Artículo

Gomez, I.; Losada, M.; Fortin, S.; Castagnino, M.; Portesi, M. "A Semiclassical Condition for Chaos Based on Pesin Theorem" (2015) International Journal of Theoretical Physics. 54(7):2192-2203
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:

A semiclassical method to determine if the classical limit of a quantum system shows a chaotic behavior or not based on Pesin theorem, is presented. The method is applied to a phenomenological Gamow–type model and it is concluded that in the classical limit the dynamics exhibited by its effective Hamiltonian is chaotic. © 2014, Springer Science+Business Media New York.

Registro:

Documento: Artículo
Título:A Semiclassical Condition for Chaos Based on Pesin Theorem
Autor:Gomez, I.; Losada, M.; Fortin, S.; Castagnino, M.; Portesi, M.
Filiación:Instituto de Física de Rosario (IFIR-CONICET), BV. 27 de Febrero 210 Bis Rosario, Santa Fe, 2000, Argentina
Departamento de Física (FCE, Universidad Nacional de La Plata), Instituto de Física La Plata (IFLP), C.C. 67, 1900, La Plata, Argentina
Instituto de Física de Rosario (IFIR-CONICET), BV. 27 de Febrero 210 Bis Rosario, Santa Fe, 2000, Argentina
CONICET - Departamento de Física, FCEN (UBA), Buenos Aires, Argentina
Instituto de Física de La Plata (CONICET-UNLP), Departamento de Física (FCE, Universidad Nacional de La Plata), C.C. 67, 115 y 49, (1900), La Plata, Argentina
Palabras clave:Classical limit; Kolmogorov–Sinai entropy; Lyapunov exponents; Pesin theorem
Año:2015
Volumen:54
Número:7
Página de inicio:2192
Página de fin:2203
DOI: http://dx.doi.org/10.1007/s10773-014-2437-6
Título revista:International Journal of Theoretical Physics
Título revista abreviado:Int. J. Theor. Phys.
ISSN:00207748
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207748_v54_n7_p2192_Gomez

Referencias:

  • Alicki, R., Lozinski, A., Pakonski, P., Zyczkowski, K., Quantum dynamical entropy and decoherence rate (2004) J. Phys. A, 37, pp. 5157-5172
  • Slomczynski, W., Zyczkowski, K., Quantum chaos: an entropy approach (1994) J. Math. Phys., 35, pp. 5674-5700
  • Slomczynski, W., Zyczkowski, K., Mean dynamical entropy of quantum maps on the sphere diverges in the semiclassical limit (1998) Phys. Rev. Lett., 80, pp. 1880-1883
  • Zyczkowski, K., Wiedemann, H., Slomczynski, W., How to generalize Lyapunov exponents for quantum mechanics (1993) Vistas Astron., 37, pp. 153-156
  • Cucchietti, F.M., Dalvit, D.A.R., Paz, J.P., Zurek, W.H., Decoherence and the Loschmidt Echo (2003) Phys. Rev. Lett., 91, p. 210403
  • Cucchietti, F.M., Pastawski, H.M., Jalabert, R.A., Universality of the Lyapunov regime of the Loschmidt echo (2004) Phys. Rev. B, 70, p. 035311
  • Monteoliva, D., Paz, J.P., Decoherence and the Rate of Entropy Production in Chaotic Quantum Systems (2000) Phys. Rev. Lett., 85, p. 3373
  • Monteoliva, D., Paz, J.P., Decoherence in a classically chaotic quantum system: Entropy production and quantum-classical correspondence (2001) Phys. Rev. E., 64, p. 056238
  • Bellot, G., Earman, J., Studies in History and Philosophy of Modern Physics (1997) Chaos out of order: Quantum mechanics, the correspondence principle and chaos, 28, pp. 147-182
  • Berkovitz, J., Frigg, R., Kronz, F., The Ergodic Hierarchy Randomness and Hamiltonian Chaos (2006) Stud. Hist. Philos. Mod. Phys., 37, pp. 661-691
  • Berry, M., Quantum chaology, not quantum chaos (1989) Phys. Scr., 40, pp. 335-336
  • Castagnino, M., Lombardi, O., Towards a definition of the quantum ergodic hierarchy: Ergodicity and mixing (2009) Phys. A, 388, pp. 247-267
  • Gomez, I., Castagnino, M., Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems (2014) Phys. A, 393, pp. 112-131
  • Gomez, I., Castagnino, M., On the classical limit of quantum mechanics, fundamental graininess and chaos: Compatibility of chaos with the correspondence principle, Chaos (2014) Solitons Fractals, 68, pp. 98-113
  • Stockmann, H., (1999) Quantum Chaos: An Introduction, page numbers, , Cambridge University Press, Cambridge
  • Haake, F., (2001) Quantum Signatures of Chaos, page numbers, , Springer-Verlag, Heidelberg
  • Gutzwiller, M.C., (1990) Chaos in Classical and Quantum Mechanics, page numbers, , Springer Verlag, New York
  • Casati, G., Chirikov, B., (1995) Quantum Chaos: between order and disorder, page numbers, , Cambridge University Press, Cambridge
  • Tabor, M., (1988) Chaos and Integrability in Nonlinear Dynamics: An Introduction, page numbers, , Wiley, New York
  • Omnès, R., (1994) The Interpretation of Quantum Mechanics, vol. 288, , Princeton University, Princeton
  • Laura, R., Castagnino, M., Functional approach for quantum systems with continuous spectrum (1998) Phys. Rev. E, 57, p. 3948
  • Lichtenberg, A.J., Lieberman, M.A., (2010) Regular and Chaotic Dynamics (Applied Mathematical Sciences), vol. 304, , Springer, Berlin
  • Pesin, Y., Characteristic exponents and smooth ergodic theory (1977) Russ. Math. Surv., 32, pp. 55-114
  • Young, L., (2003) Entropy, p. 283. , Princeton University Press, Princeton
  • Hillery, M., O’Connell, R., Scully, M., Wigner, E., Distribution functions in physics: Fundamentals (1984) Phys. Rep., 106, pp. 121-167
  • Dito, G., Sternheimer, D., Deformation quantization: genesis, development and metamorphosis (2002) IRMA Lect. Math. Theor. Phys., 1, pp. 9-54
  • Bayern, F., Flato, M., Fronsdal, M., Lichnerowicz, A., Sternheimer, D., Deformation theory and quantization. II, Physical applications (1978) Ann. Phys., 110, pp. 111-151
  • Antoniou, I., Suchanecki, Z., Laura, R., Tasaki, S., Intrinsic irreversibility of quantum systems with diagonal singularity (1997) Phys. A, 241, pp. 737-772
  • Gadella, M., Pronko, G., (2011) Fortschritte der Physik The Friedrichs model and its use in resonance phenomena, 59, pp. 795-859
  • Castagnino, M., Fortin, S., New bases for a general definition for the moving preferred basis (2011) Mod. Phys. Lett. A, 26, pp. 2365-2373
  • Ordonez, G., Kim, S., Complex collective states in a one-dimensional two-atom system (2004) Phys. Rev. A, 70, p. 032702
  • Bohm, A., (1986) Quantum mechanics, foundations and applications, pp. 549-563. , Springer Verlag, Berlin
  • Gilary, I., Fleischer, A., Moiseyev, N., Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution (2005) Phys. Rev. A, 72, p. 012117

Citas:

---------- APA ----------
Gomez, I., Losada, M., Fortin, S., Castagnino, M. & Portesi, M. (2015) . A Semiclassical Condition for Chaos Based on Pesin Theorem. International Journal of Theoretical Physics, 54(7), 2192-2203.
http://dx.doi.org/10.1007/s10773-014-2437-6
---------- CHICAGO ----------
Gomez, I., Losada, M., Fortin, S., Castagnino, M., Portesi, M. "A Semiclassical Condition for Chaos Based on Pesin Theorem" . International Journal of Theoretical Physics 54, no. 7 (2015) : 2192-2203.
http://dx.doi.org/10.1007/s10773-014-2437-6
---------- MLA ----------
Gomez, I., Losada, M., Fortin, S., Castagnino, M., Portesi, M. "A Semiclassical Condition for Chaos Based on Pesin Theorem" . International Journal of Theoretical Physics, vol. 54, no. 7, 2015, pp. 2192-2203.
http://dx.doi.org/10.1007/s10773-014-2437-6
---------- VANCOUVER ----------
Gomez, I., Losada, M., Fortin, S., Castagnino, M., Portesi, M. A Semiclassical Condition for Chaos Based on Pesin Theorem. Int. J. Theor. Phys. 2015;54(7):2192-2203.
http://dx.doi.org/10.1007/s10773-014-2437-6