Statistics of Wave Functions in Disordered Systems with Applications to Coulomb Blockade Peak Spacing

TL;DR

This paper investigates wavefunction and energy-level statistics in disordered quantum systems, revealing complexities beyond random matrix theory and applying findings to Coulomb blockade phenomena in quantum dots.

Contribution

It provides the first comprehensive numerical analysis of wavefunction statistics relevant for electron interactions in disordered mesoscopic systems.

Findings

Good agreement with RMT for simple statistics

Discrepancies in complex spatial-energy statistics

Altered conductance peak spacings and wider spin distributions in Coulomb blockade

Abstract

Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this gap by using a tight-binding model to study a wide variety of statistics for the two-dimensional, disordered quantum system in the diffusive regime. Our results are in good agreement with random matrix theory (or its extensions) for simple statistics such as the probability distribution of energy levels or spatial correlation of a wavefunction. However, we see substantial disagreement in several statistics which involve both integrating over space and different energy levels, indicating that disordered systems are more complex than previously thought. These are exactly the quantities relevant to electron-electron interaction effects in quantum dots; in fact, we apply these results to the Coulomb blockade, where we find altered spacings between conductance peaks and wider spin distributions than traditionally expected.