Enhanced mesoscopic fluctuations in the crossover between random-matrix ensembles

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 16, 2002, Pages 1653101-1653104

  Adam, Shaffique ^a   Brouwer, Piet W ^a   Sethna, James P ^a   Waintal, Xavier ^b  

^a Cornell University ^*  (United States)

^b SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CORRELATION ANALYSIS; ELECTRON; MATHEMATICAL ANALYSIS; QUANTUM MECHANICS; QUANTUM THEORY; SEMICONDUCTOR;

EID: 0037110077     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. M. L. Mehta, Random Matrices (Academic, New York, 1991).
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3. H.-J. Sommers and S. Iida, Phys. Rev. E 49, 2513 (1994).
4. V.I. Fal'ko and K.B. Efetov, Phys. Rev. B 50, 11 267 (1994); Phys. Rev. Lett. 77, 912 (1996).
5. V.I. Fal'ko and K.B. Efetov, Phys. Rev. B 50, 11 267 (1994); Phys. Rev. Lett. 77, 912 (1996).
6. S.A. van Langen, P.W. Brouwer, and C.W.J. Beenakker, Phys. Rev. E 55, 1 (1997).
7. P.W. Brouwer, X. Waintal, and B.I. Halperin, Phys. Rev. Lett. 85, 369 (2000).
8. K.A. Matveev, L.I. Glazman, and A.I. Larkin, Phys. Rev. Lett. 85, 2789 (2000).
9. The full eigenvalue distribution for the GOE-GUE crossover is calculated in A. Pandey and M.L. Mehta, Commun. Math. Phys. 87, 449.(1983); see also Ref. 1.
10. Single-eigenvector statistics for this case are studied in A. Tschersich and K.B. Efetov, Phys. Rev. E 62, 2042 (2000).
11. Renormalization group ideas have been applied previously to study universality and deviations from universality in the three basic ensembles of random matrix theory. See, e.g., E. Brézin and J. Zinn-Justin, Phys. Lett. B 288, 54 (1992); E. Brézin and A. Zee, C. R. Acad. Sci., Ser. II 317, 735 (1993); S. Higuchi, C. Itoi, S. Hishigaki, and N. Sakai, Nucl. Phys. B 434, 283 (1995).
12. Renormalization group ideas have been applied previously to study universality and deviations from universality in the three basic ensembles of random matrix theory. See, e.g., E. Brézin and J. Zinn-Justin, Phys. Lett. B 288, 54 (1992); E. Brézin and A. Zee, C. R. Acad. Sci., Ser. II 317, 735 (1993); S. Higuchi, C. Itoi, S. Hishigaki, and N. Sakai, Nucl. Phys. B 434, 283 (1995).
13. Renormalization group ideas have been applied previously to study universality and deviations from universality in the three basic ensembles of random matrix theory. See, e.g., E. Brézin and J. Zinn-Justin, Phys. Lett. B 288, 54 (1992); E. Brézin and A. Zee, C. R. Acad. Sci., Ser. II 317, 735 (1993); S. Higuchi, C. Itoi, S. Hishigaki, and N. Sakai, Nucl. Phys. B 434, 283 (1995).
14. 2, in agreement with the exact result, Eq. (7).
15. E. Brézin and A. Zee, Phys. Rev. E 49, 2588 (1994).
16. M. Wilkinson and P.N. Walker, J. Phys. A 28, 6143 (1995).
17. I.L. Aleiner, P.W. Brouwer, and L.I. Glazman, Phys. Rep. 358, 309 (2002).
18. J. von Delft and D.C. Ralph, Phys. Rep. 345, 61 (2001).
19. O. Agam, N.S. Wingreen, B.L. Altshuler, D.C. Ralph, and M. Tinkham, Phys. Rev. Lett. 78, 1956 (1997).
20. For repulsive interactions, the last term in Eq. (11) also vanishes in the GOE once the renormalization of the Cooper channel of the local interaction is taken into account, see, e.g., Ref. 14. The Cooper channel renormalization also affects the enhanced fluctuations in the GOE-GUE crossover. The enhancement of the fluctuations of interaction matrix elements in other crossovers, such as the crossover GOE-GSE or the crossover of Ref. 9 is not renormalized.