Level Spacings in Random Matrix Theory and Coulomb Blockade Peaks in Quantum Dots

D. Herman, T. T. Ong, Gonzalo Usaj, H. Mathur, H. U. Baranger

Published 2007-07-11, updated 2008-02-04Version 2

We obtain analytic formulae for the spacing between conductance peaks in the Coulomb blockade regime, based on the universal Hamiltonian model of quantum dots. New random matrix theory results are developed in order to treat correlations between two and three consecutive spacings in the energy level spectrum. These are generalizations of the Wigner surmise for the probability distribution of single level spacing. The analytic formulae are shown to be in good agreement with numerical evaluation.