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Triviality of Bloch and Bloch-Dirac bundles
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
for any d < 4, 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.Comment: 20 pages, no figure
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