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

We explain the observation of clusters in the tunneling resonance spectra of ultrasmall metallic particles of a 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 Δ/g where Δ is the single particle mean level spacing and g is the dimensionless conductance of the grain.