| Project/Area Number |
15540361
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
SHIZUME Kosuke University of Tsukuba, Graduate School of library, Information and Media Studies, Associate Professor, 大学院・図書館情報メディア研究科, 助教授 (90211953)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥2,600,000 (Direct Cost: ¥2,600,000)
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| Keywords | Quantum-Classical Correspondence / Quantum chaos / Quantum continuous measurement / Quantum-classical transition / Duffing oscillator / Quantum Lyapunov exponents / Quantum storoboscopic map / 量子 / カオス / 力学 / リヤプノフ指数 / ストロボ図 / 波束の収縮 / 連続測定 |
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| Research Abstract |
The derivation of classical Lyapunov exponents based only on quantum mechanics has till recently been one of the important open questions of quantum-classical correspondence. Recently Bhattacharya and other authors made great progress by showing that the trajectories of wave packets under continuous measurement of the Caves-Milburn type have the same Lyapunov exponents as the classical one in the classical limit (where "measurement strength" k is large, and Plack constant is small enough).
Recalling that unitary evolution (k=0) gives zero Lyapunov exponent, their answer suggests the existence of "non-chaos to chaos" transition due to the continuous measurement. In this research project, we investigated the nature of this transition by computing the Lyapunov exponents, and constructing the stroboscopic maps, of the Duffing system with various values of k, especially small values of k (too small to be in the classical limit). We found that even when the wave packet is extended, its motion can be characterized by a finite (>0) Lyapunov exponent. Remarkably, our result implies the existence of chaos even in a quantum dynamical regime.
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