The first passage time in quantum dynamics

The concept of the first passage (FPT) time is shown to offer a meaningful extension to quantum dynamics, providing a framework within which a vast class of quantum phenomena can be described as processes unfolding in real, rather than complex time. The Fokker – Planck and Kolmogorov’s backward equations for the quantum probability density permit a closed-form definition of the quantum FPT, allowing all its moments to be found by a repeated inversion of a non-Hermitian operator serving as a generator of Kolmogorov’s backward equation. The first moment of the quantum FPT can be expressed, in close analogy with classical passage times, as a ratio of the distance to the effective speed. In respective approximations, the quantum FPT is shown to recover the key time scales of quantum dynamics, including the free-particle propagation time, tunneling rates, the lifetime of quasi-stationary states, and the period of tunneling-induced oscillatory dynamics of superposition states in a bistable potential.