Irrational mode locking in quasiperiodic systems

TL;DR

This paper demonstrates that ac-driven quasiperiodic systems can exhibit stable irrational mode locking, with numerical evidence showing convergence and robustness to noise, expanding understanding of nonlinear dynamical behaviors.

Contribution

It introduces a model showing stable irrational mode locking in quasiperiodic systems, supported by detailed numerical analysis and discussion of experimental implications.

Findings

Irrational mode locking occurs in quasiperiodic driven systems.

Mode locking remains stable under small thermal noise and disorder.

Numerical evidence confirms convergence in large systems.

Abstract

A model for ac-driven systems, based on the Tang-Wiesenfeld-Bak-Coppersmith-Littlewood automaton for an elastic medium, exhibits mode-locked steps with frequencies that are irrational multiples of the drive frequency, when the pinning is spatially quasiperiodic. Detailed numerical evidence is presented for the large-system-size convergence of such a mode-locked step. The irrational mode locking is stable to small thermal noise and weak disorder. Continuous time models with irrational mode locking and possible experimental realizations are discussed.