Level dynamics and avoided level crossings in driven disordered quantum dots

TL;DR

This paper studies the energy level dynamics in driven disordered quantum dots, revealing universal behaviors in Landau-Zener transitions and energy level statistics that are independent of system specifics.

Contribution

It introduces a detailed analysis of level velocities, curvatures, and avoided crossings in disordered quantum dots under external perturbations, highlighting universal transition behaviors.

Findings

Landau-Zener transition strength shows universal behavior.

Energy level statistics align with Random Matrix Theory predictions.

Universal single-particle dynamics observed for slow perturbations.

Abstract

The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the first model the external drivings are realized by a continuous variation of the on-site energies, in the second one it is generated by deformations of a parabolic potential. We concentrate on the effects of the potential on the localization properties and investigate the statistics of the energy level velocities and curvatures regarding their typical magnitudes and domain of agreement with the predictions of Random Matrix Theory (RMT) for the Gaussian Orthogonal, Unitary and Symplectic ensembles. Moreover, the statistical properties of the avoided level crossings are investigated in terms of the corresponding Landau-Zener parameters. We find that the strength of the Landau-Zener transitions exhibits universal behavior which also implies universal single-particle dynamics for slow perturbations independent of the disorder and potential strength, the system size and the symmetry class. These results can be verified experimentally by measurements of single-particle energy spectra in quantum dots.