Universal Features of Interacting Chaotic Quantum Dots. Application to Statistics of Coulomb Blockade Peak Spacings

We present a complete classification of the electron-electron interaction in chaotic quantum dots based on expansion in inverse powers of $1/M$, the number of the electron states in the Thouless window, $M \simeq k_F R$. This classification is quite universal and extends and enlarges the universal non interacting RMT statistical ensembles. We show that existing Coulomb blockade peak spacing data for $B=0$ and $B\ne 0$ is described quite accurately by the interacting GSE and by its extension to $B\ne 0$. The bimodal structure existing in the interacting GUE case is completely washed out by the combined effect of the spin orbit, pairing and higher order residual interactions.