Quantum ratchets in dissipative chaotic systems

Physical Review Letters

Volumn 94, Issue 16, 2005, Pages

  Carlo, Gabriel G ^a   Benenti, Giuliano ^a   Casati, Giulio ^a   Shepelyansky, Dima L ^b  

^a UNIVERSITY OF INSUBRIA   (Italy)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

OPTICAL LATTICES; PLANCK CONSTANT; QUANTUM RATCHETS; QUANTUM TRAJECTORIES;

BIFURCATION (MATHEMATICS); CHAOS THEORY; CRYSTAL LATTICES; HAMILTONIANS; ITERATIVE METHODS; NONLINEAR SYSTEMS; PARTICLE OPTICS; QUANTUM OPTICS;

QUANTUM THEORY;

EID: 18144407680     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.94.164101     Document Type: Article

References (41)

1. F. L. Moore et al., Phys. Rev. Lett. 75, 4598 (1995).
2. J. Ringot et al., Phys. Rev. Lett. 85, 2741 (2000).
3. H. Ammann et al., Phys. Rev. Lett. 80, 4111 (1998).
4. M.B. d'Arcy et al., Phys. Rev. Lett. 87, 074102 (2001).
5. D. A. Steck et al., Science 293, 274 (2001).
6. W. K. Hensinger et al., Nature (London) 412, 52 (2001).
7. Quantum Chaos: Between Order and Disorder, edited by G. Casati and B. Chirikov (Cambridge University Press, Cambridge, England, 1995); F.M. Izrailev, Phys. Rep. 196, 299 (1990).
8. Quantum Chaos: Between Order and Disorder, edited by G. Casati and B. Chirikov (Cambridge University Press, Cambridge, England, 1995); F.M. Izrailev, Phys. Rep. 196, 299 (1990).
9. C. Mennerat-Robilliard et al., Phys. Rev. Lett. 82, 851 (1999).
10. M. Schiavoni et al., Phys. Rev. Lett. 90, 094101 (2003).
11. P. H. Joncs et al., quant-ph/0309149.
12. R. D. Astumian and P. Hänggi, Phys. Today 55, No. 11, 33 (2002).
13. P. Reimann, Phys. Rep. 361, 57 (2002).
14. S. Flach et al., Phys. Rev. Lett. 84, 2358 (2000).
15. F. Jülicher et al., Rev. Mod. Phys. 69, 1269 (1997).
16. P. Jung et al., Phys. Rev. Lett. 76, 3436 (1996).
17. M. Porto et al., Phys. Rev. Lett. 85, 491 (2000).
18. H. Schanz et al., Phys. Rev. Lett. 87, 070601 (2001); L. Hufnagel et al., ibid. 89, 154101 (2002).
19. H. Schanz et al., Phys. Rev. Lett. 87, 070601 (2001); L. Hufnagel et al., ibid. 89, 154101 (2002).
20. T. S. Monteiro et al., Phys. Rev. Lett. 89, 194102 (2002).
21. T. Jonckheere et al., Phys. Rev. Lett 91, 253003 (2003).
22. T. Cheon et al., J. Phys. Soc. Jpn. 72, 1087 (2003).
23. J. Gong and P. Brumer, Phys. Rev. E 70, 016202 (2004).
24. R. Bartussek et al., Europhys. Lett. 28, 459 (1994).
25. J.L. Mateos, Phys. Rev. Lett. 84, 258 (2000).
26. M. Barbi and M. Salerno, Phys. Rev. E 62, 1988 (2000).
27. D. Dan et al., Phys. Rev. E 63, 056307 (2001).
28. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, England, 1993).
29. T. Dittrich and R. Graham, Ann. Phys. (N.Y.) 200, 363 (1990).
30. R. Z. Sagdeev et al., Nonlinear Physics (Harwood Academic Publishers, New York, 1988).
31. G. Lindblad, Commun. Math. Phys. 48, 119 (1976); V. Gorini et al., J. Math. Phys. (N.Y.) 17, 821 (1976).
32. G. Lindblad, Commun. Math. Phys. 48, 119 (1976); V. Gorini et al., J. Math. Phys. (N.Y.) 17, 821 (1976).
33. These Lindblad operators can be obtained, similarly to [27], by considering the interaction between the system and a bosonic bath. The master equation (3) is then derived, at zero temperature, in the usual weak coupling and Markov approximations.
34. J. Dalibard et al., Phys. Rev. Lett. 68, 580 (1992).
35. There are also other similar parameter values where the system exhibits a simple or a chaotic attractor.
36. The Husimi function is obtained from smoothing of the Wigner function on a scale of Planck constant; see, e.g., S.-J. Chang and K.-J. Shi, Phys. Rev. A 34, 7 (1986).
37. G. Casati et al., Physica (Amsterdam) 131D, 311 (1999).
38. That is to say, a repelling chaotic limit set.
39. L. This is significantly larger than the experimental resolution equal to 0.03 [5].
40. E.L. Raab et al., Phys. Rev. Lett. 59, 2631 (1987).
41. M. Bienert et al., Phys. Rev. Lett. 89, 050403 (2002).