REGULARITY OF SOLUTIONS TO QUANTUM MASTER EQUATIONS: A STOCHASTIC APPROACH

被引:9
|
作者
Mora, Carlos M. [1 ]
机构
[1] Univ Concepcion, Fac Ciencias Fis & Matemat, Dept Ingn Matemat, CI2MA, Casilla 160 C, Concepcion, Chile
来源
ANNALS OF PROBABILITY | 2013年 / 41卷 / 3B期
关键词
Quantum master equations; stochastic Schrodinger equations; regular solutions; probabilistic representations; open quantum systems; SCHRODINGER-EQUATIONS; SUFFICIENT CONDITIONS; CONSERVATIVITY; STATES; TIME;
D O I
10.1214/11-AOP692
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码:1978 / 2012
页数:35
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