Quantum Fokker-Planck structure of the Lindblad equation

• URL: http://arxiv.org/abs/2305.05805v1
• Date: Tue, 9 May 2023 23:37:20 GMT
• Title: Quantum Fokker-Planck structure of the Lindblad equation
• Authors: M\'ario J. de Oliveira
• Abstract summary: We show that the quantum Fokker-Planck equation can be transformed into an equation of the Lindblad form. This result allows us to conclude that the quantum Fokker-Planck equation preserves the trace and positivity of the density operator.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that the quantum Fokker-Planck equation, obtained by a canonical quantization of its classical version, can be transformed into an equation of the Lindblad form. This result allows us to conclude that the quantum Fokker-Planck equation preserves the trace and positivity of the density operator. The Fokker-Planck structure gives explicit expression for the quantum equivalence of probability current as well as the quantum equivalence of detailed balance. We also propose expression for the rate of entropy production and show that it does not vanish for a closed system except in equilibrium.

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