Artículo

Castagnino, M.; Lombardi, O. "Non-integrability and mixing in quantum systems: On the way to quantum chaos" (2007) Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics. 38(3):482-513
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In spite of the increasing attention that quantum chaos has received from physicists in recent times, when the subject is considered from a conceptual viewpoint the usual opinion is that there is some kind of conflict between quantum mechanics and chaos. In this paper we follow the program of Belot and Earman, who propose to analyze the problem of quantum chaos as a particular case of the classical limit of quantum mechanics. In particular, we address the problem on the basis of our account of the classical limit, which in turn is grounded on the self-induced approach to decoherence. This strategy allows us to identify the conditions that a quantum system must satisfy to lead to non-integrability and to mixing in the classical limit. © 2006 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Non-integrability and mixing in quantum systems: On the way to quantum chaos
Autor:Castagnino, M.; Lombardi, O.
Filiación:CONICET-IAFE, Universidad Nacional de Buenos Aires, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires, Argentina
CONICET-Universidad de Buenos Aires, C. Larralde 3440, 6D, 1430 Buenos Aires, Argentina
Palabras clave:Classical limit; Decoherence; Quantum chaos; Quantum mechanics; Quantum mixing; Quantum non-integrability
Año:2007
Volumen:38
Número:3
Página de inicio:482
Página de fin:513
DOI: http://dx.doi.org/10.1016/j.shpsb.2006.07.002
Título revista:Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Título revista abreviado:Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys.
ISSN:13552198
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13552198_v38_n3_p482_Castagnino

Referencias:

  • Abraham, R., Marsden, J.E., (1967) Foundations of Mechanics, , Benjamin, New York
  • Antoniou, I., Suchanecki, Z., Laura, R., Tasaki, S., Intrinsic irreversibility of quantum systems with diagonal singularity (1997) Physica A, 241, pp. 737-772
  • Batterman, R.W., Chaos, quantization and the correspondence principle (1991) Synthese, 89, pp. 189-227
  • Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., Sternheimer, D., Deformation theory and quantization II. Physical applications (1978) Annals of Physics, 110, pp. 111-151
  • Belot, G., Earman, J., Chaos out of order: Quantum mechanics, the correspondence principle and chaos (1997) Studies in History and Philosophy of Modern Physics, 28, pp. 147-182
  • Benatti, F., (1993) Deterministic Chaos in Infinite Quantum Systems, , Springer, New York
  • Berry, M.V., Quantum chaology, not quantum chaos (1989) Physica Scripta, 40, pp. 335-336
  • Berry, M.V., Some quantum-to-classical asymptotics (1991) Chaos and Quantum Physics, , Giannoni M.J., Voros A., and Zinn-Justin J. (Eds), North Holland, Amsterdam
  • Bruer, J.T., The classical limit of quantum theory (1982) Synthese, 50, pp. 167-212
  • Casati, G., Prosen, T., (2004) Quantum chaos and the double-slit experiment, , Los Alamos National Laboratory, CD/0403038
  • Castagnino, M., The classical-statistical limit of quantum mechanics (2004) Physica A, 335, pp. 511-518
  • Castagnino, M., Classical limit of non-integrable sytems (2005) Brazilian Journal of Physics, 35, pp. 375-379
  • Castagnino, M., The equilibrium limit of the Casati-Prosen model (2006) Physics Letters A, 357, pp. 97-100
  • Castagnino, M., Gadella, M., The problem of the classical limit of quantum mechanics and the role of self-induced decoherence (2006) Foundations of Physics, 36, pp. 920-952
  • Castagnino, M., Laura, R., Functional approach to quantum decoherence and the classical final limit (2000) Physical Review A, 62, p. 022107
  • Castagnino, M., Laura, R., Functional approach to quantum decoherence and the classical limit: the Mott and cosmological problems (2000) International Journal of Theoretical Physics, 39, pp. 1737-1765
  • Castagnino, M., Lombardi, O., The self-induced approach to decoherence in cosmology (2003) International Journal of Theoretical Physics, 42, pp. 1281-1299
  • Castagnino, M., Lombardi, O., Self-induced decoherence: A new approach (2004) Studies in History and Philosophy of Modern Physics, 35, pp. 73-107
  • Castagnino, M., Lombardi, O., Decoherence time in self-induced decoherence (2005) Physical Review A, 72, p. 012102
  • Castagnino, M., Lombardi, O., The classical limit of non-integrable quantum systems, a route to quantum chaos (2006) Chaos, Solitons and Fractals, 28, pp. 879-898
  • Castagnino, M., Ordoñez, A., Algebraic formulation of quantum decoherence (2004) International Journal of Theoretical Physics, 43, pp. 695-719
  • Ford, J., Mantica, G., Ristow, G.H., The Arnol'd cat: Failure of the correspondence principle (1991) Physica D, 50, pp. 493-520
  • Ford, J., Mantica, G., Does quantum mechanics obey the correspondence principle? Is it complete? (1992) American Journal of Physics, 60, pp. 1086-1098
  • Ghirardi, G.C., Rimini, A., Weber, T., Unified dynamics for microscopic and macroscopic systems (1986) Physical Review D, 34, pp. 470-491
  • Hillery, M., O'Connell, R.F., Scully, M.O., Wigner, E.P., Distribution functions in physics: Fundamentals (1984) Physics Reports, 106, pp. 121-167
  • Iguri, S., Castagnino, M., The formulation of quantum mechanics in terms of nuclear algebras (1999) International Journal of Theoretical Physics, 38, pp. 143-164
  • Koopman, B.O., Hamiltonian systems and transformations in Hilbert space (1931) Proceedings of the National Academy of Sciences, 18, pp. 315-318
  • Kronz, F.M., Nonseparability and quantum chaos (1998) Philosophy of Science, 65, pp. 50-75
  • Lasota, A., Mackey, M.C., (1985) Probabilistic Properties of Deterministic Systems, , Cambridge University Press, Cambridge
  • Laura, R., Castagnino, M., Minimal irreversible quantum mechanics: Mixed states and the diagonal singularity (1998) Physical Review A, 57, pp. 4140-4152
  • Laura, R., Castagnino, M., Functional approach for quantum systems with continuous spectrum (1998) Physical Review E, 57, pp. 3948-3961
  • Leggett, A.J., Quantum measurement at the macroscopic level (1986) The Lessons of Quantum Theory, , de Boer J., Dal E., and Ulfbeck O. (Eds), Elsevier, Amsterdam
  • Lombardi, O., El problema de la ergodicidad en mecánica estadística (2003) Crítica, 35, pp. 3-41
  • Paz, J.P., Zurek, W.H., (2000) Environment-induced decoherence and the transition from quantum to classical, , Los Alamos National Laboratory, quant-ph/0010011
  • Rohrlich, F., The logic of reduction: The case of gravitation (1989) Foundations of Physics, 19, pp. 1151-1170
  • Schuster, H.G., (1984) Deterministic Chaos, , VCH, Weinheim
  • Stamp, P.C.E., Magnets get their act together (1992) Nature, 359, pp. 365-366
  • Treves, A., (1967) Topological Vector Spaces, Distributions and Kernels, , Academic Press, New York
  • van Hove, L., Energy corrections and persistent perturbation effects in continuous spectra (1955) Physica, 21, pp. 901-923
  • Weinberg, S., Testing quantum mechanics (1989) Annals of Physics, 194, pp. 336-386
  • Zurek, W.H., Decoherence, einselection, and the quantum origins of the classical (2003) Reviews of Modern Physics, 75, pp. 715-776
  • Zurek, W.H., Paz, J.P., Decoherence, chaos and the second law (1994) Physical Review Letters, 72, pp. 2508-2511

Citas:

---------- APA ----------
Castagnino, M. & Lombardi, O. (2007) . Non-integrability and mixing in quantum systems: On the way to quantum chaos. Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics, 38(3), 482-513.
http://dx.doi.org/10.1016/j.shpsb.2006.07.002
---------- CHICAGO ----------
Castagnino, M., Lombardi, O. "Non-integrability and mixing in quantum systems: On the way to quantum chaos" . Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics 38, no. 3 (2007) : 482-513.
http://dx.doi.org/10.1016/j.shpsb.2006.07.002
---------- MLA ----------
Castagnino, M., Lombardi, O. "Non-integrability and mixing in quantum systems: On the way to quantum chaos" . Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics, vol. 38, no. 3, 2007, pp. 482-513.
http://dx.doi.org/10.1016/j.shpsb.2006.07.002
---------- VANCOUVER ----------
Castagnino, M., Lombardi, O. Non-integrability and mixing in quantum systems: On the way to quantum chaos. Stud. Hist. Philos. Sci. Part B Stud. Hist. Philos. Mod. Phys. 2007;38(3):482-513.
http://dx.doi.org/10.1016/j.shpsb.2006.07.002