Navegar

Colección

Datos Estadísticas

Artículo

El editor solo permite decargar el artículo en su versión post-print desde el repositorio. Por favor, si usted posee dicha versión, enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [12]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [13,14] and the kicked rotator [6-8]. © 2013 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
Autor:Gomez, I.; Castagnino, M.
Filiación:Instituto de Física de Rosario (IFIR-CONICET), Rosario, Argentina
Instituto de Astronomía y Física Del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires, Argentina
Palabras clave:Bernoulli; EH; Ergodic; Kolmogorov; Mixing; QEH; Bernoulli; EH; Ergodics; Kolmogorov; QEH; Mixing; Physics
Año:2014
Volumen:393
Página de inicio:112
Página de fin:131
DOI: http://dx.doi.org/10.1016/j.physa.2013.08.070
Título revista:Physica A: Statistical Mechanics and its Applications
Título revista abreviado:Phys A Stat Mech Appl
ISSN:03784371
CODEN:PHYAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v393_n_p112_Gomez

Referencias:

  • Belot, G., Earman, J., (1997) Stud. Hist. Philos. Modern. Phys., 28, pp. 147-182
  • Lichtenberg, A.J., Lieberman, M.A., (1992) Regular and Chaotic Dynamics, , Springer Verlag New York
  • Castagnino, M., Lombardi, O., (2009) Physica A, 388, pp. 247-267
  • Gutzwiller, M.C., (1990) Chaos in Classical and Quantum Mechanics, , Springer Verlag New York
  • Benatti, F., (1993) Deterministic Chaos in Infinite Quantum Systems, , Springer Verlag Berlin
  • Stockmann, H., (1999) Quantum Chaos - An Introduction, , Cambridge Univ. Press Cambridge
  • Casati, G., Chirikov, B., (1995) Quantum Chaos: Between Order and Disorder, , Cambridge Univ. Press Cambridge
  • Haake, F., (2001) Quantum Signatures of Chaos, , second ed. Springer-Verlag Heidelberg
  • Ballentine, L., (1998) Quantum Mechanics - A Modern Development, , World Scientific Publish Company
  • Berry, M., (1989) Phys. Scr., 40, pp. 335-336
  • Berkovitz, J., Frigg, R., Kronz, F., (2006) Stud. Hist. Philos. Modern. Phys., 37, pp. 661-691
  • Hillery, M., O'Connell, M., Scully, R., Wigner, E., (1984) Phys. Rep., 106, pp. 121-167
  • Casati, G., Prosen, T., (2005) Phys. Lett. A, 72, p. 032111
  • Castagnino, M., (2006) Phys. Lett. A, 357, pp. 97-100
  • Clifton, R., Halvorson, H., (1999) Phys. Rev. A, 61, p. 012108
  • Clifton, R., Halvorson, H., Kent, A., (2000) Phys. Rev. A, 61, p. 042101
  • Lasotta, A., Mackey, M., (1985) Probabilistic Properties of Deterministic Systems, , Cambridge Univ. Press Cambridge
  • Mackey, M., (1989) Rev. Modern Phys., 61, pp. 981-1015
  • G. Dito, D. Sternheimer, 2002. arxiv:math.QA/0201168; Cornfeld, I., Fomin, S.V., Sinai, Y.G., (1982) Ergodic Theory, , Springer New York
  • Mackey, M., (1992) Time's Arrow: The Origin of Thermodynamic Behavior, , Springer Verlag Berlin
  • Knuth, K., (2005) Neurocomputing, 67, pp. 245-274
  • Bocchieri, P., Loinger, A., (1957) Phys. Rev. A, 107, pp. 337-338
  • Bocchieri, P., Loinger, A., (2012) J. Phys. A, 4, p. 45
  • Castagnino, M., Lombardi, O., (2005) Philos. Sci., 72, pp. 764-776

Citas:

---------- APA ----------
Gomez, I. & Castagnino, M. (2014) . Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems. Physica A: Statistical Mechanics and its Applications, 393, 112-131.
http://dx.doi.org/10.1016/j.physa.2013.08.070
---------- CHICAGO ----------
Gomez, I., Castagnino, M. "Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems" . Physica A: Statistical Mechanics and its Applications 393 (2014) : 112-131.
http://dx.doi.org/10.1016/j.physa.2013.08.070
---------- MLA ----------
Gomez, I., Castagnino, M. "Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems" . Physica A: Statistical Mechanics and its Applications, vol. 393, 2014, pp. 112-131.
http://dx.doi.org/10.1016/j.physa.2013.08.070
---------- VANCOUVER ----------
Gomez, I., Castagnino, M. Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems. Phys A Stat Mech Appl. 2014;393:112-131.
http://dx.doi.org/10.1016/j.physa.2013.08.070