On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI:10.1134/S1061920825600825

V.N. Kolokoltsov

引用次数: 0

Abstract

Quantum filtering equations for mixed states were developed in the eighties of the last century. Since then, the problem of constructing a rigorous mathematical theory for these equations in the basic infinite-dimensional settings has been a challenging open mathematical problem. In a previous paper, the author developed the theory of these equations in the case of bounded coupling operators, including a new version that arises as the law of large numbers for interacting particles under continuous observation and thus leading to the theory of quantum mean field games. In this paper, the main body of these results is extended to the basic cases of unbounded coupling operators.

DOI 10.1134/S1061920825600825

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混合态量子随机滤波方程的数学理论

混合态的量子滤波方程是在上世纪八十年代发展起来的。从那时起，在基本的无限维环境中为这些方程构造一个严格的数学理论的问题一直是一个具有挑战性的开放数学问题。在之前的一篇论文中，作者在有界耦合算子的情况下发展了这些方程的理论，包括一个新的版本，作为连续观察下相互作用粒子的大数定律，从而导致量子平均场博弈理论。本文将这些结果的主体推广到无界耦合算子的基本情况。DOI 10.1134 / S1061920825600825

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.