Chaos, interactions, and nonequilibrium effects in the tunneling resonance spectra of small metallic particles

We explain the observation of clusters in the tunneling resonance spectra of small metallic particles of few nanometer size. Each cluster of resonances is identified with one excited single--electron state of the metal particle, shifted as a result of the different nonequilibrium occupancy configurations of the other single--electron states. Assuming the underlying classical dynamics of the electrons to be chaotic, we determine the typical shift to be $\Delta/g$ where $g$ is the dimensionless conductance of the grain.