Nonequilibrium Effects in the Tunneling Conductance Spectra of Small Metallic Particles

Trace formulae and the non-linear supersymmetric σ-model are basic analytical tools used successfully in the fields of quantum chaos and disordered systems. Both are designed to treat systems with a small number of degrees of freedom. Hence they are limited in their possibility of analyzing many-body systems where interparticle interactions play an important role, and the number of degrees of freedom is large. On the other hand, many experimental studies of quantum chaos use systems which consist in a large number of interacting particles, for example quantum dots or disordered metallic particles. Having an elaborate single-particle description of these systems, it is of prominent importance to understand the role of interactions, the range of applicability of a single-particle picture, and the interplay between chaos and interparticle interactions. In this respect, an important observation is that strong chaotic dynamics, on the level of non-interacting single-particle description, provides us with the possibility of analyzing interacting many-body systems by a systematic perturbative approach. The small parameter of this perturbation theory is 1/g, where g = tH/tc is the dimensionless conductance, i.e. the ratio of the Heisenberg time, tH (the inverse mean level spacing), to the classical relaxation time, tc. The general form of the interaction Hamiltonian in which particles interact via a two-body potential U(r, r) is