Explicit expressions for stationary states of the Lindblad equation for a finite state space

• URL: http://arxiv.org/abs/2208.04954v1
• Date: Tue, 9 Aug 2022 13:42:29 GMT
• Title: Explicit expressions for stationary states of the Lindblad equation for a finite state space
• Authors: Bernd Michael Fernengel, Barbara Drossel
• Abstract summary: The Lindblad equation describes the time evolution of a density matrix of a quantum mechanical system. We provide an analytical expression for the steady states of the Lindblad equation using the quantum jump unraveling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Lindblad equation describes the time evolution of a density matrix of a quantum mechanical system. Stationary solutions are obtained by time-averaging the solution, which will in general depend on the initial state. We provide an analytical expression for the steady states of the Lindblad equation using the quantum jump unraveling, a version of an ergodic theorem, and the stationary probabilities of the corresponding discret-time Markov chains. Our result is valid when the number of states appearing the in quantum trajectory is finite. The classical case of a Markov jump-process is recovered as a special case, and differences between the two are discussed.

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