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Stretched Exponential Decay of a Quasiparticle in a Quantum Dot | P.G.Silvestrov
; | Date: |
9 Mar 2001 | Journal: | Phys. Rev. B 64, 113309 (2001) | Subject: | Mesoscopic Systems and Quantum Hall Effect | cond-mat.mes-hall | 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: $P(t)sim exp(-Gamma t)$, 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 $sim (Delta_3/Gamma)^n exp(-Gamma t/(2n+1))$ for $2n+1$ final particles. Here $Delta_3 ll Gamma$ 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. | Source: | arXiv, cond-mat/0103222 | Services: | Forum | Review | PDF | Favorites |
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