Semiclassical theory of the Ehrenfest-time dependence of quantum transport

Physical Review B - Condensed Matter and Materials Physics

Volumn 76, Issue 16, 2007, Pages

  Brouwer, Piet W ^a,b  

^a Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35448929428     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.165313     Document Type: Article

References (78)

1. Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, New York, 2002).
2. Mesoscopic Quantum Physics, edited by, E. Akkermans,,, G. Montambaux,,, J.-L. Pichard,, and, J. Zinn-Justin, (North-Holland, Amsterdam, 1995).
3. K. B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, England, 1997).
4. B. L. Altshuler and A. G. Aronov, in Electron-Electron Interactions in Disordered Systems, edited by, A. L. Efros, and, M. Pollak, (Elsevier, Amsterdam, 1985).
5. C. W. J. Beenakker, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys. 69.731 69, 731 (1997).
6. L. P. Kouwenhoven, C. M. Marcus, P. L. McEuen, S. Tarucha, R. M. Westervelt, and N. S. Wingreen, in Mesoscopic Electron Transport, NATO Advanced Studies Institute, Series E: Applied Science, edited by, L. L. Sohn,,, L. P. Kouwenhoven,, and, G. Schön, (Kluwer, Dordrecht, 1997), Vol. 345.
7. M. L. Roukes and A. Scherer, Bull. Am. Phys. Soc. BAPSA6 0003-0503 34, 633 (1989);
8. K. Ensslin and P. M. Petroff, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.41.12307 41, 12307 (1990).
9. O. Bohigas, M.-J. Giannoni, and C. Schmit, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.1 52, 1 (1984).
10. I. L. Aleiner and A. I. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.14423 54, 14423 (1996).
11. A. I. Larkin and Y. N. Ovchinnikov, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 55, 2262 (1968)
12. A. I. Larkin and Y. N. Ovchinnikov, [Sov. Phys. JETP SPHJAR 0038-5646 28, 1200 (1969)].
13. C. W. J. Beenakker and H. van Houten, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.43.12066 43, 12066 (1991).
14. B. L. Altshuler and B. D. Simons, Mesoscopic Quantum Physics (Ref.).
15. O. Agam, I. Aleiner, and A. Larkin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3153 85, 3153 (2000).
16. O. Yevtushenko, G. Lütjering, D. Weiss, and K. Richter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.542 84, 542 (2000).
17. S. Oberholzer, E. V. Sukhorukov, and C. Schönenberger, Nature (London) NATUAS 0028-0836 10.1038/415765a 415, 765 (2002).
18. I. Adagideli, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.233308 68, 233308 (2003).
19. P. G. Silvestrov, M. C. Goorden, and C. W. J. Beenakker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.241301 67, 241301 (R) (2003).
20. J. Tworzydlo, A. Tajic, and C. W. J. Beenakker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.165318 69, 165318 (2004);
21. P. Jacquod and E. V. Sukhorukov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.116801 92, 116801 (2004).
22. J. Tworzydlo, A. Tajic, and C. W. J. Beenakker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.205324 70, 205324 (2004).
23. J. Tworzydlo, A. Tajic, H. Schomerus, P. W. Brouwer, and C. W. J. Beenakker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.186806 93, 186806 (2004).
24. S. Rahav and P. W. Brouwer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.056806 95, 056806 (2005);
25. S. Rahav and P. W. Brouwer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.035324 73, 035324 (2006).
26. R. S. Whitney and P. Jacquod, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.206804 96, 206804 (2006).
27. P. Jacquod and R. S. Whitney, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.195115 73, 195115 (2006);
28. S. Rahav and P. W. Brouwer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.196804 96, 196804 (2006).
29. P. W. Brouwer and S. Rahav, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.075322 74, 075322 (2006).
30. S. Rahav and P. W. Brouwer, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.205327 74, 205327 (2006).
31. P. W. Brouwer and S. Rahav, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.201303 75, 201303 (R) (2007).
32. A. Altland, P. W. Brouwer, and C. Tian, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.036804 99, 036804 (2007).
33. C. Petitjean, P. Jacquod, and R. S. Whitney, arXiv:cond-mat/0612118.
34. R. S. Whitney, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.235404 75, 235404 (2007).
35. K. B. Efetov and V. R. Kogan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.245312 67, 245312 (2003);
36. K. B. Efetov, G. Schwiete, and K. Takahashi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.026807 92, 026807 (2004).
37. C. Tian, A. Kamenev, and A. Larkin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.124101 93, 124101 (2004);
38. C. Tian, A. Kamenev, and A. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.045108 72, 045108 (2005).
39. J. Müller and A. Altland, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/14/003 38, 3097 (2005).
40. R. A. Jalabert, H. U. Baranger, and A. D. Stone, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.2442 65, 2442 (1990).
41. E. Doron, U. Smilansky, and A. Frenkel, Physica D PDNPDT 0167-2789 10.1016/0167-2789(91)90005-T 50, 367 (1991);
42. C. H. Lewenkopf and H. A. Weidenmüller, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(91)90372-F 212, 53 (1991).
43. H. U. Baranger, R. A. Jalabert, and A. D. Stone, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.3876 70, 3876 (1993);
44. H. U. Baranger, R. A. Jalabert, and A. D. Stone, Chaos CHAOEH 1054-1500 10.1063/1.165928 3, 665 (1993).
45. M. Sieber and K. Richter, Phys. Scr., T PHSTER 0281-1847 10.1238/Physica.Topical.090a00128 T90, 128 (2001);
46. M. Sieber, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/42/104 35, L613 (2002).
47. K. Richter and M. Sieber, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.206801 89, 206801 (2002).
48. U. Smilansky, S. Tomsovic, and O. Bohigas, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/25/11/029 25, 3261 (1992).
49. N. Argaman, Y. Imry, and U. Smilansky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.4440 47, 4440 (1993).
50. M. G. Vavilov and A. I. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.115335 67, 115335 (2003).
51. P. Silvestrov, in XXXIXth Rencontres de Moriond on Quantum Informarion and Decoherence in Nanosystems, edited by, D. C. Glattli,,, M. Sanquer,, and, J. Tran Thanh Van, (Gioi, Hanoi, Vietnam, 2004).
52. H. Hennig, R. Fleischmann, L. Hufnagel, and T. Geisel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.015202 76, 015202 (R) (2007).
53. M. Büttiker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 65.2901 65, 2901 (1990).
54. P. W. Brouwer and S. Rahav, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.085313 74, 085313 (2006).
55. H. Schanz, M. Puhlmann, and T. Geisel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.134101 91, 134101 (2003).
56. P. Braun, S. Heusler, S. Müller, and F. Haake, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/11/L01 39, L159 (2006).
57. S. Müller, S. Heusler, P. Braun, and F. Haake, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/1/012 9, 12 (2007).
58. S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.014103 93, 014103 (2004);
59. S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.046207 72, 046207 (2005).
60. M. Turek and K. Richter, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 36/30/101 36, L455 (2003);
61. D. Spehner, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/26/304 36, 7269 (2003).
62. J. H. Hannay and A. M. Ozorio de Almeida, J. Phys. A JPHAC5 0305-4470 17, 3429 (1984).
63. C. W. J. Beenakker and M. Büttiker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.1889 46, 1889 (1992).
64. S. Heusler, S. Müller, P. Braun, and F. Haake, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.066804 96, 066804 (2006).
65. B. L. Altshuler, JETP Lett. JTPLA2 0021-3640 41, 648 (1985).
66. P. A. Lee and A. D. Stone, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.1622 55, 1622 (1985);
67. P. A. Lee, A. D. Stone, and H. Fukuyama, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.35.1039 35, 1039 (1987).
68. B. L. Altshuler and B. I. Shklovskii, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 91, 220 (1986)
69. B. L. Altshuler and B. I. Shklovskii, [Sov. Phys. JETP SPHJAR 0038-5646 64, 127 (1986)].
70. R. A. Smith, I. V. Lerner, and B. L. Altshuler, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.10343 58, 10343 (1998).
71. M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
72. M. V. Berry, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 400, 229 (1985).
73. I. L. Aleiner and A. I. Larkin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.R1243 55, R1243 (1997);
74. C. Tian and A. I. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.035305 70, 035305 (2004).
75. P. W. Brouwer, S. Rahav, and C. Tian, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.066208 74, 066208 (2006).
76. B. L. Altshuler and D. E. Khmelnitskii, Pis'ma Zh. Eksp. Teor. Fiz. PZETAB 0370-274X 42, 291 (1985)
77. B. L. Altshuler and D. E. Khmelnitskii, [JETP Lett. JTPLA2 0021-3640 42, 359 (1985)].
78. M. Büttiker and T. Christen, in Quantum Transport in Submicron Structures, edited by, B. Kramer, (Kluwer, Dordrecht, 1996).