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Diffusive-ballistic crossover in 1D quantum walks | | Daniel K. Wojcik
; J.R. Dorfman
; | | Date: |
4 Sep 2002 | | Journal: | Phys. Rev. Lett. 90 (2003) 230602 | | Subject: | Quantum Physics; Statistical Mechanics; Chaotic Dynamics | quant-ph cond-mat.stat-mech nlin.CD | | Abstract: | We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck’s constant. However, for fixed times, the semi-classical limit leads to diffusion. Random matrix theory provides explicit analytical predictions for the mean square displacement of a particle in the system. These results exhibit a crossover from diffusive to ballistic motion, with crossover time from diffusive to ballistic motion on the order of the inverse of Planck’s constant. We can argue, that for a large class of 1D quantum random walks, similar to the quantum multi-baker, a sufficient condition for diffusion in the semi-classical limit is classically chaotic dynamics in each cell. Using an initial equilibrium density matrix, we find that diffusive behavior is recovered in the semi-classical limit for such systems, without further interactions with the environment. | | Source: | arXiv, quant-ph/0209036 | | Services: | Forum | Review | PDF | Favorites | |
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