Geodesic
The multiparticle quantum Arnol'd Cat: a~test case for the decoherence approach to quantum chaos
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 369-380.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: symbolic dynamics, quantum mechanics, dynamical entropies, decoherence.
Mots-clés : chaos 
@article{JSFU_2010_3_3_a10,
     author = {Giorgio Mantica},
     title = {The multiparticle quantum {Arnol'd} {Cat:} a~test case for the decoherence approach to quantum chaos},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {369--380},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a10/}
}
TY  - JOUR
AU  - Giorgio Mantica
TI  - The multiparticle quantum Arnol'd Cat: a~test case for the decoherence approach to quantum chaos
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2010
SP  - 369
EP  - 380
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a10/
LA  - en
ID  - JSFU_2010_3_3_a10
ER  - 
%0 Journal Article
%A Giorgio Mantica
%T The multiparticle quantum Arnol'd Cat: a~test case for the decoherence approach to quantum chaos
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2010
%P 369-380
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a10/
%G en
%F JSFU_2010_3_3_a10
Giorgio Mantica. The multiparticle quantum Arnol'd Cat: a~test case for the decoherence approach to quantum chaos. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 369-380. http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a10/

[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

[2] E. Joos, H. D. Zeh, Z. Phys. B, 59 (1985), 223–243 | DOI

[3] T. Dittrich, R. Graham, Phys. Rev. A, 42 (1990), 4647 | DOI

[4] A. R. Kolovsky, Europhys. Lett., 27 (1994), 79 ; Chaos, 6 (1996), 534–542 | DOI | DOI | MR | Zbl

[5] W. H. Zurek, J. P. Paz, Phys. Rev. Lett., 72 (1994), 2508 ; Physica D, 83 (1995), 300 | DOI | DOI

[6] I. Guarneri, Lett. Nuovo Cimento, 40 (1984), 171–175 | DOI | MR

[7] E. Ott, T. M. Antonsen, J. D. Hanson, Phys. Rev. Lett., 53 (1984), 2187 | DOI

[8] A. K. Pattanayak, B. Sundaram, B. J. Greenbaum, Phys. Rev. Lett., 90 (2003), 14103 | DOI

[9] V. I. Arnold, A. Avez, Ergodic problems of classical mechanics, Benjamin, New York, 1968 | MR

[10] J. H. Hannay, M. V. Berry, Physica D, 1 (1980), 267–291 | DOI | MR

[11] J. Ford, G. Mantica, G. Ristow, Physica D, 50 (1991), 493–520 ; J. Ford, G. Mantica, Am. J. Phys., 60 (1992), 1086–1098 | DOI | MR | Zbl | DOI | MR

[12] G. Casati, B. V. Chirikov, Phys. Rev. Lett., 75 (1995), 350 | DOI

[13] A. Ostruszka, P. Pakoński, W. Slomczyński, K. Zyczkowski, Phys. Rev. E, 62 (2000), 2018 | DOI | MR

[14] A. J. Scott, T. A. Brun, C. M. Caves, R. Schack, J. Phys. A, 39 (2006), 13405–13433 | DOI | MR | Zbl

[15] G. Benenti, G. Casati, Phys. Rev. E, 79 (2009), 025201(R) | DOI | MR

[16] V. V. Sokolov, O. V. Zhirov, G. Benenti, G. Casati, Phys. Rev. E, 78 (2008), 046212 | DOI | MR

[17] M.-J. Giannoni, A. Voros, J. Zinn-Justin (eds.), Chaos and Quantum Physics, Les Houches Lecture Series, 52, North-Holland, Amsterdam, 1991 | MR

[18] J. Ford, Physics Today, 36 (1983), 40 | DOI

[19] R. Kosloff, S. A. Rice, J. Chem. Phys., 74 (1980), 1340–1349 | DOI | MR

[20] J. W. Helton, M. Tabor, J. Phys. A Math. Gen., 18 (1985), 2743 | DOI | MR

[21] B. V. Chirikov, F. Vivaldi, Physica D, 129 (1999), 223 | DOI | MR | Zbl

[22] G. Mantica, Phys. Rev. E, 61 (2000), 6434–6443 | DOI

[23] A. Crisanti, M. Falcioni, G. Mantica, A. Vulpiani, Phys. Rev. E, 50 (1994), 1959–1967 | DOI | MR

[24] R. Alicki, M. Fannes, Lett. Math. Phys., 32 (1994), 75–82 | DOI | MR | Zbl

[25] R. Alicki, D. Makowiec, W. Miklaszewski, Phys. Rev. Lett., 77 (1996), 838–841 | DOI

[26] R. Griffiths, J. Stat. Phys., 36 (1984), 219 ; R. Omnès, J. Stat. Phys., 53 (1988), 893 ; J. Stat. Phys., 53 (1988), 933 ; J. Stat. Phys., 53 (1988), 957 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | DOI | MR

[27] R. Alicki, A. Lozinski, P. Pakoński, K. Zyczkowski, J. Phys. A Math. Gen., 37 (2004), 5157–5172 | DOI | MR | Zbl

[28] W. H. Zurek, Rev. Modern Phys., 75 (2003), 715–775 | DOI | MR

[29] P. Bianucci, J. P. Paz, M. Saraceno, Phys. Rev. E, 65 (2002), 46226 | DOI

[30] D. Monteoliva, J. P. Paz, Phys. Rev. Lett., 85 (2000), 3373 | DOI

[31] T. A. Brun, I. Percival, R. Schack, J. Phys. A Math. Gen., 28 (1995), 5401–5413 ; J. Phys. A Math. Gen., 29 (1996), 2077–2090 | DOI | MR | Zbl | DOI | MR | Zbl

[32] M. Degli Esposti, S. Graffi, S. Isola, Comm. Math. Phys., 167 (1995), 471–507 | DOI | MR | Zbl

[33] J. Schwinger, Proc. National Academy of Sciences, 46 (1960), 570 | DOI | MR | Zbl

[34] G. F. Dell'Antonio, R. Figari, A. Teta, Ann. Inst. H. Poincare A, 60 (199), 253–290 ; R. Carlone, R. Figari, A. Teta, Int. Journal of Mod. Phys. B, 18 (2004), 667–674 | MR | DOI | Zbl

[35] G. Mantica, Electron. Trans. Numer. Anal., 28 (2007), 190–205 | MR | Zbl

[36] M. Pogorzelska, R. Alicki, J. Phys. A Math. Gen., 40 (2007), 3379–3388 | DOI | MR | Zbl

[37] J. Halliwell, A. Zoupas, Phys. Rev. D, 52 (1995), 7294–7307 | DOI | MR

[38] I. Percival, Quantum State Diffusion, Cambridge Univ. Press, Cambridge, UK, 1998 | MR | Zbl

[39] F. Benatti, V. Cappellini, F. Zertuche, J. Phys. A Math. Gen., 37 (2004), 105–130 | DOI | MR | Zbl

[40] M. Falcioni, G. Mantica, S. Pigolotti, A. Vulpiani, Phys. Rev. Lett., 91 (2003), 044101 | DOI