Time crystalline solitons and their stochastic dynamics in a driven-dissipative ϕ^4 model
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918243973726208 |
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| author | Luo, Xingdong Chen, Zhizhen |
| author_facet | Luo, Xingdong Chen, Zhizhen |
| contents | 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 $ϕ^4$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time crystalline solitons and their stochastic dynamics in a driven-dissipative ϕ^4 model Luo, Xingdong Chen, Zhizhen Statistical Mechanics Computational Physics 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 $ϕ^4$ 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. |
| title | Time crystalline solitons and their stochastic dynamics in a driven-dissipative ϕ^4 model |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2510.19587 |