Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution

TL;DR

This paper investigates how the energy resolution of experiments affects the observed decay of quasiparticles in quantum dots, challenging previous predictions of a sharp transition and suggesting a continuous growth of satellite peaks.

Contribution

It introduces a correction to the predicted quasiparticle decay energy considering experimental resolution and argues against a delocalization transition in Fock space.

Findings

Observed decay energy depends on experimental resolution.

Satellite peaks grow continuously with energy, not abruptly.

Logarithmic distribution of inter-peak spacings predicted.

Abstract

The disintegration of quasiparticle in a quantum dot due to the electron interaction is considered. It was predicted recently that above the energy $\eps^{*} = \Delta(g/\ln g)^{1/2}$ each one particle peak in the spectrum is split into many components ($\Delta$ and $g$ are the one particle level spacing and conductance). We show that the observed value of $\eps^{*}$ should depend on the experimental resolution $\delta \eps$. In the broad region of variation of $\delta \eps$ the $\ln g$ should be replaced by $\ln(\Delta/ g\delta \eps)$. We also give the arguments against the delocalization transition in the Fock space. Most likely the number of satellite peaks grows continuously with energy, being $\sim 1$ at $\eps \sim \eps^{*}$, but remains finite at $\eps > \eps^{*}$. The predicted logarithmic distribution of inter-peak spacings may be used for experimental confirmation of the below-Golden-Rule decay.