The Annals of Probability

Regularity of solutions to quantum master equations: A stochastic approach

Carlos M. Mora

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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.

Article information

Source
Ann. Probab., Volume 41, Number 3B (2013), 1978-2012.

Dates
First available in Project Euclid: 15 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1368623517

Digital Object Identifier
doi:10.1214/11-AOP692

Mathematical Reviews number (MathSciNet)
MR3098064

Zentralblatt MATH identifier
1274.60206

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 81C20 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Keywords
Quantum master equations stochastic Schrödinger equations regular solutions probabilistic representations open quantum systems

Citation

Mora, Carlos M. Regularity of solutions to quantum master equations: A stochastic approach. Ann. Probab. 41 (2013), no. 3B, 1978--2012. doi:10.1214/11-AOP692. https://projecteuclid.org/euclid.aop/1368623517


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