Transient chaos induces anomalous transport properties of an underdamped Brownian particle

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

Volumn 76, Issue 5, 2007, Pages

  Speer, David ^a   Eichhorn, Ralf ^a   Reimann, Peter ^a  

^a BIELEFELD UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; PERIODIC STRUCTURES; TRANSPORT PROPERTIES; VELOCITY MEASUREMENT;

ONE-DIMENSIONAL PERIODIC POTENTIAL; PARTICLE MOTION; STATIC BIAS FORCE; TRANSIENT CHAOS;

BROWNIAN MOVEMENT;

EID: 36148929424     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.051110     Document Type: Article

References (93)

1. For a review see T. Tél in Directions in Chaos, edited by, Hao Bai-Lin, (World Scientific, Singapore, 1990), Vol. 3.
2. M. Franaszek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44.4065 44, 4065 (1991);
3. P. Reimann, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02183392 82, 1467 (1996).
4. E. R. Kay, D. A. Leigh, and F. Zerbetto, Angew. Chem., Int. Ed. ACIEF5 1433-7851 10.1002/anie.200504313 46, 72 (2007);
5. P. Reimann, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00081-3 361, 57 (2002);
6. H. Linke (special issue guest editor), Appl. Phys. A APAMFC 0947-8396 10.1007/s003390201401 75, 167 (2002);
7. J. Klafter and M. Urbakh (special issue guest editors), J. Phys.: Condens. Matter JCOMEL 0953-8984 17, S3661 (2005).
8. K. Wiesenfeld and F. Moss, Nature (London) NATUAS 0028-0836 10.1038/373033a0 373, 33 (1995);
9. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.223 70, 223 (1998).
10. Hu Gang, A. Daffertshofer, and H. Haken, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4874 76, 4874 (1996);
11. G. Costantini and F. Marchesoni, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1999-00510-7 48, 491 (1999);
12. P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J. M. Rubi, and A. Pérez-Madrid, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 87.010602 87, 010602 (2001).
13. J. M. G. Vilar and J. M. Rubi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.950 86, 950 (2001);
14. Y. Seol, K. Visscher, and D. B. Walton, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.160602 93, 160602 (2004).
15. R. Eichhorn, P. Reimann, B. Cleuren, and C. Van den Broeck, Chaos CHAOEH 1054-1500 10.1063/1.1869932 15, 026113 (2005).
16. R. Eichhorn, P. Reimann, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.190601 88, 190601 (2002);
17. R. Eichhorn, P. Reimann, and P. Hänggi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.066132 66, 066132 (2002);
18. B. Cleuren and C. Van den Broeck, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.055101 67, 055101 (R) (2003);
19. R. Eichhorn and P. Reimann, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10391-2 69, 517 (2005).
20. B. Cleuren and C. Van den Broeck, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.030101 65, 030101 (R) (2002);
21. B. Jiménez de Cisneros, P. Reimann, and J. M. R. Parrondo, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00270-x 64, 599 (2003).
22. A. Ros, R. Eichhorn, J. Regtmeier, T. Duong, P. Reimann, and D. Anselmetti, Nature (London) NATUAS 0028-0836 10.1038/436928a 436, 928 (2005);
23. R. Eichhorn, A. Ros, J. Regtmeier, T. Duong, P. Reimann, and D. Anselmetti, Eur. Phys. J. Special Topics 143, 159 (2007);
24. J. Regtmeier, R. Eichhorn, T. Duong, P. Reimann, D. Anselmetti, and A. Ros, Eur. Phys. J. E EPJSFH 1292-8941 10.1140/epje/e2007-00040-y 22, 335 (2007);
25. J. Regtmeier, S. Grauwin, R. Eichhorn, P. Reimann, D. Anselmetti, and A. Ros, J. Sep. Sci. 30, 1461 (2007).
26. T. J. Banis, I. V. Parshelyunas, and Y. K. Pozhela, Sov. Phys. Semicond. SPSEAX 0038-5700 5, 1727 (1972).
27. B. J. Keay, S. Zeuner, S. J. Allen, K. D. Maranowski, A. C. Gossard, U. Bhattacharya, and M. J. W. Rodwell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.4102 75, 4102 (1995).
28. R. Eichhorn, P. Reimann, and P. Hänggi, Physica A PHYADX 0378-4371 10.1016/S0378-4371(03)00188-2 325, 101 (2003);
29. R. Eichhorn and P. Reimann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.035106 70, 035106 (R) (2004).
30. D. Speer, R. Eichhorn, and P. Reimann, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/79/10005 79, 10005 (2007).
31. L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.040601 98, 040601 (2007).
32. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).
33. M. Borromeo and F. Marchesoni, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.203 84, 203 (2000);
34. P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J. M. Rubi, and A. Pérez-Madrid, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.031104 65, 031104 (2002).
35. E. G. Gwinn and R. M. Westervelt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.1613 54, 1613 (1985).
36. M. Iansiti, Q. Hu, R. M. Westervelt, and M. Tinkham, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.746 55, 746 (1985).
37. R. L. Kautz, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.329132 52, 3528 (1981).
38. R. L. Kautz and R. Monaco, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.334687 57, 875 (1985).
39. R. L. Kautz, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/59/8/001 59, 935 (1996).
40. P. Jung, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(93)90022-6 234, 175 (1993).
41. Y. Yu and S. Han, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 91.127003 91, 127003 (2003).
42. F. Marchesoni, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(97) 00232-6 231, 61 (1997).
43. R. L. Kautz, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(87)90151-4 125, 315 (1987).
44. P. Jung and P. Hänggi, Ber. Bunsenges. Phys. Chem. BBPCAX 0005-9021 95, 311 (1991).
45. M. Borromeo, G. Costantini, and F. Marchesoni, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2820 82, 2820 (1999).
46. H.-J. Breymayer, Appl. Phys. A: Solids Surf. APSFDB 0721-7250 10.1007/BF01197078 33, 1 (1984);
47. P. Jung, J. G. Kissner, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.3436 76, 3436 (1996);
48. J. L. Mateos, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84. 258 84, 258 (2000);
49. J. L. Mateos, Acta Phys. Pol. B APOBBB 0587-4254 32, 307 (2001);
50. J. L. Mateos, Physica A PHYADX 0378-4371 10.1016/S0378-4371(03)00187-0 325, 92 (2003);
51. M. Barbi and M. Salerno, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.1988 62, 1988 (2000);
52. C. M. Arizmendi, F. Family, and A. L. Salas-Brito, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.061104 63, 061104 (2001);
53. M. Borromeo, G. Costantini, and F. Marchesoni, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.041110 65, 041110 (2002);
54. W. S. Son, I. Kim, Y. J. Park, and C. M. Kim, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.067201 68, 067201 (2003);
55. F. Marchesoni, S. Savel'ev, and F. Nori, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.021102 73, 021102 (2006);
56. M. Kostur, L. Machura, P. Hänggi, J. Luczka, and P. Talkner, Physica A PHYADX 0378-4371 10.1016/j.physa.2006.04.086 371, 20 (2006).
57. H. Schanz, T. Dittrich, and R. Ketzmerick, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.026228 71, 026228 (2005);
58. S. Denisov, S. Flach, and P. Hänggi, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10565-4 74, 588 (2006).
59. R. K. P. Zia, E. L. Praestgaard, and O. G. Mouritsen, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1427088 70, 384 (2002).
60. G. A. Cecchi and M. O. Magnasco, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1968 76, 1968 (1996).
61. C. C. Chi and C. Vanneste, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.42.9875 42, 9875 (1990).
62. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.1507 48, 1507 (1982);
63. R. L. Kautz, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.339182 62, 198 (1987).
64. F. T. Arecchi, R. Badii, and A. Politi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.402 32, 402 (1985);
65. R. L. Kautz, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.335642 58, 424 (1985);
66. P. Reimann, R. Müller, and P. Talkner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.49.3670 49, 3670 (1994).
67. J. Lehmann, P. Reimann, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.1639 84, 1639 (2000);
68. J. Lehmann, P. Reimann, and P. Hänggi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.6282 62, 6282 (2000).
69. J. C. Sommerer, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93) 90320-Y 176, 85 (1993).
70. W. C. Steward, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.1651991 12, 277 (1968);
71. D. E. McCumber, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1656743 39, 3113 (1968);
72. K. K. Likharev, Dynamics of Josephson Junctions and Circuits (Gordon and Breach, Philadelphia, 1986);
73. W. Buckel and R. Kleiner, Superconductivity: Fundamentals and Applications (Wiley-VHC, Berlin, 2004).
74. A. Sterck, R. Kleiner, and D. Koelle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.177006 95, 177006 (2005);
75. M. Beck, E. Goldobin, M. Neuhaus, M. Siegel, R. Kleiner, and D. Koelle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.090603 95, 090603 (2005).
76. N. F. Pedersen, O. H. Soerensen, B. Dueholm, and J. Mygind, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00115266 38, 1 (1980).
77. G. Grynberg and C. Robilliard, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00017-5 355, 335 (2001).
78. R. Gommers, S. Bergamini, and F. Renzoni, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.073003 95, 073003 (2005).
79. T. Ala-Nissila, R. Ferrando, and S. C. Ying, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110107902 51, 949 (2002).
80. M. Azzouz, H. J. Kreuzer, and M. R. A. Shegelski, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.125403 66, 125403 (2002).
81. G. Antczak and G. Ehrlich, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.115422 71, 115422 (2005).
82. M. Borromeo and F. Marchesoni, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00733-6 249, 199 (1998);
83. C. Van den Broeck, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1999- 00553-2 46, 1 (1999);
84. R. Landauer and M. Büttiker, Phys. Scr. PHSTBO 0031-8949 T9, 155 (1985);
85. L. P. Faucheux, G. Stolovitzky, and A. Libchaber, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.5239 51, 5239 (1995);
86. V. I. Talyanskii, J. M. Shilton, M. Pepper, C. G. Smith, C. J. B. Ford, E. H. Linfield, D. A. Ritchie, and G. A. C. Jones, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.56.15180 56, 15180 (1997);
87. C. Rocke, S. Zimmermann, A. Wixforth, J. P. Kotthaus, G. Böhm, and G. Weimann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.4099 78, 4099 (1997).
88. H. Fujisaka and S. Grossmann, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01420589 48, 261 (1982);
89. T. Geisel and J. Nierwetberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.7 48, 7 (1982);
90. M. Schell, S. Fraser, and R. Kapral, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.26.504 26, 504 (1982).
91. A. Ajdari, D. Mukamel, L. Peliti, and J. Prost, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1994206 4, 1551 (1994).
92. R. Bartussek, P. Hänggi, and J. G. Kissner, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/28/7/001 28, 459 (1994).
93. D. C. Cronemeyer, C. C. Chi, A. Davidson, and N. F. Pedersen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.31.2667 31, 2667 (1985).