Mesoscopic rings driven by time-dependent magnetic flux: Level correlations and localization in energy space.

Abstract

A mesoscopic ring threaded by a magnetic flux that varies linearly in time (\ensuremath{\varphi}=\ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}t) is considered. A tight-binding model of the problem is formulated, and the transitions among the adiabatic energy levels induced by the time dependence of the Hamiltonian are analyzed. When \ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{} is not small, the problem cannot be expressed in terms of a set of decouple two-level Zener problems. It is found that the system is localized in the basis of the adiabatic energy levels. The localization ``length'' in the energy space is shown to be finite even for arbitrarily large \ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}, in contradistinction to previous analyses of free-electron models. The dynamics of the model is governed by a linear equation with time-periodic coefficients; consequently, it is characterized by appropriate Floquet exponents. The latter have a statistical structure that bears similarities to spectra obtained in the context of ``quantum-chaos'' problems. In particular, one obtains Poisson-like or Wigner-like level-spacing distributions depending on the degree of energy localization.