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From Dirac to Diffusion: Decoherence in Quantum Lattice Gases

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Abstract

We describe a model for the interaction of the internal (spin) degree of freedom of a quantum lattice-gas particle with an environmental bath. We impose the constraints that the particle-bath interaction be fixed, while the state of the bath is random, and that the effect of the particle-bath interaction be parity invariant. The condition of parity invariance defines a subgroup of the unitary group of actions on the spin degree of freedom and the bath. We derive a general constraint on the Lie algebra of the unitary group which defines this subgroup, and hence guarantees parity invariance of the particle-bath interaction. We show that generalizing the quantum lattice gas in this way produces a model having both classical and quantum discrete random walks as different limits. We present preliminary simulation results illustrating the intermediate behavior in the presence of weak quantum noise

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  1. Peter J. Love

    Present address: D-Wave Systems Inc., Suite 100, 4401 Still Creek Drive, Burnaby, British Columbia, Canada, V5C 6G9

Authors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, Massachusetts, 02155, USA

    Peter J. Love & Bruce M. Boghosian

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  1. Peter J. Love
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  2. Bruce M. Boghosian
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Correspondence to Peter J. Love.

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Love, P.J., Boghosian, B.M. From Dirac to Diffusion: Decoherence in Quantum Lattice Gases. Quantum Inf Process 4, 335–354 (2005). https://doi.org/10.1007/s11128-005-7852-4

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