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Statistical complexity of the kicked top model considering chaos

   | Jan 29, 2021

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[1] C. Adami, N. T. Cerf, Physical complexity of symbolic sequences, Physica D: Nonlinear Phenomena137 (2000) 62–69. doi:10.1016/S0167-2789(99)00179-7 ⇒28410.1016/S0167-2789(99)00179-7Search in Google Scholar

[2] C. Anteneodo, A. R. Plastino, Some features of the López-Ruiz-Manchini-Calbet (LMC) statistical measure of complexity, Physics Letters A223 (1996) 348–354. doi:10.1016/S0375-9601(96)00756-6 ⇒28410.1016/S0375-9601(96)00756-6Search in Google Scholar

[3] J. N. Bandyopadhyay, A. Lakshminarayan, Entanglement production in coupled chaotic systems: Case of the kicked tops Phys. Rev. E69 (2004) 016201. doi:10.1103/PhysRevE.69.016201 ⇒285, 29110.1103/PhysRevE.69.016201Search in Google Scholar

[4] J. N. Bandyopadhyay, A. Lakshminarayan, Testing Statistical Bounds on Entanglement Using Quantum Chaos Phys. Rev. Lett.89 (2002) 060402. doi:10.1103/PhysRevLett.89.060402 ⇒28410.1103/PhysRevLett.89.060402Search in Google Scholar

[5] M. Basseville, Information: Entropies, Divergences et Mayennes, (IRISA) Publication Interne 1020 (1996) (Campus Universitaire de Beaulieu, 35042 Rennes Cedex, France). ⇒287Search in Google Scholar

[6] J. Bene, P. Szépfalusy, A. Fülöp Generic dynamical phase-transition in chaotic Hamiltonian-systems Phys. Rev. A40 (1989) 6719–6722. doi:10.1103/physreva.40.6719 ⇒29310.1103/PhysRevA.40.6719Search in Google Scholar

[7] D. Bensimon, L. P. Kadano, Extended chaos and disappearance of KAM trajectories Physica D: Nonlinear Phenomena13 (1984) 82–89. doi:10.1016/0167-2789(84)90271-9 ⇒29310.1016/0167-2789(84)90271-9Search in Google Scholar

[8] P. M. Binder, N. Perry, Comment II on: Simple measure of complexity. Phys. Rev. E62 (2000) 2998–2999. ⇒288Search in Google Scholar

[9] U. T. Bhosale and M. S. Santhanam, Signatures of bifurcation on quantum correlations: Case of the quantum kicked top Phys. Rev. E95 (2016) 012216. doi:10.1103/PhysRevE.95.012216 ⇒284, 285, 29110.1103/PhysRevE.95.012216Search in Google Scholar

[10] U. T. Bhosale, M. S. Santhanam Periodicity of quantum correlations in the quantum kicked top, Phys. Rev. E98 (2018) 052228. doi:10.1103/physreve.98.052228 ⇒28510.1103/PhysRevE.98.052228Search in Google Scholar

[11] G. Boffetta, M. Cencini, M. Falcioni, A. Vulpiani, Predictability: a way to characterize complexity, Phys. Reports356 (2002) 367–474. doi:10.1016/S0370-1573(01)00025-4 ⇒28410.1016/S0370-1573(01)00025-4Search in Google Scholar

[12] J. Briet, P. Harremoes, Properties of classical and quantum Jensen-Shannon divergence. Phys. Rev. A79 (2009) 052311. ⇒288Search in Google Scholar

[13] X. Calbet, R. López-Ruiz, Tendency towards maximum complexity in a nonequlibrium isolated system, Phys. Rev. E63 066116. ⇒28910.1103/PhysRevE.63.06611611415182Search in Google Scholar

[14] S. Chaudhury, A. Smith, B. E. Anderson, S. Ghose, P. S. Jessen, Quantum signatures of chaos in a kicked top Nature461 (2009) 768. ⇒285Search in Google Scholar

[15] B. V. Chirikov A universal instability of many-dimensional oscillator systems Phys. Rep.52 (1979) 265. ⇒29310.1016/0370-1573(79)90023-1Search in Google Scholar

[16] J. P. Crutchfield, D.P. Feldman, C.R. Shalizi Comment I on: simple measure of complexity. Phys.Rev. E62 (2000) 2996–2997. ⇒288Search in Google Scholar

[17] J. P. Crutchfield, K. Young, Inferring statistical complexity, Phys. Rev. Lett.63 (1989) 105. ⇒283, 28410.1103/PhysRevLett.63.105Search in Google Scholar

[18] D. P. Feldman, J. P. Crutchfield, Measures of statistical complexity: Why? Phys. Lett. A238 (1998)244–252. ⇒28410.1016/S0375-9601(97)00855-4Search in Google Scholar

[19] G. L. Ferri, F. Pennini, A. Plastino, LMC-complexity and various chaotic regime, Physics Letters A373 (2009) 2210–2214. ⇒28410.1016/j.physleta.2009.04.062Search in Google Scholar

[20] H. Fujisaki, T. Miyadera, A. Tanaka, Dynamical aspects of quantum entanglement for weakly coupled kicked tops Phys. Rev. E67, (2003)066201. ⇒285Search in Google Scholar

[21] Á. Fülöp, Estimation of the Kolmogorov entropy in the generalized number system, Annales Univ. Sci. Budapest Sect. Comp.40 (2013) 245–256. ⇒295Search in Google Scholar

[22] Á. Fülöp, Statistical complexity and generalized number system, Acta Univ. Sapientiae, Informatica 6 (2) (2014) 230–251. ⇒284Search in Google Scholar

[23] T. Geisel, G. Radons, J. Rubner, Kolmogorov-Arnold-Moser Barriers in the Quantum Dynamics of Chaotic Systems Phys Rew. Letters57 (1986) 2883. ⇒293, 294Search in Google Scholar

[24] S. Ghose, R. Stock, P. Jessen, R. Lal, A. Silberfarb, Chaos, entanglement, and decoherence in the quantum kicked top Phys. Rev. A78 (2008) 042318. ⇒284Search in Google Scholar

[25] C. M. Gonzalez, H. A Larrondo, O. A. Rosso, Statistical complexity measure of pseudorandom bit generators, Physica A354 (2005) 281. ⇒284Search in Google Scholar

[26] P. Grassberger, Toward a Quantitative Theory of self-generated complexity, Int. Journ. Theor. Phys.25 (1988) 907–938. ⇒28310.1007/BF00668821Search in Google Scholar

[27] J. M. Greene A method for determining a stochastic transition J. Math. Phys.20 (1979) 1183. ⇒29310.1063/1.524170Search in Google Scholar

[28] F. Haake, M. Kus, R. Scharf, Classical and quantum chaos for a kicked top Z. Phys. B65 (1987) 381. ⇒291Search in Google Scholar

[29] F. Haake, D. L. Shepelyansky, The kicked rotator as a limit of the kicked top, EPL (Europhys Lett.)5 (1988) 671. ⇒29410.1209/0295-5075/5/8/001Search in Google Scholar

[30] A. N. Kolmogorov, Entropy per unit time as a metric invariant of automorphism, Doklady of Russian Academy of Sciences, 124 (1959) 754–755. ⇒283Search in Google Scholar

[31] A. M. Kowalski, M. T. Martin, A. Plastino, O. A. Rosso, M. Casas, Distances in probability space and the statistical complexity setup, Entropy13 (2011) 1055–1075. ⇒28610.3390/e13061055Search in Google Scholar

[32] S. Kullback, R. A Leibler, On information and sufficiency Ann. Math. Stat.22 (1951)79—86. ⇒28710.1214/aoms/1177729694Search in Google Scholar

[33] M. Kumari, S. Ghose Quantum-classical correspondence in the vicinity of periodic orbits Phys. Rev. E97 (2018) 052209. ⇒284, 291Search in Google Scholar

[34] A. Lakshminarayan, Entangling power of quantized chaotic systems Phys. Rev. E64 2001 036207. ⇒28410.1103/PhysRevE.64.03620711580422Search in Google Scholar

[35] P. W. Lamberti, M. T. Martin, A. Plastino, O. A. Rosso, Intensive entropic nontriviality measure, Physica A334 (2004) 119—131. ⇒284, 286, 28710.1016/j.physa.2003.11.005Search in Google Scholar

[36] A. Lempel, J. Ziv On the complexity of finite sequences, IEEE Trans. Inform Theory22 (1976) 75–81. ⇒283, 28410.1109/TIT.1976.1055501Search in Google Scholar

[37] M. Lombardi, A. Matzkin, Entanglement and chaos in the kicked top Phys. Rev. E83, 2001 016207 (2011). ⇒284, 28510.1103/PhysRevE.83.016207Search in Google Scholar

[38] R. López-Ruiz, H.L. Mancini, X. Calbet, A statistical measure of complexity, Phys. Letters A209 (1995) 321–326. ⇒284, 286, 287, 28910.1016/0375-9601(95)00867-5Search in Google Scholar

[39] M. Lovallo, V. Lapenna, L. Telesca, Transitionmatrix analysis of earthquake magnitude sequences Chaos, soliton and fractals24 (1) (2005) 33–43. ⇒284Search in Google Scholar

[40] R. S. Mackay, J. D. Meiss, I. C. Shepelyanski Transport in Hamiltonian systems, Physica13D (1984) 55. ⇒293Search in Google Scholar

[41] V. Madhok, V. Gupta, D. A. Trottier, S. Ghose, Signatures of chaos in the dynamics of quantum discord, Phys. Rev. E91 (2015) 032906. ⇒285, 291Search in Google Scholar

[42] V. Madhok, S. Dogra, A. Lakshminarayan, Quantum correlations as probes of chaos and ergodicity Opt. Commun.420(2018) 189. ⇒284Search in Google Scholar

[43] M. T. Martin, A. Plastino, O. A. Rosso, Statistical complexity and disequilibrium, Physics Letters A311 (2003) 126–132. ⇒284, 286, 28710.1016/S0375-9601(03)00491-2Search in Google Scholar

[44] M. T. Martin, A. Plastino, O. A. Rosso, Generalized statistical complexity measures: Geometrical and analytical properties, Physica A369 (2006) 439–462. ⇒288Search in Google Scholar

[45] P. A. Miller, S. Sarkar, Signatures of chaos in the entanglement of two coupled quantum kicked tops Phys. Rev. E60 (1999) 1542. ⇒284Search in Google Scholar

[46] H. Ming-Lian, X. Xiao-Qiang, Mixedness of the N-qubit states with exchange symmetry Chinese Physics B17, 10 (2008) 3559. doi:10.1088/1674-1056/17/10/006 ⇒29010.1088/1674-1056/17/10/006Search in Google Scholar

[47] C. Neill, P. Roushan, M. Fang, Y. Chen, M. Kolodrubetz, Z. Chen, A. Megrant, R. Barends, B. Campbell, B. Chiaro et al., Ergodic dynamics and thermalization in an isolated quantum system Nat. Phys.12 (2016) 1037–1041. doi:10.1038/nphys3830 ⇒285, 29110.1038/nphys3830Search in Google Scholar

[48] A. Piga, M. Lewenstein, J. Q. Quach Quantum chaos and entanglement in ergodic and nonergodic systems, Phys. Rev. E99 (2019) 032213. ⇒284Search in Google Scholar

[49] A. R. Plastino, A. Plastino, Symmetries of the Fokker-Plank equation and Fisher-Frieden arrow of time, Phys. Rev. E54 (1996) 4423–4326. ⇒28910.1103/PhysRevE.54.4423Search in Google Scholar

[50] O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino, M. A. Fuentes, Distinguishing noise from chaos, Phys. Rev. Lett.99 (2007) 154102. doi:10.1103/PhysRevLett.99.154102 ⇒28910.1103/PhysRevLett.99.15410217995170Search in Google Scholar

[51] O. A. Rosso, L. De Micco, H. A. Larrondo, M. T. Martin, A. Plastino, Generalized statistical complexity measure, Int. J. Bif. Chaos20 (2010) 775—785. doi:10.1142/S021812741002606X ⇒286, 28910.1142/S021812741002606XSearch in Google Scholar

[52] J. B. Ruebeck, J. Lin, and A. K. Pattanayak, Entanglement and its relationship to classical dynamics Phys. Rev. E95 (2017)062222. ⇒284, 285Search in Google Scholar

[53] C.E. Shannon, The Mathematical Theory of Communication, Bell System Technical Journal, 27 (1948) 379–423, 623–656. ⇒286Search in Google Scholar

[54] S.J. Shenker, L.P. Kadanoff Critical behavior of a KAM surface: I. Empirical results J. Stat. Phys.27 (1982) 631. ⇒293Search in Google Scholar

[55] J.S. Shiner, M. Davison, P.T. Landsberg, Simple measure for complexity, Phys. Rev. E59(2)(1999)1459–1464. ⇒284, 288Search in Google Scholar

[56] J.S. Shiner, M. Davison, P.T Landsberg, Replay to comments on: simple measure for complexity. Phys. Rev. E62 (2000) 3000–3003. ⇒288Search in Google Scholar

[57] G. Stamatiou and D. P. K. Ghikas, Quantum entanglement dependence on bifurcations and scars in non-autonomous systems. The case of quantum kicked top Phys. Lett. A368 (2007) 206. ⇒284Search in Google Scholar

[58] C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys.52 (1988) 479. ⇒284Search in Google Scholar

[59] R. Wackerbauer, R.A. Witt, H. Atmanspacher, J. Kurths, H. Scheingraber, A comparative classification of complexity-measures. Chaos Solitons Fractals4 (1994) 133–173. ⇒284Search in Google Scholar

[60] X. Wang, S. Ghose, B. C. Sanders, and B. Hu Entanglement as a signature of quantum chaos Phys. Rev. E70 (2004) 016217. ⇒284Search in Google Scholar

[61] W.K. Wootters, Statistical distance and Hilbert space, Phys. Rev. D23 (1981) 357. ⇒284, 287Search in Google Scholar

[62] R. Zarum and S. Sarkar Quantum-classical correspondence of entropy contours in the transition to chaos Phys. Rev. E57 (1998) 5467. ⇒285Search in Google Scholar

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