Lyapunov stability analysis for invariant states of quantum systems

Muhammad F. Emzir; Ian R. Petersen; Matthew J. Woolley

doi:10.1109/CDC.2017.8264475

Lyapunov stability analysis for invariant states of quantum systems

Muhammad F. Emzir
, Ian R. Petersen
, Matthew J. Woolley

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of having multiple isolated invariant density operators. We then show how to analyze the stability of this set via a candidate Lyapunov operator.

Original language	English
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5505-5510
Number of pages	6
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8264475
State	Published - 28 Jun 2017
Externally published	Yes

Publication series

Name	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume	2018-January

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

ASJC Scopus subject areas

Decision Sciences (miscellaneous)
Industrial and Manufacturing Engineering
Control and Optimization

Access to Document

10.1109/CDC.2017.8264475

Cite this

Emzir, M. F., Petersen, I. R., & Woolley, M. J. (2017). Lyapunov stability analysis for invariant states of quantum systems. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 5505-5510). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8264475

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title = "Lyapunov stability analysis for invariant states of quantum systems",

abstract = "In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of having multiple isolated invariant density operators. We then show how to analyze the stability of this set via a candidate Lyapunov operator.",

author = "Emzir, \{Muhammad F.\} and Petersen, \{Ian R.\} and Woolley, \{Matthew J.\}",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",

year = "2017",

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doi = "10.1109/CDC.2017.8264475",

language = "English",

series = "2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017",

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Emzir, MF, Petersen, IR & Woolley, MJ 2017, Lyapunov stability analysis for invariant states of quantum systems. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 5505-5510. https://doi.org/10.1109/CDC.2017.8264475

Lyapunov stability analysis for invariant states of quantum systems. / Emzir, Muhammad F.; Petersen, Ian R.; Woolley, Matthew J.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 5505-5510 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of having multiple isolated invariant density operators. We then show how to analyze the stability of this set via a candidate Lyapunov operator.

AB - In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of having multiple isolated invariant density operators. We then show how to analyze the stability of this set via a candidate Lyapunov operator.

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Lyapunov stability analysis for invariant states of quantum systems

Abstract

Publication series

Bibliographical note

ASJC Scopus subject areas

Access to Document

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Cite this