Stretched exponential decay of a quasiparticle in a quantum dot

The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: P (t) (-), in accordance with the golden rule. However, the contributions to P (t) accounting for the discreteness of final three-particle states, five-particle states, etc. decay much slower being (₃/) ^nexp-/ (2n+1) for 2n+1 final particles. Here ₃ is the level spacing for three-particle states available via the direct decay. These corrections are dominant at large-enough time and slow down the decay to become ln (P) -t asymptotically. P (t) fluctuates strongly in this regime and the analytical formula for the distribution W (P) is found.