2020/08/01 by Muhammad F. Emzir, Emzir, Muhammad F., Matthew J. Woolley +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #math.OC #quant-ph
paper · pdf · doi:10.48550/arxiv.2008.01534
17 pages, 4 figures. arXiv admin note: text overlap with arXiv:1707.07372
arxiv created 2020/08/01 · openalex publication_date 2020/08/01 · arxiv updated 2020/08/05 · openalex created_date 2022/10/22 · openalex updated_date 2026/07/28
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant density operators is both closed and convex. We then show how to analyze the stability of this set via a candidate Lyapunov operator. We complete our analysis of the set of invariant density operators by introducing an analog of the Barbashin-Krasovskii-La Salle theorem on the dynamics of quantum systems.