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arXiv · 1205.5744

Thermodynamic formalism for dissipative quantum walks

Silvano Garnerone
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Abstract

We consider the dynamical properties of dissipative continuous-time quantum walks on directed graphs. Using a large-deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify transitions between dynamical regimes. For a particular class of dissipative quantum walks we propose a quantum generalization of the the classical PageRank vector, used to rank the importance of nodes in a directed graph. We also provide an example where one can characterize the dynamical transition from an effective classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct dynamical regimes.

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Silvano Garnerone. 2012-05-25. Thermodynamic formalism for dissipative quantum walks. https://doi.org/10.1103/physreva.86.032342

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