Dynamical entanglement and chaos: The case of Rydberg molecules

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 6, 2006, Pages

  Lombardi, M ^a   Matzkin, A ^a  

^a LIPHY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; COLLISION AVOIDANCE; COLLOIDS; CONTINUUM MECHANICS; EIGENVALUES AND EIGENFUNCTIONS; OPTICAL CORRELATION;

CLASSICAL DYNAMICS; CORE-ELECTRON COLLISION; DYNAMICAL ENTANGLEMENT; RYDBERG MOLECULES;

MOLECULES;

EID: 33745652493     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.062335     Document Type: Article

References (26)

1. U. Fano, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.2.353 2, 353 (1970).
2. Molecular Applications of Quantum Defect Theory, edited by, Ch. Jungen, (Institute of Physics, Bristol, 1996).
3. M. Lombardi, P. Labastie, M. C. Bordas, and M. Broyer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.454918 89, 3479 (1988).
4. M. Lombardi and T. H. Seligman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.47.3571 47, 3571 (1993).
5. K. Furuya, M. C. Nemes, and G. Q. Pellegrino, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5524 80, 5524 (1998).
6. P. A. Miller and S. Sarkar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.1542 60, 1542 (1999).
7. H. Fujisaki, T. Miyadera, and A. Tanaka, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066201 67, 066201 (2003).
8. J. N. Bandyopadhyay and A. Lakshminarayan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.016201 69, 016201 (2004).
9. Ph. Jacquod, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 150403 92, 150403 (2004);
10. P. Jacquod, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93. 219903 93, 219903 (E) (2004).
11. R. Demkowicz-Dobrzanski and M. Kus, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.066216 70, 066216 (2004).
12. T. Gorin and T. H. Seligman, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00131-2 309, 61 (2003).
13. H. Fujisaki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.012313 70, 012313 (2004).
14. K. W. Ford and J. A. Wheeler, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(59)90026-0 7, 259 (1959).
15. B. Dietz, M. Lombardi, and T. H. Seligman, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/j.aop.2004.03.004 312, 441 (2004).
16. B. d'Espagnat, Conceptual Foundations of Quantum Mechanics (Perseus, New York, 1976).
17. M. Znidaric and T. Prosen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032103 71, 032103 (2005).
18. G. Herzberg, Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules, 2nd ed. (Van Nostrand, New York, 1950), p. 217.
19. M. Lombardi and A. Matzkin, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10028-6 74, 771 (2006).
20. M. Nauenberg, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/23/15/001 23, L385 (1990).
21. R. H. Bell and M. J. Seaton, J. Phys. B JPAMA4 0022-3700 10.1088/0022-3700/18/8/016 18, 1589 (1985).
22. A. Matzkin and T. S. Monteiro, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.046215 70, 046215 (2004);
23. A. Matzkin and T. S. Monteiro, J. Phys. A JPHAC5 0305-4470 37, L225 (2004).
24. R. R. Jones and L. D. Noordam, Adv. At., Mol., Opt. Phys. AAMPE9 1049-250X 38, 1 (1998).
25. In fact, relative to we choose in this work a situation with identical classical parameters (in particular the coupling constant k and the crucial ratio Te Tc), and thus identical Poincaré surfaces of sections, but with an effective divided by 5, and thus all quantum numbers (L,J,N,ν) are multiplied by 5, and Br is divided by 54.
26. This must be done with care, as Eq. 22 supposes a channel normalization to unity, whereas the MQDT wave functions are normalized globally per unit energy. Failure to normalize correctly the radial channel functions FL results in an imperfect cancellation when taking the scalar product of two different eigenstates, leading to errors of the order of several 10-3. Still perfect cancellation does not occur, as errors due to the approximate nature of MQDT itself remain. These errors are, however, in the fully negligible range 10-5 - 10-6, as we have checked by an independent test calculation that makes an "exact" computation with a given short-range potential.