Chaos and complexity in the classical-quantum transition

International Journal of Applied Mathematics and Statistics

Volumn 26, Issue 2, 2012, Pages 67-80

  Kowalski, A M ^a,d   Martin M T ^a,e   Plastino, A ^a,e   Rosso, O A ^b,c,e  

^a INSTITUTO DE FÍSICA LA PLATA   (Argentina)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^c INSTITUTO DE CÁLCULO   (Argentina)

^d Comisíon de Investigaciones Cient́ificas ^*  (Argentina)

^e Universidad Nacional de Río Cuarto Consejo Nacional de Investigaciones Científicas y Técnicas   (Argentina)

Author keywords

Quantum chaos; Semiclassical theories; Statistical complexity

Indexed keywords

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;

EID: 84866745321     PISSN: 09731377     EISSN: 09737545     Source Type: Journal    
DOI: None     Document Type: Article

References (44)

1. Bandt, C. and Pompe, B. 2002. Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett. 88: 174102.
2. Bandt, C. and Shiha, F. 2007. Order patterns in time series, Journal of Time Series Analysis 28: 646-665.
3. Bloch, F. 1946. Nuclear induction, Phys. Rev. 70: 460-474.
4. Bonilla, L. L. and Guinea, F. 1992. Collapse of the wave packet and chaos in a model with classical and quantum degrees of freedom, Phys. Rev. A 45: 7718-7728.
5. Brun, T. A. 2000. Continuous measurements, quantum trajectories, and decoherent histories, Phys. Rev. A 61: 042107.
6. Brun, T. A. and Halliwell, J. J. 1996. Decoherence of hydrodynamic histories: A simple spin model, Phys. Rev. D 54: 2899-2912.
7. Clark, T. D., Diggins, J., Ralph, J. F., Everitt, M., Prance, R. J., H., P., Whiteman, R., Widom, A. and Srivastava, Y. N. 1998. Coherent evolution and quantum transitions in a two level model of a SQUID ring, Annals of Physics 268: 1-30.
8. Cooper, F., Dawson, J., Habib, S. and Ryne, R. D. 1998. Chaos in time-dependent variational approximations to quantum dynamics, Phys. Rev. E 57: 1489-1498.
9. Díosi, L., Gisin, N., Halliwell, J. and Percival, I. C. 1995. Decoherent histories and quantum state diffusion, Phys. Rev. Lett. 74: 203-207.
10. Everitt, M. J. 2007. Recovery of classical chaotic-like behavior in a conservative quantum three-body problem, Phys. Rev. E 75: 036217.
11. Everitt, M. J., Munro, W. J. and Spiller, T. P. 2009. Quantum-classical crossover of a field mode, Phys. Rev. A 79: 032328.
12. Ghose, S., Alsing, P., Deutsch, I., Bhattacharya, T. and Habib, S. 2004. Transition to classical chaos in a coupled quantum system through continuous measurement, Phys. Rev. A 69: 052116.
13. Ghose, S., Alsing, P., Deutsch, I., Bhattacharya, T., Habib, S. and Jacobs, K. 2003. Recovering classical dynamics from coupled quantum systems through continuous measurement, Phys. Rev. A 67: 052102.
14. Greenbaum, B. D., Habib, S., Shizume, K. and Sundaram, B. 2005. The semiclassical regime of the chaotic quantum-classical transition, Chaos 15: 033302.
15. Habib, S., Shizume, K. and Zurek, W. H. 1998. Decoherence, chaos, and the correspondence principle, Phys. Rev. Lett. 80: 4361-4365.
16. Halliwell, J. J. and Yearsley, J. M. 2009. Arrival times, complex potentials, and decoherent histories, Phys. Rev. A 79: 062101.
17. Katz, I., Retzker, A., Straub, R. and Lifshitz, R. 2007. Signatures for a classical to quantum transition of a driven nonlinear nanomechanical resonator, Phys. Rev. Lett. 99: 040404.
18. Kociuba, G. and Heckenberg, N. R. 2002. Controlling the complex Lorenz equations by modulation, Phys. Rev. E 66: 026205.
19. Kolmogorov, A. N. 1958. A new metric invariant of transitive dynamic system and automorphysms in lebesgue spaces, Dokl. Akad. Nauk. SSSR 119: 861.
20. Kowalski, A. M., Mart́in, M. T., Nuñez, J., Plastino, A. and Proto, A. N. 1998. Quantitative indicator for semiquantum chaos, Phys. Rev. A 58: 2596-2599.
21. Kowalski, A. M., Mart́in, M. T., Plastino, A., Proto, A. N. and Rosso, O. A. 2003. Wavelet statistical complexity analysis of classical limit, Phys. Lett. A 311: 180-191.
22. Kowalski, A. M., Mart́in, M. T., Plastino, A. and Rosso, O. A. 2005. Entropic non-triviality, the classical limit, and geometry-dynamics correlations, Int. J. of Modern Phys. B 14: 2273-2285.
23. Kowalski, A. M., Mart́in, M. T., Plastino, A. and Rosso, O. A. 2007. Bandt-pompe approach to the classical-quantum transition, Physica D 233: 21-31.
24. Kowalski, A. M., Plastino, A. and Proto, A. N. 2002. Classical limits, Phys. Lett. A 297: 162-172.
25. Lamberti, P. W., Mart́in, M. T., Plastino, A. and Rosso, O. A. 2004. Intensive entropic nontriviality measure, Physica A 334: 119-131.
26. Ĺopez-Ruiz, R., Mancini, H. L. and Calbet, X. 1995. A statistical measure of complexity, Phys. Lett. A 209: 321-326.
27. Mallat, S. 1999. A wavelet tour of signal processing, University Press, Cambridge.
28. Mart́in, M. T., Plastino, A. and Rosso, O. A. 2003. Statistical complexity and disequilibrium, Phys. Lett. A 311: 126-132.
29. Meystre, P. and Sargent III, M. 1991. Elements of Quantum Optics, Springer-Verlag.
30. Milonni, P., Shih, M. and Ackerhalt, J. R. 1987. Chaos in Laser-Matter Interactions, World Scientific Publishing Co.
31. Mischaikow, K., Mrozek, M., Reiss, J. and Szymczak, A. 1999. Construction of symbolic dynamics from experimental time series, Phys. Rev. Lett. 82: 1114-1147.
32. Powell, G. E. and Percival, I. C. 1979. A spectral entropy method for distinguishing regular and irregular motion of hamiltonian systems, J. Phys. A: Math. Gen. 12: 2053-2071.
33. Ring, P. and Schuck, P. 1980. The Nuclear Many-Body Problem, Springer-Verlag.
34. Rosso, O. A., De Micco, L., Plastino, A. and Larrondo, H. A. 2010. Info-quantifiers' mapcharacterization revisited, Physica A 389: 4604-4612.
35. Rosso, O. A. and Mairal, L. 2002. Characterization of time dynamical evolution of electroencephalographic records, Physica A 312: 469-504.
36. Samar, V., Bopardikar, A., Rao, R. and Swartz, K. 1999. Wavelet analysis of neuroelectric waveforms: a conceptual tutorial, Brain Lang 66: 7-60.
37. Shannon, C. E. 1948. A mathematical theory of communication, Bell Syst. Technol. J. 27: 379-423; 623-56.
38. Shiner, J. S., Davison, M. and Landsberg, P. T. 1999. Simple measure for complexity, Phys. Rev. E 59: 1459-1464.
39. Sinai, Y. G. 1959. On the concept of entropy of dynamical system, Dokl. Akad. Nauk. SSSR 124: 768-771.
40. Thevenaz, P., Blue, T. and Unser, M. 2000. Interpolation revisited, IEEE Trans Med Imaging 19: 739758.
41. Zeh, H. D. 1999. Why bohm's quantum theory?, Found. Phys. Lett. 12: 197-200.
42. Zurek, W. H. 1981. Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?, Phys. Rev. D 24: 1516-1525.
43. Zurek, W. H. 2003. Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75: 715-775.
44. Zurek, W., Habib, S. and Paz, J. 1993. Coherent states via decoherence, Phys. Rev. Lett. 70: 1187-1190.