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May 2013 Regularity of solutions to quantum master equations: A stochastic approach
Carlos M. Mora
Ann. Probab. 41(3B): 1978-2012 (May 2013). DOI: 10.1214/11-AOP692

Abstract

Applying probabilistic techniques we study regularity properties of quantum master equations (QMEs) in the Lindblad form with unbounded coefficients; a density operator is regular if, roughly speaking, it describes a quantum state with finite energy. Using the linear stochastic Schrödinger equation we deduce that solutions of QMEs preserve the regularity of the initial states under a general nonexplosion condition. To this end, we develop the probabilistic representation of QMEs, and we prove the uniqueness of solutions for adjoint quantum master equations. By means of the nonlinear stochastic Schrödinger equation, we obtain the existence of regular stationary solutions for QMEs, under a Lyapunov-type condition.

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Carlos M. Mora. "Regularity of solutions to quantum master equations: A stochastic approach." Ann. Probab. 41 (3B) 1978 - 2012, May 2013. https://doi.org/10.1214/11-AOP692

Information

Published: May 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1274.60206
MathSciNet: MR3098064
Digital Object Identifier: 10.1214/11-AOP692

Subjects:
Primary: 60H15
Secondary: 46L55, 60H30, 81C20

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3B • May 2013
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