Ratchet effect and the transporting Islands in the chaotic sea

Physical Review Letters

Volumn 99, Issue 24, 2007, Pages

  Wang, Lei ^a,b   Benenti, Giuliano ^c,d   Casati, Giulio ^a,c,d   Li, Baowen ^a,e  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b RENMIN UNIVERSITY OF CHINA   (China)

^c UNIVERSITY OF INSUBRIA   (Italy)

^d INFN SEZIONE DI MILANO   (Italy)

^e NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; EMBEDDED SYSTEMS; ENERGY DISSIPATION; HAMILTONIANS; SYSTEM STABILITY;

CHAOTIC SEA; INITIAL STATES; RATCHET EFFECTS;

ELECTRON TRANSITIONS;

EID: 37249001334     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.99.244101     Document Type: Article

References (18)

1. R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1966), Vol. 1, Chap..
2. S. Flach, O. Yevtushenko, and Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000); PRLTAO 0031-9007 10.1103/PhysRevLett.84.2358
3. I. Goychuk and P. Hänggi, J. Phys. Chem. B JPCBFK 1520-6106 105, 6642 (2001). 10.1021/jp010102r
4. R.D. Astumian and P. Hänggi, Phys. Today 55, No. 11, 33 (2002). PHTOAD 0031-9228 10.1063/1.1535005
5. P. Reimann and P. Hänggi, Appl. Phys. A 75, 169 (2002). APSFDB 0721-7250 10.1007/s003390201331
6. F. Jülicher, A. Ajdari, and J. Prost, Rev. Mod. Phys. 69, 1269 (1997). RMPHAT 0034-6861 10.1103/RevModPhys.69.1269
7. Special issue on Ratchets and Brownian Motors: Basics, Experiments and Applications, edited by, H.Linke, [Appl. Phys. A 75, 167 (2002)]. APSFDB 0721-7250 10.1007/s003390201401
8. P. Jung, J.G. Kissner, and P. Hänggi, Phys. Rev. Lett. 76, 3436 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.76.3436
9. J.L. Mateos, Phys. Rev. Lett. 84, 258 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.84.258
10. H. Schanz, M.-F. Otto, R. Ketzmerick, and T. Dittrich, Phys. Rev. Lett. 87, 070601 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.87.070601
11. J. Gong and P. Brumer, Phys. Rev. E 70, 016202 (2004); PLEEE8 1063-651X 10.1103/PhysRevE.70.016202
12. A. Kenfack, S.M. Sweetnam, and A.K. Pattanayak, Phys. Rev. E PLEEE8 1063-651X 75, 056215 (2007). 10.1103/PhysRevE.75.056215
13. Note that at a=0 map 2 reduces to the Zaslavsky map, a paradigmatic model in the study of dissipative chaotic systems; see R.Z. Sagdeev, D.A. Usikov, and G.M. Zaslavsky, Nonlinear Physics (Harwood Academic Publishers, New York, 1988). In this limit the potential V(x,t) becomes symmetric (for x→-x), and therefore the ratchet effect is absent.
14. We note that the quantum version of map 2 for a particular set of parameters has been recently studied in G.G. Carlo, G. Benenti, G. Casati, and D.L. Shepelyansky, Phys. Rev. Lett. 94, 164101 (2005); see also Ref.. PRLTAO 0031-9007 10.1103/PhysRevLett.94.164101
15. C. Liverani and M. Martens, Commun. Math. Phys. 260, 527 (2005). CMPHAY 0010-3616 10.1007/s00220-005-1420-8
16. G. Ritt, C. Geckeler, T. Salger, G. Cennini, and M. Weitz, Phys. Rev. A 74, 063622 (2006). PLRAAN 1050-2947 10.1103/PhysRevA.74.063622
17. M.O. Scully and M.S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).
18. M.G. Raizen, V. Milner, W.H. Oskay, and D.A. Steck, in New Directions in Quantum Chaos, Proceedings of the "E. Fermi" Varenna School, edited by, G. Casati, I. Guarneri, and, U. Smilansky, (IOS Press, Amsterdam, 2000).