Observation of prethermalization in weakly nonintegrable unitary maps
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912187738488832 |
|---|---|
| author | Zhang, Xiaodong Lando, Gabriel M. Dietz, Barbara Flach, Sergej |
| author_facet | Zhang, Xiaodong Lando, Gabriel M. Dietz, Barbara Flach, Sergej |
| contents | We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $Λ(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for different initial conditions and compute the mean $μ(t)$ and standard deviation $σ(t)$ of $Λ(t)$. Thermalization implies a temporal decay $σ\sim t^{-1/2}$ at a converged finite value of $μ$. We report prethermalization plateaus that persist for long times where both $μ$ and $σ$ appear to have converged to finite values, seemingly implying differing saturated Lyapunov exponent values for different trajectories. The lifetime of such plateaus furnishes a novel time scale characterizing the thermalization dynamics of many-body systems close to integrability. We also find that the plateaus converge to their respective thermal values for long enough times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Observation of prethermalization in weakly nonintegrable unitary maps Zhang, Xiaodong Lando, Gabriel M. Dietz, Barbara Flach, Sergej Chaotic Dynamics Statistical Mechanics We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $Λ(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for different initial conditions and compute the mean $μ(t)$ and standard deviation $σ(t)$ of $Λ(t)$. Thermalization implies a temporal decay $σ\sim t^{-1/2}$ at a converged finite value of $μ$. We report prethermalization plateaus that persist for long times where both $μ$ and $σ$ appear to have converged to finite values, seemingly implying differing saturated Lyapunov exponent values for different trajectories. The lifetime of such plateaus furnishes a novel time scale characterizing the thermalization dynamics of many-body systems close to integrability. We also find that the plateaus converge to their respective thermal values for long enough times. |
| title | Observation of prethermalization in weakly nonintegrable unitary maps |
| topic | Chaotic Dynamics Statistical Mechanics |
| url | https://arxiv.org/abs/2501.07956 |