Statistics of Hartree-Fock Levels in Small Disordered Systems

摘要: We study the statistics of quasiparticle and quasihole levels in small interacting disordered systems within Hartree-Fock approximation. The distribution inverse compressibility, given according to Koopmans' theorem by distance between two across Fermi energy, evolves from a Wigner noninteracting limit shifted Gaussian for strong interactions. On other hand, nature spacings neighboring on same side energy (corresponding differences excited states system with one missing or extra electron) is not affected interaction follows Wigner-Dyson statistics. These results are derived analytically isolating solving appropriate equations levels. They substantiated numerical simulations full set quantum dot Coulomb find enhanced fluctuations compressibility compared prediction random matrix theory, possibly due localization wave functions around edge dot. calculated discrete second derivative respect number particles ground state deviates level spacing energy. distributions have similar shapes but each other. deviation increases strength thus indicating breakdown strongly limit.