Time Quasilattices in Dissipative Dynamical Systems

TL;DR

This paper demonstrates the existence of stable time quasilattices in dissipative systems, characterized by two specific tilings of the time axis, and explores their properties, generation, and potential physical realizations.

Contribution

It introduces the concept of time quasilattices as stable trajectories in dissipative systems and identifies the two admissible types, Pell and Clapeyron words, as well as their experimental relevance.

Findings

Existence of two stable time quasilattices: Pell and Clapeyron words.

Systematic periodic approximations to time quasilattices.

Application to various dynamical systems and quantum many-body systems.

Abstract

We establish the existence of `time quasilattices' as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice spanned by two orthogonal directions of time. We show that there are precisely two admissible time quasilattices, which we term the infinite Pell and Clapeyron words, reached by a generalization of the period-doubling cascade. Finite Pell and Clapeyron words of increasing length provide systematic periodic approximations to time quasilattices which can be verified experimentally. The results apply to all systems featuring the universal sequence of periodic windows. We provide examples of discrete-time maps, and periodically-driven continuous-time dynamical systems. We identify quantum many-body systems in which time quasilattices develop rigidity via the interaction of many degrees of freedom, thus constituting dissipative discrete `time quasicrystals'.