Artículo

Kowalski, A.M.; Mart́in, M.T.; Plastino, A.; Rosso, O.A. "Chaos and complexity in the classical-quantum transition" (2012) International Journal of Applied Mathematics and Statistics. 26(2):67-80
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Abstract:

By recourse to the concept of Statistical Complexity we study here the classical-quantum transition in a special system that represents the matter-field interaction. Our work considers two distinct disequilibrium forms based on Euclidean norm and Jensen-Shannon divergence, on the one hand, and analyzes things, on the other one, by using two different numerical approaches for probability distribution, namely, relative wavelet energy and permutation patterns. © 2011-12 by IJAMAS, CESER Publications.

Registro:

Documento: Artículo
Título:Chaos and complexity in the classical-quantum transition
Autor:Kowalski, A.M.; Mart́in, M.T.; Plastino, A.; Rosso, O.A.
Filiación:Instituto de F́isica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata, Argentina
Departamento de F́isica, Instituto de Cîencias Exatas, Universidade Federal de Minas Gerais, Av. Ant̂onio Carlos, 6627 - Campus Pampulha, CEP 31.270-901, Belo Horizonte, MG, Brazil
Chaos and Biology Group, Instituto de Ćalculo Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Pabell ́on II, Ciudad Universitaria, 1428 Ciudad Autonoma de Buenos Aires, Argentina
Comisíon de Investigaciones Cient́ificas (CICPBA), Argentina
Consejo Nacional de Investigaciones Cient́ificas y T́ecnicas (CONICET), Argentina
Palabras clave:Quantum chaos; Semiclassical theories; Statistical complexity; Classical-quantum; Euclidean norm; Jensen-Shannon divergence; Numerical approaches; Permutation patterns; Quantum chaos; Semiclassical theories; Statistical complexity; Wavelet energy; Probability distributions; Quantum theory; Quantum interference devices
Año:2012
Volumen:26
Número:2
Página de inicio:67
Página de fin:80
Título revista:International Journal of Applied Mathematics and Statistics
Título revista abreviado:Int. J. Appl. Math. Stat.
ISSN:09731377
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09731377_v26_n2_p67_Kowalski

Referencias:

  • Bandt, C., Pompe, B., Permutation entropy: A natural complexity measure for time series (2002) Phys. Rev. Lett., 88, p. 174102
  • Bandt, C., Shiha, F., Order patterns in time series (2007) Journal of Time Series Analysis, 28, pp. 646-665
  • Bloch, F., Nuclear induction (1946) Phys. Rev., 70, pp. 460-474
  • Bonilla, L.L., Guinea, F., Collapse of the wave packet and chaos in a model with classical and quantum degrees of freedom (1992) Phys. Rev. A, 45, pp. 7718-7728
  • Brun, T.A., Continuous measurements, quantum trajectories, and decoherent histories (2000) Phys. Rev. A, 61, p. 042107
  • Brun, T.A., Halliwell, J.J., Decoherence of hydrodynamic histories: A simple spin model (1996) Phys. Rev. D, 54, pp. 2899-2912
  • Clark, T.D., Diggins, J., Ralph, J.F., Everitt, M., Prance, R.J.H.P., Whiteman, R., Widom, A., Srivastava, Y.N., Coherent evolution and quantum transitions in a two level model of a SQUID ring (1998) Annals of Physics, 268, pp. 1-30
  • Cooper, F., Dawson, J., Habib, S., Ryne, R.D., Chaos in time-dependent variational approximations to quantum dynamics (1998) Phys. Rev. E, 57, pp. 1489-1498
  • Díosi, L., Gisin, N., Halliwell, J., Percival, I.C., Decoherent histories and quantum state diffusion (1995) Phys. Rev. Lett., 74, pp. 203-207
  • Everitt, M.J., Recovery of classical chaotic-like behavior in a conservative quantum three-body problem (2007) Phys. Rev. E, 75, p. 036217
  • Everitt, M.J., Munro, W.J., Spiller, T.P., Quantum-classical crossover of a field mode (2009) Phys. Rev. A, 79, p. 032328
  • Ghose, S., Alsing, P., Deutsch, I., Bhattacharya, T., Habib, S., Transition to classical chaos in a coupled quantum system through continuous measurement (2004) Phys. Rev. A, 69, p. 052116
  • Ghose, S., Alsing, P., Deutsch, I., Bhattacharya, T., Habib, S., Jacobs, K., Recovering classical dynamics from coupled quantum systems through continuous measurement (2003) Phys. Rev. A, 67, p. 052102
  • Greenbaum, B.D., Habib, S., Shizume, K., Sundaram, B., The semiclassical regime of the chaotic quantum-classical transition (2005) Chaos, 15, p. 033302
  • Habib, S., Shizume, K., Zurek, W.H., Decoherence, chaos, and the correspondence principle (1998) Phys. Rev. Lett., 80, pp. 4361-4365
  • Halliwell, J.J., Yearsley, J.M., Arrival times, complex potentials, and decoherent histories (2009) Phys. Rev. A, 79, p. 062101
  • Katz, I., Retzker, A., Straub, R., Lifshitz, R., Signatures for a classical to quantum transition of a driven nonlinear nanomechanical resonator (2007) Phys. Rev. Lett., 99, p. 040404
  • Kociuba, G., Heckenberg, N.R., Controlling the complex Lorenz equations by modulation (2002) Phys. Rev. E, 66, p. 026205
  • Kolmogorov, A.N., A new metric invariant of transitive dynamic system and automorphysms in lebesgue spaces (1958) Dokl. Akad. Nauk. SSSR, 119, p. 861
  • Kowalski, A.M., Mart́in, M.T., Nuñez, J., Plastino, A., Proto, A.N., Quantitative indicator for semiquantum chaos (1998) Phys. Rev. A, 58, pp. 2596-2599
  • Kowalski, A.M., Mart́in, M.T., Plastino, A., Proto, A.N., Rosso, O.A., Wavelet statistical complexity analysis of classical limit (2003) Phys. Lett. A, 311, pp. 180-191
  • Kowalski, A.M., Mart́in, M.T., Plastino, A., Rosso, O.A., Entropic non-triviality, the classical limit, and geometry-dynamics correlations (2005) Int. J. of Modern Phys. B, 14, pp. 2273-2285
  • Kowalski, A.M., Mart́in, M.T., Plastino, A., Rosso, O.A., Bandt-pompe approach to the classical-quantum transition (2007) Physica D, 233, pp. 21-31
  • Kowalski, A.M., Plastino, A., Proto, A.N., Classical limits (2002) Phys. Lett. A, 297, pp. 162-172
  • Lamberti, P.W., Mart́in, M.T., Plastino, A., Rosso, O.A., Intensive entropic nontriviality measure (2004) Physica A, 334, pp. 119-131
  • Ĺopez-Ruiz, R., Mancini, H.L., Calbet, X., A statistical measure of complexity (1995) Phys. Lett. A, 209, pp. 321-326
  • Mallat, S., (1999) A wavelet tour of signal processing, , University Press, Cambridge
  • Mart́in, M.T., Plastino, A., Rosso, O.A., Statistical complexity and disequilibrium (2003) Phys. Lett. A, 311, pp. 126-132
  • Meystre, P., Sargent III, M., (1991) Elements of Quantum Optics, , Springer-Verlag
  • Milonni, P., Shih, M., Ackerhalt, J.R., (1987) Chaos in Laser-Matter Interactions, , World Scientific Publishing Co
  • Mischaikow, K., Mrozek, M., Reiss, J., Szymczak, A., Construction of symbolic dynamics from experimental time series (1999) Phys. Rev. Lett., 82, pp. 1114-1147
  • Powell, G.E., Percival, I.C., A spectral entropy method for distinguishing regular and irregular motion of hamiltonian systems (1979) J. Phys. A: Math. Gen., 12, pp. 2053-2071
  • Ring, P., Schuck, P., (1980) The Nuclear Many-Body Problem, , Springer-Verlag
  • Rosso, O.A., De Micco, L., Plastino, A., Larrondo, H.A., Info-quantifiers' mapcharacterization revisited (2010) Physica A, 389, pp. 4604-4612
  • Rosso, O.A., Mairal, L., Characterization of time dynamical evolution of electroencephalographic records (2002) Physica A, 312, pp. 469-504
  • Samar, V., Bopardikar, A., Rao, R., Swartz, K., Wavelet analysis of neuroelectric waveforms: a conceptual tutorial (1999) Brain Lang, 66, pp. 7-60
  • Shannon, C.E., A mathematical theory of communication (1948) Bell Syst. Technol. J., 27, pp. 379-423. , 623-656
  • Shiner, J.S., Davison, M., Landsberg, P.T., Simple measure for complexity (1999) Phys. Rev. E, 59, pp. 1459-1464
  • Sinai, Y.G., On the concept of entropy of dynamical system (1959) Dokl. Akad. Nauk. SSSR, 124, pp. 768-771
  • Thevenaz, P., Blue, T., Unser, M., Interpolation revisited (2000) IEEE Trans Med Imaging, 19, p. 739758
  • Zeh, H.D., Why bohm's quantum theory? (1999) Found. Phys. Lett., 12, pp. 197-200
  • Zurek, W.H., Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? (1981) Phys. Rev. D, 24, pp. 1516-1525
  • Zurek, W.H., Decoherence, einselection, and the quantum origins of the classical (2003) Rev. Mod. Phys., 75, pp. 715-775
  • Zurek, W., Habib, S., Paz, J., Coherent states via decoherence (1993) Phys. Rev. Lett., 70, pp. 1187-1190

Citas:

---------- APA ----------
Kowalski, A.M., Mart́in, M.T., Plastino, A. & Rosso, O.A. (2012) . Chaos and complexity in the classical-quantum transition. International Journal of Applied Mathematics and Statistics, 26(2), 67-80.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09731377_v26_n2_p67_Kowalski [ ]
---------- CHICAGO ----------
Kowalski, A.M., Mart́in, M.T., Plastino, A., Rosso, O.A. "Chaos and complexity in the classical-quantum transition" . International Journal of Applied Mathematics and Statistics 26, no. 2 (2012) : 67-80.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09731377_v26_n2_p67_Kowalski [ ]
---------- MLA ----------
Kowalski, A.M., Mart́in, M.T., Plastino, A., Rosso, O.A. "Chaos and complexity in the classical-quantum transition" . International Journal of Applied Mathematics and Statistics, vol. 26, no. 2, 2012, pp. 67-80.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09731377_v26_n2_p67_Kowalski [ ]
---------- VANCOUVER ----------
Kowalski, A.M., Mart́in, M.T., Plastino, A., Rosso, O.A. Chaos and complexity in the classical-quantum transition. Int. J. Appl. Math. Stat. 2012;26(2):67-80.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09731377_v26_n2_p67_Kowalski [ ]