Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization

TL;DR

This paper derives an explicit analytical expression for the distribution of level velocities in quasi 1D disordered or chaotic quantum systems, enhancing understanding of their spectral response to potential changes.

Contribution

It provides the first explicit analytical formula for the distribution of level velocities in quasi 1D chaotic quantum systems with localization.

Findings

Derived the distribution function for level velocities in quasi 1D systems.

Applicable to systems like quantum kicked rotator, domino billiard, and disordered wires.

Advances understanding of spectral sensitivity to potential variations.

Abstract

The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to the quasi 1D universality class (quantum kicked rotator, "domino" billiard, disordered wire, etc.).