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Mantica, Giorgio

The multiparticle quantum Arnol’d cat: a test case for the decoherence approach to quantum chaos. (English) Zbl 1524.81058

J. Sib. Fed. Univ., Math. Phys. 3, No. 3, 369-380 (2010).
Summary: A multi-particle extension of the Arnol’d Cat Hamiltonian system is defined and examined. We propose to compute its Alicki-Fannes quantum dynamical entropy, to validate (or disprove) the validity of the decoherence approach to quantum chaos. A first set of numerical experiments is presented and discussed.

MSC:

81Q50 Quantum chaos
81P17 Quantum entropies

Keywords:

symbolic dynamics; chaos; quantum mechanics; dynamical entropies; decoherence
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References:

[1] M. Brune, E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wunderlich, J. M. Raimond, S. Haroche, Phys. Rev. Lett., 77 (1996), 4887 · doi:10.1103/PhysRevLett.77.4887
[2] E. Joos, H. D. Zeh, Z. Phys. B, 59 (1985), 223-243 · doi:10.1007/BF01725541
[3] T. Dittrich, R. Graham, Phys. Rev. A, 42 (1990), 4647 · doi:10.1103/PhysRevA.42.4647
[4] A. R. Kolovsky, Europhys. Lett., 27 (1994), 79 · Zbl 1055.81576 · doi:10.1063/1.166201
[5] W. H. Zurek, J. P. Paz, Phys. Rev. Lett., 72 (1994), 2508 · Zbl 1194.81111 · doi:10.1016/0167-2789(94)00271-Q
[6] I. Guarneri, Lett. Nuovo Cimento, 40 (1984), 171-175 · doi:10.1007/BF02719543
[7] E. Ott, T. M. Antonsen, J. D. Hanson, Phys. Rev. Lett., 53 (1984), 2187 · doi:10.1103/PhysRevLett.53.2187
[8] A. K. Pattanayak, B. Sundaram, B. J. Greenbaum, Phys. Rev. Lett., 90 (2003), 14103 · doi:10.1103/PhysRevLett.90.014103
[9] V. I. Arnold, A. Avez, Ergodic problems of classical mechanics, Benjamin, New York, 1968 · Zbl 0715.70004
[10] J. H. Hannay, M. V. Berry, Physica D, 1 (1980), 267-291 · Zbl 1194.81107 · doi:10.1016/0167-2789(80)90026-3
[11] J. Ford, G. Mantica, G. Ristow, Physica D, 50 (1991), 493-520 · Zbl 0742.58024 · doi:10.1119/1.16954
[12] G. Casati, B. V. Chirikov, Phys. Rev. Lett., 75 (1995), 350 · doi:10.1103/PhysRevLett.75.350
[13] A. Ostruszka, P. Pakoński, W. Slomczyński, K. Zyczkowski, Phys. Rev. E, 62 (2000), 2018 · doi:10.1103/PhysRevE.62.2018
[14] A. J. Scott, T. A. Brun, C. M. Caves, R. Schack, J. Phys. A, 39 (2006), 13405-13433 · Zbl 1105.81041 · doi:10.1088/0305-4470/39/43/002
[15] G. Benenti, G. Casati, Phys. Rev. E, 79 (2009), 025201(R) · doi:10.1103/PhysRevE.79.025201
[16] V. V. Sokolov, O. V. Zhirov, G. Benenti, G. Casati, Phys. Rev. E, 78 (2008), 046212 · doi:10.1103/PhysRevE.78.046212
[17] M.-J. Giannoni, A. Voros, J. Zinn-Justin (eds.), Chaos and Quantum Physics, Les Houches Lecture Series, 52, North-Holland, Amsterdam, 1991
[18] J. Ford, Physics Today, 36 (1983), 40 · doi:10.1063/1.2915570
[19] R. Kosloff, S. A. Rice, J. Chem. Phys., 74 (1980), 1340-1349 · doi:10.1063/1.441196
[20] J. W. Helton, M. Tabor, J. Phys. A Math. Gen., 18 (1985), 2743 · doi:10.1088/0305-4470/18/14/025
[21] B. V. Chirikov, F. Vivaldi, Physica D, 129 (1999), 223 · Zbl 0960.81022 · doi:10.1016/S0167-2789(98)00319-4
[22] G. Mantica, Phys. Rev. E, 61 (2000), 6434-6443 · doi:10.1103/PhysRevE.61.6434
[23] A. Crisanti, M. Falcioni, G. Mantica, A. Vulpiani, Phys. Rev. E, 50 (1994), 1959-1967 · doi:10.1103/PhysRevE.50.1959
[24] R. Alicki, M. Fannes, Lett. Math. Phys., 32 (1994), 75-82 · Zbl 0814.46055 · doi:10.1007/BF00761125
[25] R. Alicki, D. Makowiec, W. Miklaszewski, Phys. Rev. Lett., 77 (1996), 838-841 · doi:10.1103/PhysRevLett.77.838
[26] R. Griffiths, J. Stat. Phys., 36 (1984), 219 · Zbl 0677.03042 · doi:10.1007/BF01014232
[27] R. Alicki, A. Lozinski, P. Pakoński, K. Zyczkowski, J. Phys. A Math. Gen., 37 (2004), 5157-5172 · Zbl 1054.81009 · doi:10.1088/0305-4470/37/19/004
[28] W. H. Zurek, Rev. Modern Phys., 75 (2003), 715-775 · Zbl 1205.81031 · doi:10.1103/RevModPhys.75.715
[29] P. Bianucci, J. P. Paz, M. Saraceno, Phys. Rev. E, 65 (2002), 46226 · doi:10.1103/PhysRevE.65.046226
[30] D. Monteoliva, J. P. Paz, Phys. Rev. Lett., 85 (2000), 3373 · doi:10.1103/PhysRevLett.85.3373
[31] T. A. Brun, I. Percival, R. Schack, J. Phys. A Math. Gen., 28 (1995), 5401-5413 · Zbl 0902.58034 · doi:10.1088/0305-4470/29/9/020
[32] M. Degli Esposti, S. Graffi, S. Isola, Comm. Math. Phys., 167 (1995), 471-507 · Zbl 0822.58022 · doi:10.1007/BF02101532
[33] J. Schwinger, Proc. National Academy of Sciences, 46 (1960), 570 · Zbl 0090.19006 · doi:10.1073/pnas.46.4.570
[34] G. F. Dell’Antonio, R. Figari, A. Teta, Ann. Inst. H. Poincare A, 60 (199), 253-290 · Zbl 1073.81511 · doi:10.1142/S0217979204024288
[35] G. Mantica, Electron. Trans. Numer. Anal., 28 (2007), 190-205 · Zbl 1188.65035
[36] M. Pogorzelska, R. Alicki, J. Phys. A Math. Gen., 40 (2007), 3379-3388 · Zbl 1113.81059 · doi:10.1088/1751-8113/40/13/006
[37] J. Halliwell, A. Zoupas, Phys. Rev. D, 52 (1995), 7294-7307 · doi:10.1103/PhysRevD.52.7294
[38] I. Percival, Quantum State Diffusion, Cambridge Univ. Press, Cambridge, UK, 1998 · Zbl 0946.60093
[39] F. Benatti, V. Cappellini, F. Zertuche, J. Phys. A Math. Gen., 37 (2004), 105-130 · Zbl 1042.37024 · doi:10.1088/0305-4470/37/1/007
[40] M. Falcioni, G. Mantica, S. Pigolotti, A. Vulpiani, Phys. Rev. Lett., 91 (2003), 044101 · doi:10.1103/PhysRevLett.91.044101
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