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arXiv · 1810.11144

Trees, Forests, and Stationary States of Quantum Lindblad Systems

Patrick Rooney·Anthony M. Bloch·Chitra Rangan
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Abstract

In this paper, we study the stationary orbits of quantum Lindblad systems. We show that they can be characterized in terms of trees and forests on a directed graph with edge weights that depend on the Lindblad operators and the eigenbasis of the density operator. For a certain class of typical Lindblad systems, this characterization can be used to find the asymptotic end-states. There is a unique end-state for each basin of the graph (the strongly connected components with no outgoing edges). In most cases, every asymptotic end-state must be a linear combination thereof, but we prove necessary and sufficient conditions under which symmetry in the Lindblad and Hamiltonian operators hide other end-states or stable oscillations between end-states.

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Patrick Rooney, Anthony M. Bloch, Chitra Rangan. 2018-10-26. Trees, Forests, and Stationary States of Quantum Lindblad Systems. https://arxiv.org/abs/1810.11144

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