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

TL;DR

This paper explores how classical diffusion influences quantum fluctuations in a 2D chaotic system, revealing signatures in wavefunction intensities, resonance widths, and delay times through theoretical analysis and numerical simulations.

Contribution

It introduces a 2D kicked-rotor model to study quantum diffusion signatures and compares quantum distributions with classical diffusive predictions, extending understanding of quantum chaos.

Findings

Wavefunction intensity distributions match diffusive disordered sample predictions.

Resonance width and delay time distributions reflect classical diffusive dynamics.

Classical diffusion signatures are identified in quantum scattering properties.

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 ${\cal P}(\Gamma)$ and Wigner delay times ${\cal P}(\tau_W)$ 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.