Classical limit in terms of symbolic dynamics for the quantum baker’s map

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 5, 2000, Pages 5108-5114

  Soklakov, Andrei N ^a,b   Schack, Rüdiger ^a,b  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BERNOULLI SHIFT; CLASSICAL LIMITS; DISCRETE PHASE SPACE; FORMAL PROOFS; MATRIX ELEMENTS; PLANCK'S CONSTANTS; SYMBOLIC DYNAMICS; SYMBOLIC REPRESENTATION;

PHASE SPACE METHODS;

EID: 0001399641     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.5108     Document Type: Article

References (28)

1. N. L. Balazs and A. Voros, Ann. Phys. (N.Y.) 190, 1 (1989).
2. M. Saraceno, Ann. Phys. (N.Y.) 199, 37 (1990).
3. A. M. Ozorio de Almeida and M. Saraceno, Ann. Phys. (N.Y.) 210, 1 (1991).
4. F. M. Dittes, E. Doron, and U. Smilansky, Phys. Rev. E 49, R963 (1994).
5. M. Saraceno and A. Voros, Physica D 79, 206 (1994).
6. A. Lakshminarayan, Ann. Phys. (N.Y.) 239, 272 (1995).
7. L. Kaplan and E. J. Heller, Phys. Rev. Lett. 76, 1453 (1996).
8. M. G. E. da Luz and A. M. Ozorio de Almeida, Nonlinearity 8, 43 (1995).
9. R. Schack and C. M. Caves, Phys. Rev. Lett. 71, 525 (1993).
10. R. Schack and C. M. Caves, Phys. Rev. E 53, 3257 (1996).
11. J. H. Hannay, J. P. Keating, and A. M. Ozorio de Almeida, Nonlinearity 7, 1327 (1994).
12. R. Schack, Phys. Rev. A 57, 1634 (1998).
13. T. A. Brun and R. Schack, Phys. Rev. A 59, 2649 (1999).
14. P. Pakonski, A. Ostruszka, and K. Życzkowski, Nonlinearity 12, 269 (1999).
15. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
16. M. V. Berry, N. L. Balazs, M. Tabor, and A. Voros, Ann. Phys. (N.Y.) 122, 26 (1979).
17. H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950).
18. R. Rubin and N. Salwen, Ann. Phys. (N.Y.) 269, 159 (1998).
19. A. Lesniewski, R. Rubin, and N. Salwen, J. Math. Phys. 39, 1835 (1998).
20. R. Schack and C. M. Caves, to appear in AAECC, e-print quant-ph/9810050.
21. V. M. Alekseev and M. V. Yakobson, Phys. Rep. 75, 287 (1981).
22. R. Griffiths, J. Stat. Phys. 36, 219 (1984).
23. R. Omnès, J. Stat. Phys. 53, 893, 933, 957 (1988).
24. M. Gell-Mann and J.B. Hartle, Phys. Rev. D 47, 3345 (1993).
25. M. V. Berry, in Chaos and Quantum Physics, edited by A. Voros, and J. Zinn-Justin, M.-J. Giannoni (North-Holland, Amsterdam, 1991).
26. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1994).
27. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, England, 1996).
28. H. F. Mattson, Jr., Discrete Mathematics with Applications (Wiley, New York, 1993).