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Defining and generating current in open quantum systems

Karen V. Hovhannisyan, Alberto Imparato

Defining current in open quantum systems can be problematic: No general description exists for the current of operators not conserved by the system-environment interaction. We fill this gap by deriving a general formula for probability current on an arbitrary graph, universally applicable to any system-environment interaction. We furthermore provide a representation of the average current, whereby the operator is first measured weakly, then strongly. When the dynamics is of Lindblad form, we derive an explicit formula for the current. We exemplify our theory by analysing a simple Smoluchowski-Feynman-type ratchet, operating deep in the quantum regime. Consisting of only two interacting particles, each moving on a three-site ring, the ratchet displays several novel quantum effects, such as tunnelling-induced current inversion, which we relate to the onset of quantum contextuality, and steady-state entanglement generation in the presence of arbitrarily hot environment. The role of spatial symmetry in current generation is also studied.

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ArXiv number: 1806.08779