Decoherence and Quantum Walks: anomalous diffusion and ballistic tails

Details Decoherence and Quantum Walks: anomalous diffusion and ballistic tails Decoherence and Quantum Walks: anomalous diffusion and ballistic tails

2006-05-03

arxiv.org/abs/cond-mat/0605097v1

Phys. Rev. A 74, 020102(R) (2006) (4 pages)

Physics

Condensed Matter

Other Condensed Matter

4 pages, 1 figure

Scientific paper

10.1103/PhysRevA.74.020102

The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a particle makes quantum transitions between the sites of a d-dimensional hypercubic lattice whilst strongly coupled to a bath of two-level systems which 'record' the transitions. The long-time evolution of an initial wave packet is found to be most unusual: the mean square displacement of the particle density matrix shows long-range ballitic behaviour, but simultaneously a kind of weakly-localised behaviour near the origin. This result may have important implications for the design of quantum computing algorithms, since it describes a class of quantum walks.

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