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From Dirac to Diffusion: Decoherence in Quantum Lattice Gases

Peter J. Love·Bruce M. Boghosian
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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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Peter J. Love, Bruce M. Boghosian. 2005-07-04. From Dirac to Diffusion: Decoherence in Quantum Lattice Gases. https://arxiv.org/abs/quant-ph/0507022

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