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Article type: Cover
2004 Volume 109 Issue 4 Pages
Cover1-
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Article type: Appendix
2004 Volume 109 Issue 4 Pages
App1-
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Article type: Appendix
2004 Volume 109 Issue 4 Pages
D1-D2
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Article type: Appendix
2004 Volume 109 Issue 4 Pages
D3-D4
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Marko Robnik
Article type: Article
2004 Volume 109 Issue 4 Pages
D5-D8
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In this paper I offer an overview of the problem of energy level statistics in generic Hamiltonian systems, where classically we have regular motion on invariant tori for some initial conditions, and chaotic motion for some other complementary initial conditions. We look at this problem in the semiclassical limit of sufficiently small effective Planck's constant 〓_<eff>, assuming that we do have enough objects (asymptotically infinitely many) to define the statistics in this limit.
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[in Japanese], [in Japanese], [in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D9-D12
Published: July 20, 2004
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[in Japanese], S. Habib, K. Jacobs
Article type: Article
2004 Volume 109 Issue 4 Pages
D13-D16
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D17-D20
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Ichiro Ohba, Yukihiro Ota
Article type: Article
2004 Volume 109 Issue 4 Pages
D21-D24
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[in Japanese], [in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D25-D28
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D29-D32
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D33-D35
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D36-D39
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D40-D43
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[in Japanese], [in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D44-D47
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D48-D51
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D52-D55
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D56-D59
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D60-D63
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D64-D67
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[in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D68-D71
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Antonio M. Garcia-Garcia, James C. Osborn
Article type: Article
2004 Volume 109 Issue 4 Pages
D72-D75
Published: July 20, 2004
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We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling of the (dimensionless) Thouless energy in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.
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[in Japanese], [in Japanese]
Article type: Article
2004 Volume 109 Issue 4 Pages
D76-D79
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W. D. Heiss
Article type: Article
2004 Volume 109 Issue 4 Pages
D80-D84
Published: July 20, 2004
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Exceptional points are singularities of eigenvalues and eigenvectors for complex values of, say, an interaction parameter. They occur universally and are square root branch point singularities of the eigenvalues in the vicinity of level repulsions. The intricate connection between the distribution of exceptional points and particular fluctuation properties of level spacing is discussed. The distribution of the exceptional points of the problem H_o + λH_1 is given for the situation of hard chaos. Theoretical predictions of local properties of exceptional points have recently been confirmed experimentally. This relates to the specific topological structure of an exceptional point as well as to the chiral properties of the wave functions associated with exceptional points.
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Indubala T. Satija, Radha Balakrishnan
Article type: Article
2004 Volume 109 Issue 4 Pages
D85-D88
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We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated with the phase space trajectories using Frenet-Serret formulation. For the corresponding quantum problem, the geometric phase associated with the time evolution of the wave function is computed. Our studies suggest that the classical geometric phase may be related to the the difference in the quantum geometric phases between two neighboring eigenstates.
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Gregor Veble, Tomaz Prosen
Article type: Article
2004 Volume 109 Issue 4 Pages
D89-D92
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We show that the composition of perturbed forward and unperturbed backward hamiltonian evolution can be treated as a time-dependent hamiltonian system. For strongly chaotic systems we derive a cascade of exponential decays for the classical Loschmidt echo, starting with the leading Lyapunov exponent, followed by a sum of two largest exponents, etc.
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Tetsuro KONISHI
Article type: Article
2004 Volume 109 Issue 4 Pages
D93-D96
Published: July 20, 2004
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This talk consists of two independent parts, both of which is about the classical dynamics of Hamiltonian systems. First we will see how to construct analytic expression of homoclinic oscillation of invariant manifolds, which is the origin of Hamiltonian chaos. Next we show interesting behavior we found in a long-range interaction system, where 2-point correlation function grows into power-law function.
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[in Japanese], Pierre Gaspard
Article type: Article
2004 Volume 109 Issue 4 Pages
D97-D100
Published: July 20, 2004
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Agung Budiyono, Kazuo Takatsuka
Article type: Article
2004 Volume 109 Issue 4 Pages
D101-D104
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We give a new interpretation of scars of short periodic orbits observed in quantum systems with chaotic classical limit. The enhancement of density is shown to be caused by the mutual interference between two specific paths on the periodic orbit.
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Article type: Appendix
2004 Volume 109 Issue 4 Pages
App2-
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Article type: Appendix
2004 Volume 109 Issue 4 Pages
App3-
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Article type: Cover
2004 Volume 109 Issue 4 Pages
Cover2-
Published: July 20, 2004
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Article type: Cover
2004 Volume 109 Issue 4 Pages
Cover3-
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