Abstract
This chapter will focus mainly on the kicked rotator that displays global classical chaos in its cylindrical phase space for sufficiently strong kicking. The chaotic behavior takes the form of “rapid” quasi-random jumps of the phase variable around the cylinder and “slow” diffusion of the conjugate angular momentum p along the cylinder.
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References
S. Fishman, D.R. Grempel. R.E. Prange: Phys. Rev. Lett. 49, 509 (1982); Phys. Rev. A29, 1639 (1984)
D.L. Shepelyansky: Phys. Rev. Lett. 56, 677 (1986)
G. Casati, J. Ford, I. Guarneri, F. Vivaldi: Phys. Rev. A34, 1413 (1986)
S.-J. Chang, K.-J. Shi: Phys. Rev. A34, 7 (1986)
M. Feingold, S. Fishman, D.R. Grempel, R.E. Prange: Phys. Rev. B31, 6852 (1985)
M.V. Berry, S. Klein: Eur. J. Phys. 18, 222 (1997)
T. Dittrich, U. Smilansky: Nonlinearity 4, 59 (1991);ibid. 4, 85 (1991)
N. Argaman, Y. Imry, U. Smilansky: Phys. Rev. B47, 4440 (1993)
K.B. Efetov: Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, 1997)
Y. Imry: Introduction to Mesoscopic Physics (Oxford University Press, Oxford, 1997)
J.E. Bayfield, P.M. Koch: Phys. Rev. 33, 258 (1974)
M.R.W. Bellermann, P.M. Koch, D.R. Mariani, D. Richards: Phys. Rev. Lett. 76, 892 (1996)
O. Benson, G. Raithel, H. Walther: In G. Casati, B. Chirikov: Quantum Chaos (Cambridge University Press, Cambridge, 1995)
R. Bluemel, W.P. Reinhardt: Chaos in Atomic Physics (Cambridge University Press, Cambridge, 1997)
G. Casati, B. Chirikov: Quantum Chaos (Cambridge University Press, Cambridge, 1995)
R. Graham, M. Schlautmann, P. Zoller: Phys. Rev. A 45, R19 (1992)
F.L. Moore, J.C. Robinson, C. Bharucha, P.E. Williams, M.G. Raizen: Phys. Rev. Lett. 73, 3974 (1994)
J.C. Robinson, C. Bharucha, F.L. Moore, R. Jahnke, G.A. Georgakis, Q. Niu,, M.G. Raizen, B Sundaram: Phys. Rev. Lett. 74, 3963 (1995)
F.L. Moore, J.C. Robinson, C. Bharucha, B Sundaram, M.G. Raizen: Phys. Rev. Lett. 75, 4598 (1995)
H.-J. Stöckmann: Quantum Chaos, An Introduction (Cambridge University Press, Cambridge, 1999)
B. Kramer, A. MacKinnon: Rep. Prog. Phys. 56, 1469 (1993)
P.W. Anderson: Phys. Rev. 109, 1492 (1958); Rev. Mod. Phys. 50, 191 (1978)
D.J. Thouless: In Session XXXI, 1979, Ill-Condensed Matter R. Balian, R. Maynard, G. Thoulouse (eds.) Les Houches, (North-Holland, Amsterdam, 1979)
K. Ishii: Prog. Th. Phys. Suppl. 53, 77 (1973)
H. Furstenberg: Trans. Ann. Math. Soc. 108, 377 (1963)
A. Crisanti, G. Paladin, A. Vulpiani: Products of Random Matrices (Springer, Berlin, 1993)
B.V. Chirikov: preprint no. 367, Inst. Nucl. Physics Novosibirsk (1969); Phys. Rep. 52, 263 (1979)
T. Dittrich, R. Graham: Ann. Phys. 200, 363 (1990)
H. Weyl: Math. Ann. 77, 313 (1916)
P. Lloyd: J. Phys. C2, 1717 (1969)
D.J. Thouless: J. Phys. C5, 77 (1972)
S.F. Edwards, P.W. Anderson: J. Phys. F5, 965 (1975)
B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky: Sov. Sci. Rev. 2C, 209 (1981)
D.L. Shepelyansky: Phys. Rev. Lett. 56, 677 (1986)
F. Haake, M. Kuś, J. Mostowski, R. Scharf: In F. Haake, L.M. Narducci, D.F. Walls (eds.): Coherence, Cooperation, and Fluctuations (Cambridge University Press, Cambridge, 1986)
F. Haake, M. Kuś, R. Scharf: Z. Phys. B65, 381 (1987)
M. Kuś, R. Scharf, F. Haake: Z. Phys. B66, 129 (1987)
R. Scharf, B. Dietz, M. Kuś, F. Haake, M.V. Berry: Europhys. Lett. 5, 383 (1988)
F.T. Arecchi, E. Courtens, G. Gilmore, H. Thomas: Phys. Rev. A6, 2211 (1972)
R. Glauber, F. Haake: Phys. Rev. A13, 357 (1976)
K. Zyczkowski: J. Phys. A23, 4427 (1990)
A. Peres: Quantum Theory: Concepts and Methods (Kluwer Academic, New York, 1995)
F. Haake, D.L. Shepelyansky: Europhys. Lett. 5, 671 (1988)
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Haake, F. (2010). Quantum Localization. In: Quantum Signatures of Chaos. Springer Series in Synergetics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05428-0_7
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