Abstract:
Due to their exponential proliferation, long periodic orbits constitute a serious drawback in Gutzwiller’s theory of chaotic systems. Therefore, it would be desirable that other classical invariants, not suffering from the same problem, could be used in alternative semiclassical quantization schemes. In this Rapid Communication, we demonstrate how a suitable dynamical analysis of chaotic quantum spectra unveils the role played, in this respect, by classical invariant areas related to the stable and unstable manifolds of short periodic orbits. © 2004 The American Physical Society.
Registro:
| Documento: |
Artículo
|
| Título: | Classical invariants and the quantization of chaotic systems |
| Autor: | Wisniacki, D.A.; Vergini, E.; Benito, R.M.; Borondo, F. |
| Filiación: | Departamento de Química C-IX, Universidad Autónoma de Madrid, Cantoblanco, Madrid, 28049, Spain
Departamento de Física “J. J. Giambiagi”, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Departamento de Física, Comisión Nacional de Energía Atómica, AV. del Libertador 8250, Buenos Aires, 1429, Argentina
Departamento de Física, E. T. S. I. Agrónomos, Universidad Politécnica de Madrid, Madrid, 28040, Spain
|
| Año: | 2004
|
| Volumen: | 70
|
| Número: | 3
|
| Página de inicio: | 4
|
| DOI: |
http://dx.doi.org/10.1103/PhysRevE.70.035202 |
| Título revista: | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|
| Título revista abreviado: | Phys Rev E.
|
| ISSN: | 1063651X
|
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1063651X_v70_n3_p4_Wisniacki |
Referencias:
- Haake, F., (2001) Quantum Signatures of Chaos, , Springer
- Stöckmann, H.-J., (1999) Quantum Chaos: An Introduction, , Cambridge University Press
- Ehrenfest, P., (1916) Verlagen Kon. Akad. Amsterdam, 25, p. 412
- (1967) Sources of Quantum Mechanics, , B. L. Van der Waerden, Dover
- Einstein, A., (1917) Verh. Dtsch. Phys. Ges., 19, p. 82
- Lichtenberg, A.J., Lieberman, M.A., (1992) Regular and Chaotic Dynamics, , Springer
- Gutzwiller, M.C., (1990) Chaos in Classical and Quantum Mechanics, , Springer
- Gutzwiller, M.C., (1980) Phys. Rev. Lett., 45, p. 150
- Wintgen, D., (1987) Phys. Rev. Lett., 58, p. 1589
- The Ehrenfest time is defined as (Formula presented), (Formula presented) being the Lyapunov exponent, and constitutes a rough indicator of the amount of time needed by a wave packet to fill the available configuration space; Wisniacki, D.A., Vergini, E., (2000) Phys. Rev. E, 62, p. R4513
- de Polavieja, G.G., Borondo, F., Benito, R.M., (1994) Phys. Rev. Lett., 73, p. 1613
- Vergini, E.G., Carlo, G.G., (2001) J. Phys. A, 34, p. 4525
- Vergini, E.G., Schneider, D., J. Phys. A
- Ozorio de Almeida, A.M., (1989) Nonlinearity, 2, p. 519
- Tomsovic, S., Lefebvre, J.H., (1997) Phys. Rev. Lett., 79, p. 3629
- Wisniacki, D.A., Vergini, E., Benito, R.M., Borondo, F., ; Wisniacki, D.A., Borondo, F., Vergini, E., Benito, R.M., (2000) Phys. Rev. E, 62, p. R7583
- Wisniacki, D.A., Borondo, F., Vergini, E., Benito, R.M., (2000) Phys. Rev. E, 63, p. 66220
- Vergini, E.G., (2000) J. Phys. A, 33, p. 4709
- Vergini, E.G., Carlo, G.G., (2000) J. Phys. A, 33, p. 4717
- Fromhold, P.B., (1996) Nature (London), 380, p. 608
- Takagaki, Y., Ploog, K.H., (2000) Phys. Rev. E, 62, p. 4804
Citas:
---------- APA ----------
Wisniacki, D.A., Vergini, E., Benito, R.M. & Borondo, F.
(2004)
. Classical invariants and the quantization of chaotic systems. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 70(3), 4.
http://dx.doi.org/10.1103/PhysRevE.70.035202---------- CHICAGO ----------
Wisniacki, D.A., Vergini, E., Benito, R.M., Borondo, F.
"Classical invariants and the quantization of chaotic systems"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 70, no. 3
(2004) : 4.
http://dx.doi.org/10.1103/PhysRevE.70.035202---------- MLA ----------
Wisniacki, D.A., Vergini, E., Benito, R.M., Borondo, F.
"Classical invariants and the quantization of chaotic systems"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 70, no. 3, 2004, pp. 4.
http://dx.doi.org/10.1103/PhysRevE.70.035202---------- VANCOUVER ----------
Wisniacki, D.A., Vergini, E., Benito, R.M., Borondo, F. Classical invariants and the quantization of chaotic systems. Phys Rev E. 2004;70(3):4.
http://dx.doi.org/10.1103/PhysRevE.70.035202
