Abstract
A quantum-mechanical analysis of hyperfast (faster than ballistic) diffusion of a quantum wave packet in random optical lattices is presented. The main motivation of the presented analysis is experimental demonstrations of hyperdiffusive spreading of a wave packet in random photonic lattices [L. Levi et al., Nature Phys. 8, 912 (2012)]. A rigorous quantum-mechanical calculation of the mean probability amplitude is suggested, and it is shown that the power-law spreading of the mean-squared displacement (MSD) is 〈x2(t)〉∼tα, where 2<α≤3. The values of the transport exponent α depend on the correlation properties of the random potential V(x,t), which describes random inhomogeneities of the medium. In particular, when the random potential is δ correlated in time, the quantum wave packet spreads according Richardson turbulent diffusion with the MSD ∼t3. Hyperdiffusion with α=12/5 is also obtained for arbitrary correlation properties of the random potential.
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