REGULARITY OF SOLUTIONS TO QUANTUM MASTER EQUATIONS: A STOCHASTIC APPROACH

• 成果类型: Article
• 署名作者: Mora, Carlos M.
• 署名单位: Universidad de Concepcion
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP692
• 发表日期: 2013
• 页码: 1978-2012
• 关键词: schrodinger-equations; Sufficient conditions; conservativity; STATES; time

摘要

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 Schrodinger 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 Schrodinger equation, we obtain the existence of regular stationary solutions for QMEs, under a Lyapunov-type condition.