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Prog. Theor. Phys. Vol. 116 No. 1 (2006) pp. 61-86

[ Full Text PDF : FREE ACCESS (285K) ]

Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields

— Non-Commutative Quantum Mechanics in the Keldysh Formalism —

Shigeki Onoda,1,* Naoyuki Sugimoto2 and Naoto Nagaosa3,4

1Spin Superstructure Project, ERATO, Japan Science and Technology Agency,
c/o Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
2Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
3CREST, Department of Applied Physics, University of Tokyo, Tokyo 113-8656
4Correlated Electron Research Center, National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8562, Japan

(Received May 14, 2006)

Abstract:

We develop a general theory of non-equilibrium states based on the Keldysh formalism, in particular, for charged-particle systems under static uniform electromagnetic fields. The Dyson equation for the uniform stationary state is rewritten in a compact gauge-invariant form by using the Moyal product in the phase space of energy-momentum variables, whcich originally do not commute in the case of the conventional operator algebra. Expanding the Dyson equation in electromagnetic fields, a systematic method for the order-by-order calculation of linear and non-linear responses from the zeroth-order Green's functions is obtained. In particular, we find that for impurity problems, up to linear order in the electric field, the present approach provides a diagrammatic method for the St\ureda formula. This approach also generalizes the semi-classical Boltzmann transport theory to fully quantum-mechanical and/or multi-component systems. In multi-component systems and/or for Hall transport phenomena, however, this quantum Boltzmann transport theory, constructed from the anti-symmetric combination of two different representations for the Dyson equation, does not uniquely specify the non-equilibrium state, but the symmetric combination is required. We demonstate the formalism to calculate longitudinal and Hall electric conductivities in an isotropic single-band electron system in the clean limit. It is found that the results are fully consistent with those obtained by Mott and Ziman in terms of the semi-classical Boltzmann transport theory.


URL : http://ptp.ipap.jp/link?PTP/116/61/
DOI : 10.1143/PTP.116.61


*E-mail: sonoda@appi.t.u-tokyo.ac.jp

[ Full Text PDF : FREE ACCESS (285K) ] Citation:

References:

  1. N. F. Mott, Adv. Phys. 16 (1967), 49.
  2. J. M. Ziman, Adv. Phys. 16 (1967), 551.
  3. R. Kubo, J. Phys. Soc. Jpn. 12 (1957), 570[JPSJ].
  4. S. Nakajima, Prog. Theor. Phys. 20 (1958), 948[PTP].
  5. R. Zwanzig, Lectures in Theoretical Physics, Vol. 3 (Interscience, New York, 1961).
  6. H. Mori, Prog. Theor. Phys. 33 (1965), 423[PTP]; Prog. Theor. Phys. 34 (1965), 399[PTP].
  7. H. Fukuyama, H. Ebisawa and Y. Wada, Prog. Theor. Phys. 42 (1969), 494[PTP].
  8. H. Fukuyama, Prog. Theor. Phys. 42 (1969), 1284[PTP].
  9. C. M. Hurd, The Hall Effect in Metals and Alloys (Plenum Press, New York, 1972).
  10. H. Kohno and K. Yamada, Prog. Theor. Phys. 80 (1988), 623[PTP].
  11. L. V. Keldysh, Sov. Phys. -JETP 20 (1965), 1018 [Zh. Eksp. Teor. Fiz. 47 (1964), 1515].
  12. G. Baym and L. P. Kadanoff, Phys. Rev. 124 (1961), 287[APS].
    G. Baym, Phys. Rev. 127 (1962), 1391[APS].
    L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, Menlo Park, 1962).
  13. B. L. Altshuler, Sov. Phys. -JETP 48 (1978), 670 [Zh. Eksp. Teor. Fiz. 47 (1964), 1515].
  14. J. Rammer and H. Smith, Rev. Mod. Phys. 58 (1986), 323[APS].
  15. G. D. Mahan, Many-Particle Physics (Plenum Press, New York, 1990), p. 671.
  16. J. E. Moyal, Proc. Cambridge Philos. Soc. 45 (1949), 99.
  17. M. Büttiker, H. Thomas and A. Prêtre, Z. Phys. B 94 (1994), 133[CrossRef].
  18. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge, 1995).
  19. W. R. Frensley, Rev. Mod. Phys. 62 (1990), 745[APS].
  20. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 1996).
  21. S. Y. Liu, X. L. Lei and N. J. M. Horing, Phys. Rev. B 73 (2006), 035323[APS].
  22. N. Sugimoto, S. Onoda, S. Murakami and N. Nagaosa, Phys. Rev. B 73 (2006), 113305[APS].
  23. S. Onoda, N. Sugimoto and N. Nagaosa, cond-mat/0605580[e-print arXiv].
  24. L. Smr\ucka and P. St\ureda, J. of Phys. C 10 (1977), 2153[IoP STACKS].
  25. P. St\ureda, J. of Phys. C 15 (1982), L717[IoP STACKS].
  26. A. A. Abrikosov, L. P. Gorkov and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963), revised English edition translated and edited by R. A. Silverman.
  27. N. Seiberg and E. Witten, J. High Energy Phys. 09 (1999), 032[CrossRef].
  28. A. Connes, Noncommutative Geometry (Academic, San Diego, 1994).
  29. C. Zener, Proc. R. Soc. London A 137 (1932), 696.
  30. J. Schwinger, Phys. Rev. 82 (1951), 664[APS].
  31. M. Levanda and V. Fleurov, J. of Phys.: Cond. Mat. 6 (1994), 7889[CrossRef].
  32. T. Kita, Phys. Rev. B 64 (2001), 054503[APS].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 77 (2008) 024711 (9 pages) :
    Quantum Transport Equation for Bloch Electrons in Electromagnetic Fields
    Takafumi Kita and Hiromasa Yamashita
  2. Progress of Theoretical Physics Vol. 117 No. 3 (2007) pp. 415-429 :
    Gauge Covariant Formulation of the Wigner Representation through Deformation Quantization
    Naoyuki Sugimoto, Shigeki Onoda and Naoto Nagaosa
  3. Progress of Theoretical Physics Vol. 123 No. 4 (2010) pp. 581-658 :
    Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory
    Takafumi Kita

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