Level dynamics and avoided level crossings in driven disordered quantum dots
arXiv:2208.13761 · doi:10.1103/PhysRevB.107.014206
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.
11 pages, 6 figures
References in corpus (10)
- Many-Body Physics with Ultracold Gases
- Energy level dynamics across the many-body localization transition
- Spectral statistics in an open parametric billiard system
- Avoided level crossing statistics in open chaotic billiards
- Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
- Many-Body-Localization Transition : sensitivity to twisted boundary conditions
- Statistics of Wave Functions in Disordered Systems with Applications to Coulomb Blockade Peak Spacing
- Distribution of spectral-flow gaps in the Rashba model with disorder: a new universality
- Superdiffusive quantum work and adiabatic quantum evolution in finite temperature chaotic Fermi systems
- Classical Theory of Quantum Work Distribution in Chaotic Fermion Systems