Generalized quantum baker maps as perturbations of a simple kernel

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 4, 2006, Pages

  Ermann, Leonardo ^a,b   Saraceno, Marcos ^a,c  

^a DEPARTAMENTO DE FÍSICA   (Argentina)

^b UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^c UNIVERSIDAD NACIONAL DE SAN MARTÍN   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFRACTION EFFECTS; HILBERT SPACE; QUANTUM BAKER MAPS; SPECTRAL PROPERTIES;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DIFFRACTION; EIGENVALUES AND EIGENFUNCTIONS; PERTURBATION TECHNIQUES;

QUANTUM THEORY;

EID: 33749580975     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.046205     Document Type: Article

References (28)

1. M. V. Berry, in Chaotic Behaviour in Deterministic Systems, edited by, G. Iooss, R. Hellemann, and, R. Stora, (North Holland, Amsterdam, 1983), p. 171.
2. A. J. Schnirelman, Usp. Mat. Nauk UMANA5 0042-1316 29, 181 (1974);
3. Y. Colin de Verdiere, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01209296 102, 497 (1985).
4. E. J. Heller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53. 1515 53, 1515 (1984);
5. L. Kaplan and E. Heller, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1006/aphy.1997.5773 264, 171 (1998).
6. E. Vergini, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/33/25/311 33, 4709 (2000);
7. E. Vergini and G. Carlo, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 33/25/312 33, 4717 (2000).
8. P. Leboeuf and A. Voros, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 23/10/017 23, 1765 (1990);
9. S. Nonnenmacher and A. Voros, J. Stat. Phys. JSTPBS 0022-4715 92, 431 (1998).
10. A. Lakshminarayan and N. Meenakshisundaram, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/36/006 39, 11205 (2006).
11. A. Lakshminarayan, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/37/ L01 38, L597 (2005).
12. N. Meenakshisundaram and A. Lakshminarayan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.065303 71, 065303 (R) (2005).
13. R. Shack and M. C. Caves, Appl. Algebra Eng. Commun. Comput. AAECEW 0938-1279 10.1007/s002000050133 10, 305 (2000).
14. M. Saraceno and A. Voros, Physica D PDNPDT 0167-2789 10.1016/0167- 2789(94)90085-X 79, 206 (1994).
15. N. L. Balazs and A. Voros, Ann. Phys. ANPYA2 0003-3804 190, 1 (1989).
16. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
17. M. Saraceno, Ann. Phys. ANPYA2 0003-3804 199, 37 (1990).
18. D. Coppersmith, IBM Research Report No. RC 19642, 1994 (unpublished).
19. A. J. Scott and C. M. Caves, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/36/308 36, 9553 (2003).
20. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052317 67, 052317 (2003).
21. G Tanner, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/33/18/304 33, 3567 (2000).
22. S. Nonnenmacher and M. Zworski, e-print math-ph/0505034.
23. O. Penrose, Foundations of Statistical Mechanics (Pergamon Press, New York, 1970).
24. M. M. Tracy and A. J. Scott, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/39/314 35, 8341 (2002).
25. L. Ermann, J. P. Paz, and M. Saraceno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012302 73, 012302 (2006).
26. A. N. Soklakov and R. Schack, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.5108 61, 5108 (2000).
27. N. Anantharaman and S. Nonnenmacher, e-print math-ph/0512052.
28. F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 1991).