Markov approximation techniques

The RC is an ideal system to test theoretical ideas (memory effect, coherence effect, etc.), fundamental approximations (isolated line approximation, Markov approximation, etc.), and techniques (generalized linear response theory, Forster-Dexter theory, Marcus theory, etc.) for treating ultrafast phenomena. As mentioned above, this ideality is mainly due to the fact that the electronic energy level spacing in RC is small (typically from 200 to 1500 cm-1), and the interactions between these electronic states are weak. 

Various methods have been developed that interpolate between the coherent and incoherent regimes (for reviews see, e.g. (3)-(5)). Well-known approaches use the stochastic Liouville equation, of which the Haken-Strobl-Reineker (3) model is an example, and the generalized master equation (4). A powerful technique, which in principle deals with all aspects of the problem, uses the reduced density matrix of the exciton subsystem, which is obtained by projecting out all degrees of freedom (the bath) from the total statistical operator (6). This reduced density operator obeys a closed non-Markovian (integrodifferential) equation with a memory kernel that includes the effects of (multiple) interactions between the excitons and the bath. In practice, one is often forced to truncate this kernel at the level of two interactions. In the Markov approximation, the resulting description is known as Redfield theory (7). 

In many ways modeling the repair process is difficult because the repair process is quite different from the failure process. Random failures are due to a stochastic process and most of our modeling techniques were created for these stochastic processes. Certain aspects of the repair process are deterministic. Other aspects of the repair process are stochastic. Fortunately, we can approximate the repair process more accurately with Markov models than most other techniques. 

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