Stretched Exponential Decay of a Quasiparticle in a Quantum Dot

Abstract

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: $P(t)\sim \exp(-Γt)$, 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 $\sim (Δ_3/Γ)^n \exp(-Γt/(2n+1))$ for $2n+1$ final particles. Here $Δ_3 \ll Γ$ 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 $\ln (P)\sim -\sqrt{t}$ asymptotically. $P(t)$ fluctuates strongly in this regime and the analytical formula for the distribution $W(P)$ is found.

4 pages, 1 figure