Quasiparticle Lifetime in a Finite System: A Nonperturbative Approach

The problem of electron-electron lifetime in a quantum dot is studied beyond perturbation theory by mapping onto the problem of localization in the Fock space. Localized and delocalized regimes are identified, corresponding to quasiparticle spectral peaks of zero and finite width, respectively. In the localized regime, quasiparticle states are single-particle-like. In the delocalized regime, each eigenstate is a superposition of states with very different quasiparticle content. The transition energy is ${\ensuremath{\epsilon}}_{c}\ensuremath{\simeq}\ensuremath{\Delta}(g/\mathrm{ln}g{)}^{1/2}$, where $\ensuremath{\Delta}$ is mean level spacing, and $g$ is the dimensionless conductance. Near ${\ensuremath{\epsilon}}_{c}$ there is a broad critical region not described by the golden rule.