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Homogeneous Open Quantum Random Walks on a Lattice

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Abstract

We study open quantum random walks (OQRWs) for which the underlying graph is a lattice, and the generators of the walk are homogeneous in space. Using the results recently obtained in Carbone and Pautrat (Ann Henri Poincaré, 2015), we study the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process. We study in detail the case of homogeneous OQRWs on the lattice \(\mathbb {Z}^d\), with internal space \(\mathfrak {h}=\mathbb {C}^2\).

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Authors and Affiliations

  1. Dipartimento di Matematica, dell’Universitá di Pavia, Via Ferrata, 1, 27100, Pavia, Italy

    Raffaella Carbone

  2. Laboratoire de Mathématiques, Université Paris-Sud, 91405, Orsay Cedex, France

    Yan Pautrat

Authors
  1. Raffaella Carbone
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  2. Yan Pautrat
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Correspondence to Yan Pautrat.

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Carbone, R., Pautrat, Y. Homogeneous Open Quantum Random Walks on a Lattice. J Stat Phys 160, 1125–1153 (2015). https://doi.org/10.1007/s10955-015-1261-6

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  • DOI: https://doi.org/10.1007/s10955-015-1261-6

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