an:05207467
Zbl 1375.81102
Panati, Gianluca
Triviality of Bloch and Bloch-Dirac bundles
EN
Ann. Henri Poincar?? 8, No. 5, 995-1011 (2007).
00210652
2007
j
81Q10 47F05 47N50 82D25
Summary: 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 \(d\leq 3\), thus generalizing a previous result by \textit{G. Nenciu} [Commun. Math. Phys. 91, 81--85 (1983; Zbl 0545.47012)]. We provide a general formulation of the result, aiming at the application to the Dirac equation with a periodic potential and to piezoelectricity.
Zbl 0545.47012