Stability and pre-thermalization in chains of classical kicked rotors

TL;DR

This paper investigates how to prevent heating in periodically driven classical systems, specifically chains of kicked rotors, by identifying conditions for stability and marginal localization that lead to slow or negligible energy absorption.

Contribution

It introduces two regimes—linear stability and marginal localization—in classical kicked rotor chains where heating is minimized, with universal scaling laws characterizing different dynamical phases.

Findings

Heating can be arbitrarily suppressed near fixed points and at high drive frequencies.

Universal scaling laws distinguish localized, diffusive, and sub-diffusive regimes.

Marginal localization shares features with quantum pre-thermalization without requiring quantum coherence.

Abstract

Periodic drives are a common tool to control physical systems, but have a limited applicability because time-dependent drives generically lead to heating. How to prevent the heating is a fundamental question with important practical implications. We address this question by analyzing a chain of coupled kicked rotors, and find two situations in which the heating rate can be arbitrarily small: (i) linear stability, for initial conditions close to a fixed point, and (ii) marginal localization, for drives with large frequencies and small amplitudes. In both cases, we find that the dynamics shows universal scaling laws that allow us to distinguish localized, diffusive, and sub-diffusive regimes. The marginally localized phase has common traits with recently discovered pre-thermalized phases of many-body quantum-Hamiltonian systems, but does not require quantum coherence.