Critical Phenomena of Dynamical Delocalization in Quantum Anderson Map

TL;DR

This paper investigates the critical phenomena of dynamical delocalization in a quantum Anderson map, revealing how the transition depends on the number of frequency components and identifying key scaling behaviors.

Contribution

It demonstrates the existence of critical phenomena in quantum delocalization depending on frequency components and analyzes the scaling of critical parameters.

Findings

Critical phenomena depend on the number of frequency components M.

Diffusion exponents match theoretical predictions at the transition.

Critical power decreases as epsilon_c ~ (M-1)^{-1}.

Abstract

Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of critical phenomena, which depends on the number of frequency component $M$, is demonstrated. Diffusion exponents agree with theoretical prediction for the transition, but the critical exponent of the localization length deviates from it with increase in the $M$. The critical power $\epsilon_c$ of the normalized perturbation at the transition point remarkably decreases as $\epsilon_c \sim (M-1)^{-1}$.