Abstract
The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2, 3). In order to reveal level repulsion under conditions of global classical chaos special care may be necessary: (i) subspectra referring to different values of the quantum numbers related to symmetries must be dealt with separately and (ii) for systems with quantum localization only levels whose wavefunctions have overlapping support must be admitted. A “level” may either be an energy eigenvalue E in the case of autonomous systems or, for periodically driven systems, a quasi-energy φ, i.e. an eigenphase of the unitary Floquet operator transporting the wavevector from period to period.
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References
Statistical Theory of Spectra, C.E. Porter, ed., Academic Press, New York (1965)
M.L. Mehta, Random Matrices and the Statistical Theory of Spectra, Academic Press, New York (1965)
F. Haake, ‘Quantum Signatures of Chaos’, Springer-Verlag, Berlin, to appear (1990)
E.P. Wigner, Group Theory and its Applications to the Quantum Mechanics of Atomic Spectra, Academic Press, New York (1959)
M.V. Berry, in: Chaotic Behavior of Deterministic Systems, G. Iooss, R.H.G. Hellemann, and R. Stora, eds., Les Houches Session XXXVI, 1981, North Holland, Amsterdam (1983)
R. Scharf, B. Dietz, M. Kris, F. Haake, and M.V. Berry, Europhys. Lett. 5, 383 (1988)
P. Pechukas, Phys. Rev. Lett. 51, 943 (1983)
F. Haake, M. Küs, and R. Scharf, Lecture Notes in Phys. 282, F. Ehlotzky, ed., Springer, Berlin (1987)
M. Küs, to be published
F. Calogero and C. Marchioro, J. Math. Phys. 15, 1425 (1974)
B. Sutherland, Phys. Rev. A5, 1372 (1972)
J. Moser, Adv. Math. 16, 1 (1975)
M. Küs, Europhys. Lett. 5, 1 (1988)
P.D. Lax, Comm. Pure Appl. Math. 21, 467 (1968)
T. Yukawa, Phys. Rev. Lett. 54, 1883 (1985); Phys. Lett. 116 A, 227 (1986)
B. Dietz and F. Haake, Europhys. Lett. 9, 1 (1989); Z. Phys., to be published
F. Llaake and G. Lenz, to be published
G. Lenz and F. Haake, to be published
H. Risken, The Fokker Planck Equation, Springer, Berlin (1984)
F. Dyson, J. Math. Phys. 3, 140 (1982)
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Haake, F. (1991). Quantum Signatures of Chaos. In: Kramer, B. (eds) Quantum Coherence in Mesoscopic Systems. NATO ASI Series, vol 254. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3698-1_38
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DOI: https://doi.org/10.1007/978-1-4899-3698-1_38
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