Classical and Quantum Chaos in a quantum dot in time-periodic magnetic fields

TL;DR

This paper explores the transition from regular to chaotic behavior in a quantum dot under time-periodic magnetic fields, analyzing classical dynamics, quantum spectra, and phase space distributions to understand quantum chaos phenomena.

Contribution

It provides a comprehensive analysis of classical and quantum chaos in a quantum dot with time-periodic magnetic fields, including phase boundary determination and eigenfunction statistics.

Findings

Classical motion transitions to chaos depending on magnetic field ratio and cyclotron frequency.

Quantum quasi-energy spectra show a transition from level clustering to level repulsion.

Eigenfunction statistics match Porter-Thomas distribution in the chaotic regime.

Abstract

We investigate the classical and quantum dynamics of an electron confined to a circular quantum dot in the presence of homogeneous $B_{dc}+B_{ac}$ magnetic fields. The classical motion shows a transition to chaotic behavior depending on the ratio $\epsilon=B_{ac}/B_{dc}$ of field magnitudes and the cyclotron frequency ${\tilde\omega_c}$ in units of the drive frequency. We determine a phase boundary between regular and chaotic classical behavior in the $\epsilon$ vs ${\tilde\omega_c}$ plane. In the quantum regime we evaluate the quasi-energy spectrum of the time-evolution operator. We show that the nearest neighbor quasi-energy eigenvalues show a transition from level clustering to level repulsion as one moves from the regular to chaotic regime in the $(\epsilon,{\tilde\omega_c})$ plane. The $\Delta_3$ statistic confirms this transition. In the chaotic regime, the eigenfunction statistics coincides with the Porter-Thomas prediction. Finally, we explicitly establish the phase space correspondence between the classical and quantum solutions via the Husimi phase space distributions of the model. Possible experimentally feasible conditions to see these effects are discussed.