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

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Abstract
A mesoscopic ring threaded by a magnetic flux that varies linearly in time (φ=φ̇t) 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 φ̇ 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 φ̇, 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.

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