From localization to anomalous diffusion in the dynamics of coupled kicked rotors

TL;DR

This paper investigates how many-body quantum interference influences the energy dynamics of coupled kicked rotors, revealing a transition from energy saturation to unbounded growth driven by quantum effects.

Contribution

It introduces a detailed analysis of quantum interference effects in coupled kicked rotors, showing a transition from classical ergodic behavior to quantum dynamical delocalization.

Findings

Quantum interference induces unbounded energy growth in the thermodynamic limit.

Classical systems always exhibit linear energy increase, unlike the quantum case.

Quantum effects lead to a power-law increase of energy per site over time.

Abstract

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on a $N$ coupled kicked rotors model: we find that the interplay of quantumness and interactions dramatically modifies the system dynamics inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically, through a mapping onto a $N$-dimensional Anderson model. The thermodynamic limit $N\to\infty$, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: using a mean field approximation we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than one. This wealth of phenomena is a genuine effect of quantum interference: the classical system for $N\geq 2$ always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity/ergodicity properties of a many body driven system.