Time crystalline solitons and their stochastic dynamics in a driven-dissipative \phi^4 model

TL;DR

This paper introduces a novel time-crystalline soliton state in a driven-dissipative  model, revealing unique symmetry-breaking dynamics, stochastic behavior, and deconfined soliton interactions far from equilibrium.

Contribution

It reports the discovery of time-crystalline solitons in a driven-dissipative  model, highlighting their stochastic dynamics and contrasting behavior with previously known confined monopoles.

Findings

Soliton pattern oscillates between kink and anti-kink configurations.

Soliton random walk induces phase transitions between  symmetry-breaking states.

Soliton annihilation time scales as a power law with initial separation.

Abstract

Periodically driven systems provide unique opportunities to investigate the dynamics of topological excitations far from equilibrium. In this paper, we report a time-crystalline soliton (TCS) state in a driven-dissipative $\phi^4$ model. This state exhibits spontaneous breaking of discrete time-translational symmetry while simultaneously displaying spatial soliton behavior. During time evolution, the soliton pattern periodically oscillates between kink and anti-kink configurations. We further study TCS dynamics under noise, demonstrating that soliton random walk can induce a dynamical transition between two distinct $Z_2$ symmetry-breaking time-crystalline phases in time domain. Finally, we examine the annihilation of two spatially separated TCSs under noise. Importantly, in contrast to the confined behavior of time-crystalline monopoles reported in [Phys. Rev. Lett. 131, 056502 (2023)], the dynamics of time-crystalline solitons is deconfined despite the nonequilibrium nature of our model: the statistically averaged annihilation time scales as a power law with the solitons' initial separation.