We investigate the classical-quantum correspondence for particle motion in asuperlattice in the form of a 2D channel with periodic modulated boundaries.Its classical dynamics undergoes the generic transition to chaos of Hamiltoniansystems as the amplitude of the modulation is increased. We show that forstrong chaotic motion, the classical counterpart of the structure ofeigenstates (SES) in energy space reveals an excellent agreement with thequantum one. This correspondence allows us to understand important features ofthe SES in terms of classical trajectories. We also show that for typical 2Dmodulated waveguides there exist, at any energy range, extremely localizedeigenstates (in energy) which are practically unperturbed by the modulation.These states contribute to the strong fluctuations around the classical SES.The approach to the classical limit is discussed.
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