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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2309.16198 |
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- 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.