白噪声算子的量子连续性方程和量子演化系统

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-07-19 DOI:10.1063/5.0176568

Un Cig Ji

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引用次数: 0

摘要

本文的主要目的是提出白噪声算子的规范量子连续性方程，并找到它们的显式唯一解。通过应用白噪声函数的连续性方程和白噪声算子空间与双变量白噪声函数空间之间的典型拓扑同构，我们提出了白噪声算子的典型量子连续性方程，然后我们诱导出与量子连续性方程等价的时依量子演化系统。然后，我们通过求解白噪声算子的量子演化系统，以广义傅里叶-梅勒变换的量子类似形式找到量子连续性方程唯一解的明确形式。

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Quantum continuity equations and quantum evolution systems for white noise operators

Main purpose of this paper is to formulate canonical quantum continuity equations for white noise operators and to find their explicit unique solutions. By applying the continuity equations for white noise functionals and canonical topological isomorphisms between the spaces of white noise operators and the spaces of two-variable white noise functionals, we formulate canonical quantum continuity equations for white noise operators, and then we induce time dependent quantum evolution systems which are equivalent to the quantum continuity equations. Then we find explicit forms, in terms of the quantum analogues of generalized Fourier-Mehler transforms, of the unique solutions of the quantum continuity equations by solving the quantum evolution systems for white noise operators.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.