Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach

TL;DR

This paper investigates electron-electron quasiparticle lifetimes in quantum dots beyond perturbation theory, revealing a transition between localized and delocalized regimes with multifractal states near the critical energy.

Contribution

It introduces a non-perturbative approach by mapping the problem onto localization in Fock space, identifying a transition between localized and delocalized quasiparticle states.

Findings

Identifies a transition energy scale at $ msimeq riangle(g/ mlog g)^{1/2}$.

Describes a broad critical region with multifractal states.

Distinguishes between localized and delocalized quasiparticle regimes.

Abstract

The problem of electron--electron lifetime in a quantum dot is studied beyond perturbation theory by mapping it onto the problem of localization in the Fock space. We identify two regimes, localized and delocalized, corresponding to quasiparticle spectral peaks of zero and finite width, respectively. In the localized regime, quasiparticle states are very close to single particle excitations. In the delocalized state, each eigenstate is a superposition of states with very different quasiparticle content. A transition between the two regimes occurs at the energy $\simeq\Delta(g/\ln g)^{1/2}$, where $\Delta$ is the one particle level spacing, and $g$ is the dimensionless conductance. Near this energy there is a broad critical region in which the states are multifractal, and are not described by the Golden Rule.