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Volumn 109, Issue 3-4, 2002, Pages 373-405

Long-time tails, weak localization, and classical and quantum critical behavior

Author keywords

Critical behavior; Generic scale invariance; Long time tails; Quantum phase transitions; Weak localization

Indexed keywords


EID: 0036388125     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020485809093     Document Type: Review
Times cited : (35)

References (87)
  • 13
    • 0141508152 scopus 로고
    • NBS Miscellaneous Publ., M. S. Green and J. V. Sengers, eds. (U.S. Gov't Printing Office, Washington, DC)
    • J. V. Sengers, in Critical Phenomena, NBS Miscellaneous Publ., M. S. Green and J. V. Sengers, eds. (U.S. Gov't Printing Office, Washington, DC, 1966).
    • (1966) Critical Phenomena
    • Sengers, J.V.1
  • 14
    • 85050439011 scopus 로고
    • M. Fixman, Adv. Chem. Phys. 6:175 (1964); J. Chem. Phys. 47:2808 (1967).
    • (1964) Adv. Chem. Phys. , vol.6 , pp. 175
    • Fixman, M.1
  • 15
    • 1542650237 scopus 로고
    • M. Fixman, Adv. Chem. Phys. 6:175 (1964); J. Chem. Phys. 47:2808 (1967).
    • (1967) J. Chem. Phys. , vol.47 , pp. 2808
  • 17
    • 36049060679 scopus 로고
    • K. Kawasaki, Phys. Rev. 150:291 (1966); Ann. Phys. 61:1 (1970).
    • (1966) Phys. Rev. , vol.150 , pp. 291
    • Kawasaki, K.1
  • 18
    • 0141619518 scopus 로고
    • K. Kawasaki, Phys. Rev. 150:291 (1966); Ann. Phys. 61:1 (1970).
    • (1970) Ann. Phys. , vol.61 , pp. 1
  • 19
    • 3543050845 scopus 로고
    • Most of these developments in the theory of quantum many-body systems were put in a language that makes analogies to classical LTT effects far from obvious, although early work in this area did stress the connection with classical statistical mechanics, J. S. Langer and T. Neal, Phys. Rev. Lett. 16:984 (1966). Part of our motivation in the present paper is to elucidate the hidden close relation between these phenomena.
    • (1966) Phys. Rev. Lett. , vol.16 , pp. 984
    • Langer, J.S.1    Neal, T.2
  • 22
    • 0040793613 scopus 로고
    • Historically, the term "weak localization" was first used for the transport properties of noninteracting disordered electrons in two-dimensions. It is now often used in the broader meaning of LTT and GSI phenomena in fermion systems, with or without interactions, in any dimensionality. For reviews, see, P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57:287 (1985); B. L. Altshuler and A. G. Aronov, in Electron-Electron Interactions in Disordered Systems, M. Pollak and A. L. Efros, eds. (North-Holland, Amsterdam, 1984), p. 1.
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 287
    • Lee, P.A.1    Ramakrishnan, T.V.2
  • 23
    • 0003460093 scopus 로고
    • M. Pollak and A. L. Efros, eds. (North-Holland, Amsterdam)
    • Historically, the term "weak localization" was first used for the transport properties of noninteracting disordered electrons in two-dimensions. It is now often used in the broader meaning of LTT and GSI phenomena in fermion systems, with or without interactions, in any dimensionality. For reviews, see, P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57:287 (1985); B. L. Altshuler and A. G. Aronov, in Electron-Electron Interactions in Disordered Systems, M. Pollak and A. L. Efros, eds. (North-Holland, Amsterdam, 1984), p. 1.
    • (1984) Electron-Electron Interactions in Disordered Systems , pp. 1
    • Altshuler, B.L.1    Aronov, A.G.2
  • 30
    • 0003610623 scopus 로고
    • (Pergamon, London), ch. 17
    • L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), ch. 17; D. Ronis, I. Procaccia, and J. Machta, Phys. Rev. A 22:714 (1980).
    • (1959) Fluid Mechanics
    • Landau, L.D.1    Lifshitz, E.M.2
  • 31
    • 0001158408 scopus 로고
    • L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), ch. 17; D. Ronis, I. Procaccia, and J. Machta, Phys. Rev. A 22:714 (1980).
    • (1980) Phys. Rev. A , vol.22 , pp. 714
    • Ronis, D.1    Procaccia, I.2    Machta, J.3
  • 34
    • 85204060786 scopus 로고    scopus 로고
    • note
    • With this procedure, we are able to obtain results for the velocity autocorrelation function without explicitly using the properties of the Langevin forces, Eqs. (6). We do, however, need the various equal-time correlation functions as input. This is the same information that is contained in Eqs. (6).
  • 35
    • 85204082102 scopus 로고    scopus 로고
    • note
    • We note that Eq. (15) is actually exact (see, e.g., ref. 29), although showing this requires a much more involved derivation.
  • 37
    • 4444230759 scopus 로고
    • M. H. Ernst, E. H. Hauge, and J. M. J. van Leeuwen, J. Stat. Phys. 15:7 (1976); ibid. 15:23 (1976).
    • (1976) J. Stat. Phys. , vol.15 , pp. 23
  • 38
    • 0000259367 scopus 로고
    • C. Domb and M. S. Green, eds. (Academic Press, New York)
    • K. Kawasaki, in Phase Transitions and Critical Phenomena, Vol. 5a, C. Domb and M. S. Green, eds. (Academic Press, New York, 1976), p. 165.
    • (1976) Phase Transitions and Critical Phenomena , vol.5 A , pp. 165
    • Kawasaki, K.1
  • 40
    • 85204100158 scopus 로고    scopus 로고
    • D. Forster, D. R. Nelson, and M. J. Stephen, Ref. 7.
    • D. Forster, D. R. Nelson, and M. J. Stephen, Ref. 7.
  • 44
    • 33645076860 scopus 로고
    • T. R. Kirkpatrick, E. G. D. Cohen, and J. R. Dorfman, Phys. Rev. A 26: 950 (1982), ibid. 26:995 (1982).
    • (1982) Phys. Rev. A , vol.26 , pp. 995
  • 52
    • 0011298581 scopus 로고    scopus 로고
    • W. B. Li, K. J. Zhang, J. V. Sengers, R. W. Gammon, and J. M. Ortiz de Zárate, Phys. Rev. Lett. 81:5580 (1998); J. Chem. Phys. 112:9139 (2000).
    • (2000) J. Chem. Phys. , vol.112 , pp. 9139
  • 53
    • 85204067393 scopus 로고    scopus 로고
    • T. Imeada, A. Onuki, and K. Kawasaki, Ref. 37
    • T. Imeada, A. Onuki, and K. Kawasaki, Ref. 37; B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, Vol. 17, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1995).
  • 54
    • 0003232510 scopus 로고
    • C. Domb and J. L. Lebowitz, eds. (Academic Press, New York)
    • T. Imeada, A. Onuki, and K. Kawasaki, Ref. 37; B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, Vol. 17, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1995).
    • (1995) Phase Transitions and Critical Phenomena , vol.17
    • Schmittmann, B.1    Zia, R.K.P.2
  • 61
    • 0000418381 scopus 로고
    • L. P. Gorkov, A. I. Larkin, and D. E. Khmelnitskii, Pis'ma Zh. Eksp. Teor. Fiz. 30:248 (1979) [JETP Lett. 30:228 (1979)].
    • (1979) JETP Lett. , vol.30 , pp. 228
  • 63
    • 0003065301 scopus 로고
    • Lecture Notes in Physics No. 31, G. Kirczenow and J. Marro, eds. (Springer, New York)
    • See, e.g., E. H. Hauge, in Transport Phenomena, Lecture Notes in Physics No. 31, G. Kirczenow and J. Marro, eds. (Springer, New York, 1974), p. 337.
    • (1974) Transport Phenomena , pp. 337
    • Hauge, E.H.1
  • 68
    • 0035535326 scopus 로고    scopus 로고
    • For noninteracting electrons, there is consensus that this statement is true. Until recently, it was also believed to be true for interacting electrons, but experiments showing an apparent metal-insulator transition in two-dimmsional systems have cast doubt on this, see E. Abrahams, S. V. Kravchenko, and M. P. Sarachik, Rev. Mod. Phys. 73:251 (2001). The correct explanation of these observations is still being debated.
    • (2001) Rev. Mod. Phys. , vol.73 , pp. 251
    • Abrahams, E.1    Kravchenko, S.V.2    Sarachik, M.P.3
  • 70
    • 85204044198 scopus 로고    scopus 로고
    • D. Belitz, T. R. Kirkpatrick, and T. Vojta, cond-mat/0109547
    • D. Belitz, T. R. Kirkpatrick, and T. Vojta, cond-mat/0109547.
  • 72
    • 85204083748 scopus 로고    scopus 로고
    • G. Y. Chitov and A. J. Millis, cond-mat/0103155
    • G. Y. Chitov and A. J. Millis, cond-mat/0103155.
  • 74
    • 0034632726 scopus 로고    scopus 로고
    • S. S. Saxena et al., Nature 406:587 (2000); A. Huxley et al., Phys. Rev. B 63:144519 (2001).
    • (2000) Nature , vol.406 , pp. 587
    • Saxena, S.S.1
  • 75
    • 0034894384 scopus 로고    scopus 로고
    • S. S. Saxena et al., Nature 406:587 (2000); A. Huxley et al., Phys. Rev. B 63:144519 (2001).
    • (2001) Phys. Rev. B , vol.63 , pp. 144519
    • Huxley, A.1
  • 77
    • 0001898814 scopus 로고
    • See, K. G. Wilson and J. Kogut, Phys. Rep. 12:75 (1974) for the general philosophy underlying this approach. For the application to quantum phase transitions, see J. Hertz, ref. 68, and references therein.
    • (1974) Phys. Rep. , vol.12 , pp. 75
    • Wilson, K.G.1    Kogut, J.2
  • 78
    • 85204089250 scopus 로고    scopus 로고
    • J. Hertz, ref. 68, and references therein
    • See, K. G. Wilson and J. Kogut, Phys. Rep. 12:75 (1974) for the general philosophy underlying this approach. For the application to quantum phase transitions, see J. Hertz, ref. 68, and references therein.
  • 80
    • 32844459049 scopus 로고
    • J. Hubbard, Phys. Rev. Lett. 3:77 (1959); R. L. Stratonovich, Dok. Akad. Nauk. SSSR 115:1907 (1957) [Soy. Phys. Dokl. 2:416 (1957)].
    • (1959) Phys. Rev. Lett. , vol.3 , pp. 77
    • Hubbard, J.1
  • 81
    • 0000280715 scopus 로고
    • J. Hubbard, Phys. Rev. Lett. 3:77 (1959); R. L. Stratonovich, Dok. Akad. Nauk. SSSR 115:1907 (1957) [Soy. Phys. Dokl. 2:416 (1957)].
    • (1957) Dok. Akad. Nauk. SSSR , vol.115 , pp. 1907
    • Stratonovich, R.L.1
  • 82
    • 0001043154 scopus 로고
    • J. Hubbard, Phys. Rev. Lett. 3:77 (1959); R. L. Stratonovich, Dok. Akad. Nauk. SSSR 115:1907 (1957) [Soy. Phys. Dokl. 2:416 (1957)].
    • (1957) Soy. Phys. Dokl. , vol.2 , pp. 416
  • 84
    • 0034897442 scopus 로고    scopus 로고
    • D. Belitz, T. R. Kirkpatrick, M. T. Mercaldo, and S. L. Sessions, Phys. Rev. B 63:174427 (2001); ibid. 63:174428 (2001).
    • (2001) Phys. Rev. B , vol.63 , pp. 174428


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