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Quantum anomaly and effective field description of a quantum chaotic billiard(6) Approaches from mathematical science and quantum information, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Nobuhiko Taniguchi

この論文は国立情報学研究所の電子図書館事業により電子化されました。

物性研究Jun 20, 20050 citations

Weak values and quantum-classical correspondence(6) Approaches from mathematical science and quantum information, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Atushi Tanaka

この論文は国立情報学研究所の電子図書館事業により電子化されました。

物性研究Jun 20, 20050 citations

Semiclassical Trace Formulas in Terms of Phase Space Path Integrals

Ayumu Sugita

arXiv:nlin/0005011Annals of PhysicsMar 1, 200119 citations

Semiclassical trace formulas in terms of phase space path integrals

歩杉田

Jan 1, 20000 citations

Nature of semiclassical spectrum in terms of classical trajectories(4) Quantum chaos and semiclassical theory in molecular science and nuclear theory, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Hiroshi Ushiyama, Kazuo Takatsuka

The mechanism of semiclassical quantization is examined in detail. We found an important role of destructive interference in building quantum spectrum. Based on this analysis, we propose an efficient method to calculate the semiclassical spectrum. This method is particularly promising in multidimensional chaotic systems and also very useful to identify which trajectories dominate a quantum spectrum. We numerically examine this method by applying to a two-dimensional chaotic system and show an illustrative example of identifying such a dominant trajectory that corresponds to an eigenstate.The mechanism of semiclassical quantization is examined in detail. We found an important role of destructive interference in building quantum spectrum. Based on this analysis, we propose an efficient method to calculate the semiclassical spectrum. This method is particularly promising in multidimensional chaotic systems and also very useful to identify which trajectories dominate a quantum spectrum. We numerically examine this method by applying to a two-dimensional chaotic system and show an illustrative example of identifying such a dominant trajectory that corresponds to an eigenstate.

物性研究Jun 20, 20050 citations

Semiclassical trace formulae using coherent states

B. Mehlig, Michael Wilkinson

We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum-mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum-mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.

arXiv:cond-mat/0012027Annalen der PhysikJun 1, 200130 citations

Canonically invariant formulation of the semiclassical trace formula in terms of the phase space path integral(4) Quantum chaos and semiclassical theory in molecular science and nuclear theory, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

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Canonically invariant formulation of the semiclassical trace formula in terms of the phase space path integral(4) Quantum chaos and semiclassical theory in molecular science and nuclear theory, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Abstract

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