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 , where . The values of the transport exponent depend on the correlation properties of the random potential , which describes random inhomogeneities of the medium. In particular, when the random potential is correlated in time, the quantum wave packet spreads according Richardson turbulent diffusion with the MSD . Hyperdiffusion with is also obtained for arbitrary correlation properties of the random potential.
- Received 16 June 2015
DOI:https://doi.org/10.1103/PhysRevE.92.022139
©2015 American Physical Society