Quasiresonant diffusion of wave packets in one-dimensional disordered mosaic lattices

We investigate numerically the time evolution of wave packets incident on one-dimensional semi-infinite lat-tices with mosaic modulated random on-site potentials, which are characterized by the integer-valued modulation period kappa and the disorder strength W. For Gaussian wave packets with the central energy E0 and a small spectral width, we perform extensive numerical calculations of the disorder-averaged time-dependent reflectance, (R(t)), for various values of E0, kappa, and W. We find that the long-time behavior of (R(t)) obeys a power law of the form t-gamma in all cases. In the presence of the mosaic modulation, gamma is equal to 2 for almost all values of E0, implying the onset of the Anderson localization, while at a finite number of discrete values of E0 dependent on kappa, gamma approaches 3/2, implying the onset of the classical diffusion. This phenomenon is independent of the disorder strength and arises in a quasiresonant manner such that gamma varies rapidly from 3/2 to 2 in a narrow energy range as E0 varies away from the quasiresonance values. We deduce a simple analytical formula for the quasiresonance energies and provide an explanation of the delocalization phenomenon based on the interplay between randomness and band structure and the node structure of the wave functions. We explore the nature of the states at the quasiresonance energies using a finite-size scaling analysis of the average participation ratio and find that the states are neither extended nor exponentially localized, but critical states.

Automated summary

We numerically investigate the time evolution of wave packets in one-dimensional semi-infinite lattices with mosaic modulated random on-site potentials. We find that the long-time behavior of the time-dependent reflectance obeys a power law, indicating the onset of Anderson localization or classical diffusion. The phenomena of delocalization occur at certain discrete values of the central energy and depend on the modulation period. We provide an analytical formula for the quasiresonance energies and explain the delocalization phenomenon based on the interplay between randomness and band structure. The states at the quasiresonance energies are found to be critical states through finite-size scaling analysis.