Semiclassical methods in solid state physics : two examples

Issue		J. Phys. I France Volume 3, Number 2, February 1993


Page(s)		471 - 499
DOI		10.1051/jp1:1993145

DOI: 10.1051/jp1:1993145
J. Phys. I France 3 (1993) 471-499

Semiclassical methods in solid state physics : two examples

Jean Bellissard and Armelle Barelli

Laboratoire de Physique Quantique Université Paul Sabatier 118, route de Narbonne F-31062 Toulouse Cedex, France

(Received 22 July 1992, accepted in final form 9 August 1992)

Abstract
We present here a review of two problems motivated by 2D models for high T, superconductivity. The first part concerns the energy spectrum of 2D Bloch electrons in a uniform magnetic field. A semiclassical analysis provides a qualitative as well as a quantitative understanding of this spectrum. In the second part we make the case for the application of "Quantum Chaos" to strongly correlated fermion systems. It is illustrated by the level spacing distribution for the t - J model in two dimensions.

Résumé
Ce travail est une revue de deux problèmes motivés par l'étude des modèles bidimensionnels pour la supraconductivité à haute température critique. La première partie concerne l'étude du spectre d'énergie pour des électrons de Bloch bidimensionnels soumis à un champ magnétique uniforme. Une analyse semi-classique permet d'en comprendre les propriétés qualitatives et quantitatives. La deuxième partie est un plaidoyer pour l'utilisation des méthodes du "Chaos Quantique" dans l'étude des systèmes de fermions fortement corrélés. La distribution des écarts de niveaux d'un modèle t - J en deux dimensions, en fournit une illustration.

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