Time-dependent quantum weak values: Decay law for postselected states

Weak measurements offer insights into the behavior of quantum systems. Combined with postselection, quantum mechanics predicts a range of experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent preselected and postselected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of postselection and the choice of final state. The generalized law is illustrated for two interesting choices of postselection.

Figure 1

(Color online) Comparison of the standard exponential decay law [upper curve, given by Eq. (45)] and the weak decay law [lower curve, given by Eq. (55)].