Regularity of solutions to quantum master equations: A stochastic approach
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Carlos M. Mora [1]
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[1] Universidad de Concepción
Universidad de Concepción
Comuna de Concepción, Chile
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 2, 2013, págs. 1978-2012
- Idioma: inglés
- DOI: 10.1214/11-AOP692
- Texto completo no disponible (Saber más ...)
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Resumen
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.
