×

Quantum-classical correspondence for local density of states and eigenfunctions of a chaotic periodic billiard. (English) Zbl 1064.81509

Summary: Classical-quantum correspondence for conservative chaotic Hamiltonians is investigated in terms of the structure of the eigenfunctions and the local density of states, using as a model a 2D rippled billiard in the regime of global chaos. The influence of the observed localized and sparsed states in the quantum-classical correspondence is discussed.

MSC:

81Q50 Quantum chaos
70F35 Collision of rigid or pseudo-rigid bodies
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Luna-Acosta, G. A.; Krokhin, A. A.; Rodriguez, M. A.; Hernandez-Tejeda, P. H., Phys. Rev. B, 54, 11410 (1996)
[2] Luna-Acosta, G. A.; Na, K.; Reichl, L. E.; Krokhin, A., Phys. Rev. E, 53, 3271 (1996)
[3] A.J. Lichtenberg, M.A. Lieberman, Regular and Chaotic Dynamics, 2nd ed., Springer, Berlin, 1992, Sec. 6.1b.; A.J. Lichtenberg, M.A. Lieberman, Regular and Chaotic Dynamics, 2nd ed., Springer, Berlin, 1992, Sec. 6.1b. · Zbl 0748.70001
[4] Mucciolo, E. R.; Capaz, R. B.; Altshuler, B. L.; Joannopoulos, J. D., Phys. Rev. B, 50, 8245 (1994)
[5] Agam, O.; Fishman, S.; Prange, R. E., Phys. Rev. A, 45, 6773 (1992)
[6] Wu, H.; Sprung, D. W.L; Martorel, J.; Klarsfeld, S., Phys. Rev. B, 44, 6351 (1991)
[7] Kouwenhoven, L. P.; Hekking, F. W.J; van Wees, B. J.; Harmans, C. J.P. M.; Timmering, C. E.; Foxon, C. T., Phys. Rev. Lett., 65, 361 (1990)
[8] Leng, M.; Craig, C. S., Phys. Rev. Lett., 71, 137 (1993)
[9] V.Ya. Demikhovskii, S.Yu. Potapenko, A.M. Satanin, Fiz. Tekh. Poluprovodn. 17 (1983) 213 [Sov. Semicond. 17 (1983) 137].; V.Ya. Demikhovskii, S.Yu. Potapenko, A.M. Satanin, Fiz. Tekh. Poluprovodn. 17 (1983) 213 [Sov. Semicond. 17 (1983) 137].
[10] Dittrich, T.; Mehlig, B.; Schanz, H.; Smilansky, U., Phys. Rev. E, 57, 359 (1998)
[11] Izrailev, F. M., Phys. Rep., 196, 299 (1990)
[12] F. Haake, Quantum signatures of Chaos, Springer, Berlin, 1991.; F. Haake, Quantum signatures of Chaos, Springer, Berlin, 1991. · Zbl 0741.58055
[13] L.E. Reichl, The transition to Chaos in Conservative Classical Systems: Quantum Manifestations, Springer, New York, 1992.; L.E. Reichl, The transition to Chaos in Conservative Classical Systems: Quantum Manifestations, Springer, New York, 1992.
[14] Casati, G.; Valz-Gris, F.; Guarneri, I., Lett. Nuovo Cimento., 28, 279 (1980)
[15] Bohigas, O.; Giannoni, M.-J; Schmidt, C., Phys. Rev. Let., 52, 1 (1984) · Zbl 1119.81326
[16] G.A. Luna-Acosta, M.A. Rodriguez, A.A. Krokhin, K. Na, R.A. Méndez, Rev. Mex. Fis. 44 (1998) S3 7.; G.A. Luna-Acosta, M.A. Rodriguez, A.A. Krokhin, K. Na, R.A. Méndez, Rev. Mex. Fis. 44 (1998) S3 7.
[17] G.A. Luna-Acosta, R.A. Méndez, unpublished.; G.A. Luna-Acosta, R.A. Méndez, unpublished.
[18] G. Casati, B, Chirikov, I. Guarneri, F.M. Izrailev, Phys. Lett. A 223 (1996) 430.; G. Casati, B, Chirikov, I. Guarneri, F.M. Izrailev, Phys. Lett. A 223 (1996) 430. · Zbl 1037.82525
[19] Flambaum, V. V.; Izrailev, F. M., Phys. Rev. E, 56, 5144 (1997)
[20] Borgonovi, F.; Guarneri, I.; Izrailev, F. M., Phys. Rev. E, 57, 5291 (1998)
[21] Weng-ge Wang, F.M. Izrailev, G. Casati, Phys. Rev. E 57 (1998) 323.; Weng-ge Wang, F.M. Izrailev, G. Casati, Phys. Rev. E 57 (1998) 323.
[22] L. Benet, F.M. Izrailev, T.H. Seligman, A. Suárez-Moreno, Semiclassical properties of eigenfunctions and occupation number distribution for a model of two interacting particles Chao-dyn/9912035.; L. Benet, F.M. Izrailev, T.H. Seligman, A. Suárez-Moreno, Semiclassical properties of eigenfunctions and occupation number distribution for a model of two interacting particles Chao-dyn/9912035. · Zbl 1274.81102
[23] L. Meza-Montes, F.M. Izrailev, S.E. Ulloa, Quantum-classical correspondence for two interacting particle in a one-dimensional box, Phys. Status Solidi (2000), to appear.; L. Meza-Montes, F.M. Izrailev, S.E. Ulloa, Quantum-classical correspondence for two interacting particle in a one-dimensional box, Phys. Status Solidi (2000), to appear.
[24] Borgonovi, F.; Casati, G.; Li, B., Phys. Rev. Lett., 77, 4744 (1997)
[25] Dewitt, B., Rev. Mod. Phys., 29, 377 (1957) · Zbl 0118.23301
[26] G.A. Luna, J.A. Méndez-Bermúdez, F.M. Izrailev, to be published.; G.A. Luna, J.A. Méndez-Bermúdez, F.M. Izrailev, to be published.
[27] F. Borgonovi, F.M. Izrailev, chao-dyn/9911018.; F. Borgonovi, F.M. Izrailev, chao-dyn/9911018.
[28] Dittrich, T.; Smilansky, U., Nonlinearity, 4, 59 (1991) · Zbl 0723.60127
[29] Dittrich, T.; Smilansky, U., Nonlinearity, 4, 85 (1991) · Zbl 0723.60128
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.