Signatures of Classical Diffusion in Quantum Fluctuations of 2D Chaotic Systems

Abstract

We consider a two-dimensional (2D) generalization of the standard kicked-rotor (KR) and show that it is an excellent model for the study of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution of wavefunction intensities and compare them with the predictions derived in the framework of diffusive {\it disordered} samples. Next, we turn the closed system into an open one by constructing a scattering matrix. The distribution of the resonance widths $\mathcal{P}(\Gamma )$ and Wigner delay times $\mathcal{P}({\tau }_W)$ are investigated. The forms of these distributions are obtained for different symmetry classes and the traces of classical diffusive dynamics are identified. Our theoretical arguments are supported by extensive numerical calculations.

arXiv comment20 pages; 12 figures

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• Distribution of the local density of states, reflection coefficient and Wigner delay time in absorbing ergodic systems at the point of chiral symmetry
• Weak localization of the open kicked rotator
• The statistics of Wigner delay time in Anderson disordered systems
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