期刊
JOURNAL OF STATISTICAL PHYSICS
卷 140, 期 6, 页码 1025-1053出版社
SPRINGER
DOI: 10.1007/s10955-010-0047-0
关键词
Dynamical Anderson localization; Quantum walk; Random environment; Lyapunov exponent; Aizenman-Molchanov method; Fractional moment estimates
资金
- Agence Nationale de la Recherche [ANR-09-BLAN-0098-01]
- NSERC [205247]
- Institut Fourier
- Agence Nationale de la Recherche (ANR) [ANR-09-BLAN-0098] Funding Source: Agence Nationale de la Recherche (ANR)
The dynamics of a one dimensional quantum walker on the lattice with two internal degrees of freedom, the coin states, is considered. The discrete time unitary dynamics is determined by the repeated action of a coin operator in U(2) on the internal degrees of freedom followed by a one step shift to the right or left, conditioned on the state of the coin. For a fixed coin operator, the dynamics is known to be ballistic. We prove that when the coin operator depends on the position of the walker and is given by a certain i.i.d. random process, the phenomenon of Anderson localization takes place in its dynamical form. When the coin operator depends on the time variable only and is determined by an i.i.d. random process, the averaged motion is known to be diffusive and we compute the diffusion constants for all moments of the position.
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