Colloquia

Understanding the combined effects of disorder and interactions in electronic systems has emerged as one of the most challenging theoretical problems in condensed matter physics. It turns out that one can solve this problem non-perturbatively in both disorder and interactions in the regime when the system is finite (as in a quantum dot) but its dimensionless conductance g under open-lead conditions is large. This regime is experimentally interesting for the statistics of Coulomb Blockade in quantum dots and persistent currents in rings threaded by a flux. First some RG work will be described which shows that a disordered quantum dot with Fermi liquid interactions can be in one of two phases; one controlled by the so-called Universal Hamiltonian and another regime where interactions become large. These two are separated in the infinite-g limit by a second-order phase transition. I will show how to solve for the strong-coupling phase, which is characterized by a Fermi surface distortion, by a large-N approximation (where N=g is in fact large for realistic systems). Predictions will be presented for finite but large g for the statistics of the Coulomb Blockade peak spacings and other correlators. Finally, the relationship of these results to puzzles in persistent currents in mesoscopic rings will be presented.