Triviality of Bloch and Bloch-Dirac bundles

112Citations
Citations of this article
52Readers
Mendeley users who have this article in their library.

This article is free to access.

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. © 2007 Birkhäuser Verlag Basel/Switzerland.

Cite

CITATION STYLE

APA

Panati, G. (2007). Triviality of Bloch and Bloch-Dirac bundles. Annales Henri Poincare, 8(5), 995–1011. https://doi.org/10.1007/s00023-007-0326-8

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free