On diamagnetism and de Haas-van Alphen effect
Annales de l'I.H.P. Physique théorique, Volume 52 (1990) no. 4, pp. 303-375.
@article{AIHPA_1990__52_4_303_0,
     author = {Helffer, B. and Sj\"ostrand, J.},
     title = {On diamagnetism and de {Haas-van} {Alphen} effect},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {303--375},
     publisher = {Gauthier-Villars},
     volume = {52},
     number = {4},
     year = {1990},
     mrnumber = {1062904},
     zbl = {0715.35070},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1990__52_4_303_0/}
}
TY  - JOUR
AU  - Helffer, B.
AU  - Sjöstrand, J.
TI  - On diamagnetism and de Haas-van Alphen effect
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1990
SP  - 303
EP  - 375
VL  - 52
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1990__52_4_303_0/
LA  - en
ID  - AIHPA_1990__52_4_303_0
ER  - 
%0 Journal Article
%A Helffer, B.
%A Sjöstrand, J.
%T On diamagnetism and de Haas-van Alphen effect
%J Annales de l'I.H.P. Physique théorique
%D 1990
%P 303-375
%V 52
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1990__52_4_303_0/
%G en
%F AIHPA_1990__52_4_303_0
Helffer, B.; Sjöstrand, J. On diamagnetism and de Haas-van Alphen effect. Annales de l'I.H.P. Physique théorique, Volume 52 (1990) no. 4, pp. 303-375. http://www.numdam.org/item/AIHPA_1990__52_4_303_0/

[Ad] E.N. Adamsii, Magnetic Susceptibility of the Diamagnetic Electron Gas, Phys. Rev., Vol. 89, n° 3, Feb. 1 1953, pp. 633-648. | Zbl

[As] N.W. Ashroft and N.D. Mermin, Solid state physics, Holt, Rinehart and Winston, New York-London, 1976.

[Be] J. Bellissard, [1] Almost Periodicity in Solid State Physics and C*-Algebras to appear in "Harald Bohr Centennary", Proceedings of the Symposium Held in Copenhagen, Ap. 24-25, 1987, C. BERG, B. FUGLEDE Ed. The Royal Academy of Sciences, Editions, Copenhagen, 1989. [2] C*-Algebras in Solid State Physics- 2 D Electrons in a Uniform Magnetic Field; "Operator Algebras and Applications". D. E. EVANS and M. TAKESAKI Ed., Cambridge University press, Vol. 2, 1988, pp. 49-76. | MR

[Bl] E.I. Blount, Bloch Electrons in a Magnetic Field, Phys. Rev., Vol. 126, 1962, pp. 1636-1653. | MR | Zbl

[BGH] L. Boutet De Monvel, A. Grigis and B. Helffer, Parametrixes d'opérateurs pseudo-différentiels à caractéristiques multiples, Astérisque, Vol. 34-35, pp. 93-121. | Numdam | MR | Zbl

[Bu] V.S. Buslaev, Développements semi-classiques pour des équations à coefficients périodiques, Yspehi Mat. Nayk., n° 42, 6, (258), 1987; Russian Math. Surveys, Vol. 42, 6, 1987, pp. 97-125. | Zbl

[Ca] J. Callaway, Energy band theory, Academic press, 1964. | MR | Zbl

[Di] J. Dieudonné, Calcul infinitésimal, Hermann; collection méthodes. | MR | Zbl

[Gu-Ra-Tru] J.C. Guillot, J.V. Ralston and E. Trubowitz, Semi-Classical Methods in Solid State Physics, comm. Math. Phys., Vol. 116, 1988, pp.401-415. | MR | Zbl

[He] B. Helffer, Théorie spectrale pour des opérateurs globalement elliptiques, Astérisque, n° 112.

[He-Ro] B. Helffer and D. Robert, [1] Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques. Ann. Inst. Fourier, Vol. 31, (3), 1981, pp. 169-223; [2] Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles, J. Funct. Anal., Vol. 53, 1983, pp. 246-268; [3] Semi-Classical Analysis for the Riesz Means in Connection with a Lieb-Thirring Conjecture, Asymptotic analysis (to appear). | Numdam | MR | Zbl

[He-Sj] B. Helffer and J. Sjostrand, [1] Analyse semi-classique pour l'équation de Harper (avec application à l'étude de l'équation de Schrödinger avec champ magnétique), Bull. S.M.F., Vol. 116, (4), 1988, mémoire n° 34; [2] Analyse semi-classique pour l'équation de Harper II, preprint nov. 1988, Mémoires de la S.M.F., 1989 (to appear); [3] Semi-classical analysis for Harper's equation III preprint Orsay, april 1988, Mémoires de la S.M.F., 1989 (to appear), announced in: Séminaire E.D.P. de l'école Polytechnique 87-88; [4] Équation de Schrödinger avec champ magnétique et équation de Harper, Springer L.N. Physics, No. 345, 1989, pp. 118-197; [5] Calcul semi-classique sur la densité d'état, manuscript, April 1988; [6] Puits multiples en mécanique classique I, Comm. in P.D.E., vol. 9, (4), 1984, pp. 337-498. | MR

[Ko] W. Kohn, Theory of Bloch functions in a magnetic field: the effective Hamiltonian, Phys. Rev., Vol. 115, n° 6, September, 15, 1959.

[La] L.D. Landau, Z. Phys., Vol. 64, 1930, p. 629 (see also the Translation in: collected papers of L. D. Landau, Gordon and Breach D. Ter Haar Ed., p. 35). | JFM

[Lu] J.M. Luttinger, The Effect of a Magnetic Field on Electrons in a Periodic Potential, Phys. Rev., 84, n° 4, 1951, pp. 814-817. | MR | Zbl

[Me] W. Mercouroff, La surface de Fermi des métaux, Masson, 1967.

[Ne] G. Nenciu, [1] Existence of the Exponentially Localised Wannier Functions Comm. Math. Phys., 91, 1983, pp. 81-85; [2] Stability of Energy Gaps Under Variation of the Magnetic Field Letters in Math. Phys., Vol. 11, 1986, pp. 127- 132 ; [3] Bloch Electrons in a Magnetic Field: Rigorous Justification of the Peierls-Onsager Effective Hamiltonian, preprint, april 1988. | MR | Zbl

[On] L. Onsager, Interprétation of the de Haas-van Alphen Effect, Phil. Mag., Vol. 43, 1952, pp. 1006-1008.

[Pe] R. Peierls, Zur theory des diamagnetismus von Leitungselectronen, Z. Phys., Vol. 80, 1933, pp. 763-791. | JFM | Zbl

[Ro] D. Robert [1] Propriétés spectrales d'opérateurs pseudo-différentiels Comm. P.D.E., Vol. 3, (9), 1978, pp. 755-826; [2] Autour de l'approximation semiclassique, Progress in Mathematics, n° 68, Birkhauser, 1986. | MR | Zbl

[Si] B. Simon, Almost Periodic Schrödinger Operators, A review, Adv. Appl. Math., Vol. 3, 1982, pp. 463-490. | MR | Zbl

[Sj] J. Sjöstrand, Singularités analytiques microlocales, Astérisque, n° 95, 1982. | Numdam | MR | Zbl

[So-Wi] E.H. Sondheimer and A.H. Wilson, The diamagnetism of free electrons, Proc. R. Soc., A-210, 1851, p. 173. | Zbl

[Wh] R.M. White, Quantum Theory of Magnetism, Springer Series in Solid-State Sci., 32, Springer Verlag.

[Wilk] M. Wilkinson, [1] Critical properties of electron eigenstates in incommensurate systems, Proc. R. Soc. London, A391, 1984, pp. 305-350; [2] Von Neumann Lattices of Wannier Functions for Bloch Electrons in a Magnetic Field, Proc. R. Soc. London, Vol. A403, 1986, pp. 135-166; [3] An Exact Effective Hamiltonian for a Perturbed Landau Level, J. Phys., Vol. A-20, n° 7, 11 May 1987, p.1761. | MR | Zbl

[Wi] Wilson, The theory of metals, Cambridge.