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Continuous time random walks modeling of quantum measurement and fractional equations of quantum stochastic filtering and controlстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Автор: Kolokoltsov Vassili N.
- Журнал: Fractional Calculus and Applied Analysis
- Том: 25
- Год издания: 2022
- Первая страница: 128
- Последняя страница: 165
- Аннотация: Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many branches of modern physics it became popular to extend random walk modeling to the continuous time random walk (CTRW) modeling, where the time between discrete events is taken to be non-exponential. In the present paper we apply the CTRWmodeling to the continuous quantum measurements yielding the newfractional in time evolution equations of quantum filtering and thus new fractional equations of quantum mechanics of open systems. The related quantum control problems and games turn out to be described by the fractional Hamilton-Jacobi-Bellman (HJB) equations on Riemannian manifolds. By-passing we provide a full derivation of the standard quantum filtering equations, in a modified way as compared with existing texts, which (i) provides explicit rates of convergence (that are not available via the tightness ofmartingales approach developed previously) and (ii) allows for the direct applications of the basic results of CTRWs to deduce the final fractional filtering equations.
- Добавил в систему: Колокольцов Василий Никитич