Fermi acceleration in the randomized driven Lorentz gas and the Fermi-Ulam model

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

Volumn 76, Issue 1, 2007, Pages

  Karlis, A K ^a   Papachristou, P K ^a   Diakonos, F K ^a   Constantoudis, V ^b   Schmelcher, P ^c  

^a UNIVERSITY OF ATHENS   (Greece)

^b INSTITUTE OF NANOSCIENCE AND NANOTECHNOLOGY   (Greece)

^c UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ELEMENTARY PARTICLES; LIGHT SCATTERING; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS;

FERMI ACCELERATION; FERMI-ULAM MODEL; HOPPING WALL; LORENTZ GAS;

FERMI LEVEL;

EID: 34547481302     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.016214     Document Type: Article

References (46)

1. E. Fermi, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.75.1169 75, 1169 (1949).
2. R. Blandford and D. Eichler, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(87)90134-7 154, 1 (1987).
3. A. Veltri and V. Carbone, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.143901 92, 143901 (2004).
4. K. Kobayakawa, Y. S. Honda, and T. Samura, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.66.083004 66, 083004 (2002).
5. M. A. Malkov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.4911 58, 4911 (1998).
6. G. Michalek, M. Ostrowski, and R. Schlickeiser, Sol. Phys. SLPHAX 0038-0938 10.1023/A:1005028205111 184, 339 (1999).
7. A. V. Milovanov and L. M. Zelenyi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.052101 64, 052101 (2001).
8. F. Saif, I. Bialynicki-Birula, M. Fortunato, and W. P. Schleich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.4779 58, 4779 (1998).
9. A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.4972 74, 4972 (1995).
10. G. Lanzano, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4518 83, 4518 (1999).
11. H. A. Lorentz, Proc. R. Acad. Sci. Amsterdam PKNAAU 0370-0348 7, 438 (1905)
12. A. Yu. Loskutov, A. B. Ryabov, and L. G. Akinshin, JETP JTPHES 1063-7761 10.1134/1.558939 89, 966 (1999);
13. A. Yu. Loskutov, A. B. Ryabov, and L. G. Akinshin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/33/44/309 33, 7973 (2000).
14. S. Ulam, in Proceedings of the Fourth Berkley Symposium on Mathematics, Statistics, and Probability (California University Press, Berkeley, 1961), Vol. 3, p. 315.
15. M. A. Lieberman and A. J. Lichtenberg, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.5.1852 5, 1852 (1972).
16. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, Applied Mathematical Sciences, Vol. 38 (Springer-Verlag, NewYork, 1992).
17. P. J. Holmes, J. Sound Vib. JSVIAG 0022-460X 10.1016/0022-460X(82)90215-2 84, 173 (1982).
18. R. M. Everson, Physica D PDNPDT 0167-2789 10.1016/0167-2789(86)90064-3 19, 355 (1986).
19. Z. J. Kowalik, M. Franaszek, and P. Pieranski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.37.4016 37, 4016 (1988).
20. S. Warr, Physica A PHYADX 0378-4371 10.1016/0378-4371(96)00102-1 231, 551 (1996).
21. S. Celaschi and R. L. Zimmerman, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(87)90107-1 120, 447 (1987).
22. E. D. Leonel, J. K. da Silva, and S. O. Kamphorst, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.09.027 331, 435 (2004).
23. E. D. Leonel and P. V. E. McClintock, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/4/004 38, 823 (2005).
24. A. J. Lichtenberg, M. A. Lieberman, and R. H. Cohen, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(00)00058-0 1, 291 (1980).
25. E. D. Leonel, P. V. E. McClintock, and J. K. da Silva, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.014101 93, 014101 (2004).
26. E. D. Leonel and P. V. E. McClintock, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.066223 73, 066223 (2006).
27. D. G. Ladeira and J. K. da Silva, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.026201 73, 026201 (2006).
28. A. K. Karlis, P. K. Papachristou, F. K. Diakonos, V. Constantoudis, and P. Schmelcher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.194102 97, 194102 (2006).
29. G. M. Zaslavskii and B. V. Chirikov, Sov. Phys. Dokl. SPHDA9 0038-5689 9, 989 (1965).
30. A. Brahic, Astron. Astrophys. AAEJAF 0004-6361 12, 98 (1971).
31. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, England, 1992), pp. 352-355.
32. F. Bouchet, F. Cecconi, and A. Vulpiani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.040601 92, 040601 (2004).
33. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, UK, 1993).
34. Ya. G. Sinai, Russ. Math. Surveys RMSUAF 0036-0279 10.1070/ rm1972v027n04ABEH001383 27, 21 (1972);
35. Ya. G. Sinai, Russ. Math. Surveys RMSUAF 0036-0279 10.1070/ rm1970v025n02ABEH003794 25, 137 (1970).
36. L. A. Bunimovich, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01197884 65, 295 (1979).
37. L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01942372 78, 247 (1980);
38. L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02046760 78, 479 (1980).
39. J. Machta and R. Zwanzig, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.1959 50, 1959 (1983).
40. H. v. Beijeren, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.54. 195 54, 195 (1982).
41. P. Gaspard, Chaos, Scattering, and Statistical Mechanics (Cambridge University Press, Cambridge, UK, 1998).
42. R. Klages and C. Dellago, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1026445601619 101, 145 (2000).
43. C. P. Dettmann, in Encyclopaedia of Mathematical Sciences, edited by, D. Szasz, (Springer, Berlin, 2000), Vol. 101, p. 315.
44. D. N. Armstead, B. R. Hunt, and E. Ott, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.021110 67, 021110 (2003).
45. P. K. Papachristou, F. K. Diakonos, E. Mavrommatis, and V. Constantoudis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.016205 64, 016205 (2001).
46. A. K. Karlis (unpublished).