1205.5744 (Silvano Garnerone)

Thermodynamic formalism for dissipative quantum walks    [PDF]

Silvano Garnerone

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 new quantum generalization of 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 a classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct regimes.

View original: http://arxiv.org/abs/1205.5744