$ of lossy quasi-Floquet states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates $\Gamma$ are dramatically enhanced. We find the relation $\xi \sim {\Gamma }^{-1/2}$ and explain it based upon the finite time diffusion, which can also be applied to a random unitary operator model. We conjecture that this idea is valid for the system exhibiting both the diffusion in classical dynamics and the exponential localization in quantum mechanics.

4 pages, 4 figures

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• Localized Modes in Open One-Dimensional Dissipative Random Systems
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