One of the most exciting aspectsof the quantum condensed matter physics is the interplay between interactions and disorder. Electrons placed in very small disordered cavities (called quantum dots) exhibit unusual phenomenon called Quantum Chaos. Their energy levels are expected to be distributed not completely randomly but according to special rules called Wigner-Dyson Statistics.
As it turns out interactions among the electrons modifythese rules and open a gap in the energy spectrumcalled the Coulomb gap. The quantum levels aquire awidth and become quasiparticle levels. I am presently interestedin the statistics of the quasiparticle levels, the fluctuatons of the Coulombgap and the dependence of the statistics on the spin properties andthe temperature of the electrons.
Among thetechnical tools I am working with the Random Matrix Theory, Supersymmetryand the Replica methods.