Correlations of Wave Functions in Disordered Systems

TL;DR

This paper explores how wave functions in disordered systems are correlated across different regimes, including weak localization, Anderson transition, and quantum dot fluctuations, providing insights into their complex behaviors.

Contribution

It offers a comprehensive analysis of eigenfunction correlations across various regimes in disordered systems, highlighting new phenomena at the Anderson transition.

Findings

Eigenfunction correlations are weak in the weak localization regime.

Strong correlations and level repulsion occur at the Anderson transition.

Fluctuations in quantum dot spectra are characterized by specific correlation patterns.

Abstract

This is an extended version of the talk given by the author at the NATO Advanced Study Institute "Supersymmetry and Trace Formulae" (Isaac Newton Institute, Cambridge, UK, 8-19 Septemebr 1997). Contains the following sections: 1. Eigenfunction correlations in the weak localization regime. 2. Strong correlations of eigenfunctions and level repulsion at the Anderson localization transition. 3. Fluctuations in the addition spectra of quantum dots.