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

TL;DR

This paper derives analytic formulas for conductance peak spacings in quantum dots using advanced random matrix theory, extending the Wigner surmise to include correlations between multiple energy levels, and validates these formulas numerically.

Contribution

It introduces new random matrix theory results for correlated level spacings and provides analytic formulas for conductance peak spacings in quantum dots.

Findings

Analytic formulas match numerical evaluations well.

Extended Wigner surmise for multiple level correlations.

Improved understanding of energy level statistics in quantum dots.

Abstract

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.