Spectral form factor near the Ehrenfest time

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

Volumn 74, Issue 6, 2006, Pages

  Brouwer, Piet W ^a   Rahav, Saar ^a   Tian, Chushun ^b  

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

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BALLISTICS; CHAOS THEORY; ORBITS; SPECTRUM ANALYSIS; TRAJECTORIES;

CLASSICAL ORBITS; FORM FACTOR; PERIODIC ORBIT THEORY;

QUANTUM THEORY;

EID: 33846392658     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.066208     Document Type: Article

References (37)

1. Mesoscopic Quantum Physics, edited by, E. Akkermans, G. Montambaux, J.-L. Pichard, and, J. Zinn-Justin, (North-Holland, Amsterdam, 1995).
2. K. B. Efetov, Adv. Phys. ADPHAH 0001-8732 10.1080/00018738300101531 32, 53 (1983).
3. O. Bohigas, M.-J. Giannoni, and C. Schmit, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.1 52, 1 (1984).
4. R. A. Smith, I. V. Lerner, and B. L. Altshuler, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.58.10343 58, 10343 (1998).
5. C. Tian and A. I. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.035305 70, 035305 (2004).
6. M. Sieber and K. Richter, Phys. Scr. PHSTBO 0031-8949 10.1238/Physica.Topical.090a00128 T90, 128 (2001);
7. M. Sieber, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/42/104 35, L613 (2002).
8. 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);
9. 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).
10. A. I. Larkin and Y. N. Ovchinnikov, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 55, 2262 (1968)
11. A. I. Larkin and Y. N. Ovchinnikov, [Sov. Phys. JETP SPHJAR 0038-5646 28, 1200 (1969)].
12. G. M. Zaslavsky, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(81)90127-7 80, 157 (1981).
13. B. V. Chirikov, F. M. Izrailev, and D. L. Shepelyansky, Sov. Sci. Rev., Sect. C, Math. Phys. Rev. SRCREA 0143-0416 2, 209 (1981).
14. I. L. Aleiner and A. I. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.14423 54, 14423 (1996).
15. I. L. Aleiner and A. I. Larkin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.R1243 55, R1243 (1997). Note that a mistake in this work was corrected in Ref..
16. O. Agam, I. Aleiner, and A. Larkin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3153 85, 3153 (2000).
17. M. G. Vavilov and A. I. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.115335 67, 115335 (2003).
18. P. G. Silvestrov, M. C. Goorden, and C. W. J. Beenakker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.116801 90, 116801 (2003).
19. M. L. Mehta, Random Matrices (Academic Press, New York, 1991), 2nd ed.
20. M. V. Berry, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 400, 229 (1985).
21. S. Heusler, S. Müller, P. Braun, and F. Haake, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/3/L02 37, L31 (2004).
22. M. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
23. J. Müller and A. Altland, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/14/003 38, 3097 (2005).
24. J. H. Hannay and A. M. O. de Almeida, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/18/013 17, 3429 (1984).
25. D. Spehner, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/26/304 36, 7269 (2003).
26. M. Turek and K. Richter, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 36/30/101 36, L455 (2003).
27. P. W. Brouwer and S. Rahav, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.075322 74, 075322 (2006).
28. In contrast to Refs., we here define the encounter region as the total stretch along γ at which at least two stretches of γ are within a phase space distance c.
29. P. W. Brouwer and S. Rahav, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.085313 74, 085313 (2006).
30. We should point out that the field-theoretic approach of Ref. does give a smaller and nonuniversal quantum correction to δ K2 (t) at t=2 τE.
31. J. Tworzydlo, A. Tajic, and C. W. J. Beenakker, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.165318 69, 165318 (2004).
32. P. Jacquod and E. V. Sukhorukov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.116801 92, 116801 (2004).
33. E. B. Bogomolny and J. P. Keating, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1472 77, 1472 (1996).
34. O. Agam, B. L. Altshuler, and A. V. Andreev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.4389 75, 4389 (1995).
35. A. V. Andreev, O. Agam, B. D. Simons, and B. L. Altshuler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.3947 76, 3947 (1996).
36. K. B. Efetov and V. R. Kogan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.245312 67, 245312 (2003).
37. For example, the calculation of a product of two "diffusion propagators" D(1,2) 2 in Ref. assumes that the Lyapunov regions around the phase space points "1" and "2" are well separated, thus neglecting the possibility that the Lyapunov regions overlap.