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: $P(t)\sim \exp (-\Gamma t)$, 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.

4 pages, 1 figure

Cited by in corpus (13)

• Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
• Anderson localization on the Cayley tree : multifractal statistics of the transmission at criticality and off criticality
• Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
• Many-body delocalization transition and relaxation in a quantum dot
• Decays in Quantum Hierarchical Models
• Entropy and Its Quantum Thermodynamical Implication for Anomalous Spectral Systems
• Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Quantum decay into a non-flat continuum
• An Exact Solution to the Time-dependent Schrodinger Equation for a Model One-dimensional Potential
• Statistical properties of two-particle transmission at Anderson transition