On the Dynamics of Crystal Electrons, high Momentum Regime

J. Asch (1, 2) , François Bentosela (1, 2) , P. Duclos (1, 2) , G. Nenciu

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We study the quantum dynamics generated by $H^{SW}=-{d^2\\over dx^2}+V-x$ with $V$ a real periodic function of weak regularity. We prove that the continuous spectrum of $H^{SW}$ is never empty, and furthermore that for $V$ small enough there are no bound states.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

J. Asch, François Bentosela, P. Duclos, G. Nenciu. On the Dynamics of Crystal Electrons, high Momentum Regime. Journal of Mathematical Analysis and Applications, 2001, 256, N°1, pp.99-114. ⟨hal-00011162⟩