Adiabatic theorem for classical stochastic processes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866911805097377792 |
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| author | Takahashi, Kazutaka |
| author_facet | Takahashi, Kazutaka |
| contents | We apply adiabatic theorems developed for quantum mechanics to stochastic annealing processes described by the classical master equation with a time-dependent generator. When the instantaneous stationary state is unique and the minimum decay rate g is nonzero, the time-evolved state is basically relaxed to the instantaneous stationary state. By formulating an asymptotic expansion rigorously, we derive conditions for the annealing time T that the state is close to the instantaneous stationary state. Depending on the time dependence of the generator, typical conditions are written as T> const/g^a with 1<a<2. We also find that a rigorous treatment gives the scaling T>const|ln g|/g^2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16198 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adiabatic theorem for classical stochastic processes Takahashi, Kazutaka Statistical Mechanics We apply adiabatic theorems developed for quantum mechanics to stochastic annealing processes described by the classical master equation with a time-dependent generator. When the instantaneous stationary state is unique and the minimum decay rate g is nonzero, the time-evolved state is basically relaxed to the instantaneous stationary state. By formulating an asymptotic expansion rigorously, we derive conditions for the annealing time T that the state is close to the instantaneous stationary state. Depending on the time dependence of the generator, typical conditions are written as T> const/g^a with 1<a<2. We also find that a rigorous treatment gives the scaling T>const|ln g|/g^2. |
| title | Adiabatic theorem for classical stochastic processes |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2309.16198 |