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

Abstract

The disintegration of quasiparticle in a quantum dot due to the electron interaction is considered. It was predicted recently that above the energy ${\text{eps}}^{\ast }=\Delta (g/\ln g{)}^{1/2}$ 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 ${\text{eps}}^{\ast }$ should depend on the experimental resolution $\delta \text{eps}$. In the broad region of variation of $\delta \text{eps}$ the $\ln g$ should be replaced by $\ln (\Delta /g\delta \text{eps})$. 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 $\text{eps}\sim {\text{eps}}^{\ast }$, but remains finite at $\text{eps}>{\text{eps}}^{\ast }$. The predicted logarithmic distribution of inter-peak spacings may be used for experimental confirmation of the below-Golden-Rule decay.

Comments: 5 pages, REVTEX, 2 eps figures, version accepted for publication in Phys. Rev. Lett