Stability Analysis of Quantum Systems: a Lyapunov Criterion and an Invariance Principle
Optimization and Control
2020-08-05 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.2008.01534,
title = {Stability Analysis of Quantum Systems: a Lyapunov Criterion and an Invariance Principle},
author = {Muhammad F. Emzir and Matthew J. Woolley and Ian R. Petersen},
journal= {arXiv preprint arXiv:2008.01534},
year = {2020}
}
Comments
17 pages, 4 figures. arXiv admin note: text overlap with arXiv:1707.07372