Mean First-passage Time In Quantum Mechanics

In this paper, we consider the problem of mean first-passage time(MFPT) in quantummechanics. This problem was first considered for the random walk process in statisticalmechanics, which is the average time for the walker to reach a given final site for the firsttime assuming that the walker started at a given initial site at time t=0. The approach ofmaster equation in statistical mechanics can solve this problem. In recently years, thereare many researches on the calculations and also the applications of the MFPT. Theconception of MFPT rapidly extends to ordinary Markov process and then toNon-Markov process. At present, the study and application of MFPT have reached allbranches of morden science. In quantum mechanics, however, the problem of meanfirst-passage time has not been considered so sufficiently. Similarly, the MFPT inquantum mechanics is the average time for the quantum system to transite to some givenfinal state for the first time assuming that the system started from a given initial state attime t=0.Firstly, we introduce some main results and application about MFPT. Then weillustrate our problem detailed and give the approach we use. We give some examplesand applications. Furthermore, we point out the associations and differences between theMFPT and the life time of a state. In another view of point, we consider the effect ofdisturb levels to the transition time.