Open quantum walks (OQWs) are exclusively driven by dissipation and are formulated as completely positive trace-preserving (CPTP) maps on underlying graphs. The microscopic derivation of discrete and continuous-in-time OQWs is presented. It is assumed that connected nodes are weakly interacting via a common bath. The resulting reduced master equation of the quantum walker on the lattice is in the generalized master equation form. The time discretization of the generalized master equation leads to the OQW formalism. The explicit form of the transition operators establishes a connection between dynamical properties of the OQWs and thermodynamical characteristics of the environment. The derivation is demonstrated for the examples of the OQW on a circle of nodes and on a finite chain of nodes. For both examples, a transition between diffusive and ballistic quantum trajectories is observed and found to be related to the temperature of the bath.

• Received 5 May 2015

DOI:https://doi.org/10.1103/PhysRevA.92.032105