Kibble-Zurek mechanism in driven underdamped Brownian motion
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929610588946432 |
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| author | Nazé, Pierre |
| author_facet | Nazé, Pierre |
| contents | Kibble-Zurek mechanism is widely known to appear in the transverse-field quantum Ising chain in the thermodynamic limit at zero temperature, having notorious characteristics, like the divergence of its relaxation time. In this work, I present the same effect in a simple system, the driven underdamped Brownian motion. Using linear response theory, I show the appropriate limits where the Kibble-Zurek mechanism happens. The divergence of the relaxation time, the high-temperature condition in the initial thermal equilibrium state, a new Kibble-Zurek scaling at sudden processes, and the pausing effect in the optimal protocol are presented as consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kibble-Zurek mechanism in driven underdamped Brownian motion Nazé, Pierre Statistical Mechanics Kibble-Zurek mechanism is widely known to appear in the transverse-field quantum Ising chain in the thermodynamic limit at zero temperature, having notorious characteristics, like the divergence of its relaxation time. In this work, I present the same effect in a simple system, the driven underdamped Brownian motion. Using linear response theory, I show the appropriate limits where the Kibble-Zurek mechanism happens. The divergence of the relaxation time, the high-temperature condition in the initial thermal equilibrium state, a new Kibble-Zurek scaling at sudden processes, and the pausing effect in the optimal protocol are presented as consequences. |
| title | Kibble-Zurek mechanism in driven underdamped Brownian motion |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2412.01436 |