2005 Fiscal Year Final Research Report Summary
Analytical Research on Quantum Information Dynamics
| Project/Area Number |
16540173
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
OHYA Masanori Tokyo University of Science, Department of Information Sciences, Professor, 理工学部, 教授 (90112896)
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| Co-Investigator(Kenkyū-buntansha) |
TOGAWA Yoshiro Tokyo University of Science, Department of Information Sciences, Professor, 教授 (20112899)
WATANABE Noboru Tokyo University of Science, Department of Information Sciences, Associate Professor, 助教授 (70191781)
SATO Keiko Tokyo University of Science, Department of Information Sciences, Lecturer, 講師 (30366439)
MIYADERA Takayuki National Institute of Advanced Industrial Science and Technology, Researcher, 研究員 (50339123)
IRIYAMA Satoshi Tokyo University of Science, Department of Information Sciences, Assistant, 助手 (10385528)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Quantum Probability / Quantum Entropy / Quantum Entanglement / Quantum Information Theory / Quantum Communication Theory / Quantum Chaos / Dynamical Entropy / 力学系のエントロピー |
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| Research Abstract |
(1)Analysis of Quantum Dynamical System
To proceed to investigate the quantum information theory, it is indispensable to study the border between quantum theory and classical theory. For this purpose, we took up two promising theories, Adaptive Dynamics and sector theory. Adaptive Dynamics was proposed independently by Accardi and Ohya. Application of Adaptive Dynamics to original Chaos Degree produced a slightly modified Chaos Degree, "Chaos Degree with memory effect", which shows a characteristic behavior for chaotic systems. We made an investigation of its mathematical structure.
(2)Analysis of infinite quantum chaos system
If the system is finite such as Kicked Rotator or billiards systems, it is well known by a semiclassical approximation and numerical calculation of Gutzwiller. However, in this study, we did not directly treat the system represented by the above essentially finite dimensional matrix, but we mainly study the infinite system in which the algebra of observable arrows non-equivalent representation. The examples of infinite systems are Noncommutative Bernoulli Shift and Arnold Cat Map (Narnhofer, Thirring, Sewell) defined on Weyl algebra.
The property of these systems are studied by many other groups, it is known that the mixing property is hold in the sense that time correlation function completely decay. Our group have been studied non-commutation Dynamical Entropies according to the above researches. As the results of this study, we investigated the infinite quantum chaos systems based on the information dynamical viewpoint, and developed "the chaos degree" considering the measurement of finite system. We also discussed the mathematical structure to be treated quantum chaos and studied the relation among this structure and the noncommutative dynamical entropies.
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[Book] 情報進化論2005
Author(s)
大矢雅則
Total Pages
112
Publisher
岩波書店
Description
「研究成果報告書概要(和文)」より
