Sensitivity of quantum chaotic wavefunction intensities to changes in external perturbations

TL;DR

This paper investigates how wavefunction intensities in chaotic quantum systems respond to small external perturbations, proposing a universal scaling law and deriving exact expressions for systems lacking time-reversal symmetry, supported by numerical simulations.

Contribution

It introduces a universal scaling law for wavefunction intensity sensitivity across Dyson ensembles and provides exact theoretical expressions for non-time-reversal-invariant systems.

Findings

Universal scaling law for wavefunction intensities

Exact expressions for T-violating systems

Validation through numerical simulations

Abstract

We examine the sensitivity of wavefunction intensities in chaotic quantum systems to small changes in an arbitrary external perturbation. A universal scaling is proposed for all three Dyson ensembles and a novel theoretical approach is used to determine exact expressions for systems which violate T-invariance. Analytical results are compared with numerical simulations of tight-binding Anderson Hamiltonians.