Eigenfunctions of electrons in weakly disordered quantum dots: Crossover between orthogonal and unitary symmetries

TL;DR

This paper introduces a random matrix model to describe how electron eigenfunction statistics in mesoscopic quantum dots transition between orthogonal and unitary symmetries under magnetic fields.

Contribution

It proposes a one-parameter random matrix model that links microscopic properties to the symmetry crossover in quantum dot electron statistics.

Findings

The model accurately describes the transition in eigenfunction amplitude and phase statistics.

Comparison with supersymmetry results validates the model's microscopic parameter.

Application to resonance conductance shows clear crossover behavior.

Abstract

A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained with recent results derived from first principles within the framework of supersymmetry technique allows to identify a transition parameter with real microscopic characteristics of the problem. The random-matrix model is applied to the statistics of the height of the resonance conductance of a quantum dot in the regime of the crossover between orthogonal and unitary symmetry classes.