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

The disintegration of a single particle excitation 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 splited into many components. We show that the observed value of $\eps^{*}$ should strongly depend on the experimental resolution $\delta \eps$. If the accuracy allows us to resolve the three-particle excitations, but not five-particle ones, the $\ln g$ should be replaced by $\ln(\Delta/ g\delta \eps)$. Another problem considered is: Do the exact eigenfunctions undergo the localization-delocalization transition in the Fock space at $\eps \sim \eps^{*}$? Most likely there is no delocalization there. The number of splited peaks grows continuously with energy. At $\eps \sim \eps^{*}$ each peak gets about one satellite, but at $\eps > \eps^{*}$ the number of satellites remains finite.