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
Triviality of Bloch and Bloch-Dirac bundles / Panati, Gianluca. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 8:(2007), pp. 995-1011. [10.1007/s00023-007-0326-8]
Triviality of Bloch and Bloch-Dirac bundles
PANATI, GIANLUCA
2007
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 piezoelectricityI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.