Calculation of the Hall conductivity by Abel limit

Fumihiko Nakano

Annales de l'I.H.P. Physique théorique (1998)

  • Volume: 69, Issue: 4, page 441-455
  • ISSN: 0246-0211

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Nakano, Fumihiko. "Calculation of the Hall conductivity by Abel limit." Annales de l'I.H.P. Physique théorique 69.4 (1998): 441-455. <http://eudml.org/doc/76808>.

@article{Nakano1998,
author = {Nakano, Fumihiko},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Hall conductivity; relaxation time approximation; non-diagonal component of the conductivity tensor; two-dimensional electron system in a uniform magnetic field; Bellissard's theory; Abel limit},
language = {eng},
number = {4},
pages = {441-455},
publisher = {Gauthier-Villars},
title = {Calculation of the Hall conductivity by Abel limit},
url = {http://eudml.org/doc/76808},
volume = {69},
year = {1998},
}

TY - JOUR
AU - Nakano, Fumihiko
TI - Calculation of the Hall conductivity by Abel limit
JO - Annales de l'I.H.P. Physique théorique
PY - 1998
PB - Gauthier-Villars
VL - 69
IS - 4
SP - 441
EP - 455
LA - eng
KW - Hall conductivity; relaxation time approximation; non-diagonal component of the conductivity tensor; two-dimensional electron system in a uniform magnetic field; Bellissard's theory; Abel limit
UR - http://eudml.org/doc/76808
ER -

References

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  1. [AS] J.E. Avron and R. Seiler, Quantization of the Hall conductance for general multiparticle Schrödinger Hamiltonians, Phys. Rev. Lett., Vol. 54, 1985, pp. 259-262. MR773033
  2. [ASS] J.E. Avron, R. Seiler, and B. Simon, Charge deficiency, charge transport and comparison of dimensions, Commun. Math. Phys., Vol. 159, 1994, pp. 399-422. Zbl0822.47056MR1256994
  3. [ASY] J.E. Avron, R. Seiler and L.G. Yaffe, Adiabatic theorems and applications to the quantum Hall effect, Vol. 110, 1987, pp. 33-49. Zbl0626.58033MR885569
  4. [B1] J. Bellissard, Ordinary quantum Hall effect and non-commutative cohomology, in Proceedings of the Bad Schandau conference on localization, W. WELLER, P. ZIECHE, Eds., Teubner-Verlag, Leipzig, 1987. 
  5. [B2] J. Bellissard, A. van Elst, H. Schultz-Baldes, The non-commutative geometry of the quantum Hall effect, J. Math. Phys., Vol. 35 (10), 1994, pp. 5373-5451. Zbl0824.46086MR1295473
  6. [B3] J. Bellissard, Gap labeling theorems for Schrödinger operators, in from number theory to physics, M. WALDSCHMIDT, P. MOUSSA, J. LUCK, C. ITZYKSON Eds., Springer-Verlag, Berlin, 1991. Zbl0833.47056MR1221111
  7. [JN] A. Jensen and S. Nakamura, Mapping properties of functions of Schrödinger operators between Sobolev spaces and Besov spaces, Advanced Studies in Pure Math., Vol. 23, 1994, pp. 187-210. Zbl0815.47012
  8. [L] R.B. Laughlin, Quantized hall conductivity in two dimensions, Phys. Rev., Vol. B23, 1981, p. 5632. 
  9. [NB] S. Nakamura and J. Bellissard, Low energy bands do not contribute to quantum Hall effect, Commun. Math. Phys., Vol. 31, 1990, pp. 283-305. Zbl0707.46050MR1065673
  10. [S] S. Simon, Schrödinger semigroups, Bull. Amer. Mech. Sci., Vol. 7, 1982, pp. 447-526. Zbl0524.35002MR670130
  11. [TKNN] D. Thouless, M. Kohmoto, M. Nightingale and M. den Nijis, Quantum Hall conductance in a two dimensional periodic potential, Phys. Rev. Lett, Vol. 49, 1982, p.40. 
  12. [Y] K. Yajima, The Wk,p-continuity of wave operators for Schrödinger operators III, even dimensional cases m ≥ 4, J. Math. Sci. Univ. of Tokyo, Vol. 2, 1995, pp. 311-346. Zbl0841.47009MR1366561

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