Abstract
Statistical properties of quasienergy spectra and structure of eigenfunctions are investigated for some model which is strongly chaotic in the semiclassical limit. The main attention is paid to the influence of the localization on the spacing distribution of the nearest levels depending on the degree of localization. Definition of localization length for chaotic states is discussed for the finite basis with the limiting case of fully extended random states. Scaling properties of spectra are studied in the intermediate region of suppressed quantum chaos.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B.Eckhardt, Phys. Rep., 163 (1988)205.
P.V.Elyutin, Usp. Fis. Nauk, 155 (1988) 397.
B.V.Chirikov, Phys. Rep. 52 (1979)263.
A.J.Lichtenberg and M.A.Lieberman, Motion (Springer, Berlin, 1983 ). Regular and Stochastic
B.V.Chirikov, F.M.Izrailev and D.L Rev. C2 (1981) 209..Shepelyansky, Sov. Sci.
B.V.Chirikov, F.M.Izrailev and D.L.Shepelyansky, Physica D33 (1988) 77.
G.Casati, B.V.Chirikov, J.Ford and F.M.Izrailev, Lecture Notes in Physics 93 (1979) 334.
F.M.Izrailev and D.L.Shepelyansky, Dokl. Akad. Nauk SSSR, 249 (1979) 1103 (Sov. Phys. Dokl. 24 (1979) 996); Teor. Mat. Fiz. 43 (1980) 417 (Theor. Math. Phys. 43, 553 ).
F.M.Izrailev, Phys. Lett. Al25 (1987) 250.
F.M.Izrailev, Phys. Lett. A134 (1988) 13; J. Phys., A22 (1989).
F.J.Duson, J. Math. Phys., 3 (1962) 140, 157, 166.
M.L.Mehta, Random Matrices, Academic, 1967.
T.A.Brody, J.Flores, J.B.French, P.A.Mello, A.Pandey, S.S. M.Wong, Rev. Mod. Phys., 53 (1981) 385.
F.M.Izrailev, Phys. Rev. Lett. 56 (1986) 541.
G.Casati, I.Guarneri, F.M.Izrailev, Phys. Lett. A 124 (1987) 263.
M.V.Berry and M.Robnik, J. Phys. A19 (1986) 649.
T.A.Brody, Lett. Nuov. Cim., 7 (1973) 482.
P.A.Lee, T.V.Ramakrishnan, Rev. Mod. Phys. 57 (1985) 287.
J.L.Pichard and G.J.Sarma, J. Phys. C14 (1981) L127.
G.Casati, I.Guarneri, F.Izrailev and R.Scharf, “Towards a scaling theory of localization in quantum chaos”, appear in Phys. Rev. Lett., 1989.
G.Casati, L.Molinari, and F.Izrailev, “Scaling properties of Band Random Matrices”, to be published0989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Izrailev, F.M. (1990). Relevance of the Localization to Quasienergy Statistics in Quantum Chaotic Systems. In: Exner, P., Neidhardt, H. (eds) Order,Disorder and Chaos in Quantum Systems. Operator Theory: Advances and Applications, vol 46. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7306-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7306-2_26
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7308-6
Online ISBN: 978-3-0348-7306-2
eBook Packages: Springer Book Archive