The Lindblad equation is valid only within a finite time window controlled by the timescales of the bath, the system, and the rotating-wave approximation, with failure at early and late times.
Canturk and H.-P
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abstract
There are some positively divisible non-Markovian processes whose transition matrices satisfy the Chapman-Kolmogorov equation. These processes should also satisfy the Kolmogorov consistency conditions, an essential requirement for a process to be classified as a stochastic process. Combining the Kolmogorov consistency conditions with the Chapman-Kolmogorov equation, we derive a necessary condition for positively divisible stochastic processes on a finite sample space. This necessary condition enables a systematic approach to the manipulation of certain Markov processes in order to obtain a positively divisible non-Markovian process. We illustrate this idea by an example and, in addition, analyze a classic example given by Feller in the light of our approach.
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Is Lindblad for me?
The Lindblad equation is valid only within a finite time window controlled by the timescales of the bath, the system, and the rotating-wave approximation, with failure at early and late times.
- Lecture notes on classical and quantum non-Markovianity