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完全混合的量子开放系统与量子分形

Completely Mixing Quantum Open Systems and Quantum Fractals

Ph. Blanchard, A. Jadczyk, R. Olkiewicz

备注：
Latex format, 20 pages, 6 figures in jpg format. New replacement has two more references (including one to a paper by G. Casati et al on quantum fractal eigenstates), adds example and comments concerning mixing properties of of a two-level atom driven by a laser field, and also adds a number of other remarks which should make it easier to follow mathematical arguments
发表信息：
Physica D: Nonlinear Phenomena, 148 (3-4) (2001) pp. 227-241
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摘要：

从遍历理论的经典概念出发，用概率密度表示，提出了描述量子开放系统中混沌行为和信息损失的测度。作为应用，我们讨论了EEQT框架下连续测量过程的混沌结果。同时测量四个非对易自旋分量，可以在量子自旋球上产生混沌跳跃，并产生特定的分形图像--非线性迭代函数系统。该模型是纯理论在这个阶段，和混沌行为的测量仪器在同时连续测量几个noncommuting量子可观的实验确认将构成事件增强量子理论的定量验证。

英文摘要：

Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the chaotic behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting spin components is shown to lead to a chaotic jump on quantum spin sphere and to generate specific fractal images - nonlinear ifs (iterated function system). The model is purely theoretical at this stage, and experimental confirmation of the chaotic behavior of measuring instruments during simultaneous continuous measurement of several noncommuting quantum observables would constitute a quantitative verification of Event Enhanced Quantum Theory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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