Triviality of Bloch and Bloch–Dirac Bundles
Author: Panati, Gianluca
Source: Annales Henri Poincaré, Volume 8, Number 5, August 2007 , pp. 995-1011(17)
Abstract:In the framework of the theory of an electron in a periodic potential, we reconsider the longstanding problem of the existence of smooth and periodic quasi-Bloch functions, which is shown to be equivalent to the triviality of the Bloch bundle. By exploiting the time-reversal symmetry of the Hamiltonian and some bundle-theoretic methods, we show that the problem has a positive answer in any dimension d ≤ 3, thus generalizing a previous result by G. Nenciu. We provide a general formulation of the result, aiming at the application to the Dirac equation with a periodic potential and to piezoelectricity.
Document Type: Research Article
Affiliations: Zentrum Mathematik and Physik Department, Technische Universität München, München, D-80290, Germany, Email: email@example.com
Publication date: 2007-08-01