1,720,971 research outputs found
Acceleration theorem for Bloch oscillators
No full textIn this paper, we give the Heisenberg position operator in the crystal momentum representation and weprove the acceleration theorem for Bloch oscillators. As an application, we discuss the motion of well localized states
Molecular localization induced by collisions
No full textWe consider a periodically driven double well as a simplified dynamical model for molecular localizationinduced by collisions. If the frequency of the collisions is high enough, so that the instability of the states islarger than a critical value, then the states are localized and we have the redshift of the inversion line
Weak-field magnetic bands in superlattices and the single-band approximation
No full textWe prove the existence and we give the semiclassical magnetic asymptotics of the magnetic bands in superlattices. We use the Wannier single-band approximation which leads to a dual semiclassical Bloch model with a band function as potential. A picture of x-dependent bands suggests exponentially small magnetic gap widths as given by the beating effect of a Zener double well
Wannier ladders and perturbation theory
No full textFollowing Avron we consider the Stark effect for Bloch electrons in the case of a finite number of gaps. We prove that the ladders of resonances are given by the Wannier decoupled-band approximation and the perturbation theory. The Fermi golden rule yields the width behaviour of Buslaev and Dmitrieva
Double wells: Nevanlinna analyticity, distributional borel sum and asymptotics
No full textWe consider the energy levels of a Stark family, in the parameter j, of quartic double wells with perturbation parameter g: H(g, j) = p(2) + x(2)(1 - gx)(2) - j (gx - 1/2). For non-even j (and for the symmetric case j = 0) we prove analyticity in the full Nevanlinna disk Rg(-2) > R(-1) of the g(2)-plane, as predicted by Crutchfield. By means of an approximation we give a heuristic estimate of the asymptotic small g behaviour, showing the relation between the avoided crossings and the failure of the usual perturbation series
Analyticity and asymptotics for the Stark-Wannier states
No full textIt is proved that the Stark-Wannier states, as functions of the electric field, are analytic in a disc tangential to the real axis at the origin, with asymptotic expansion to the second order which coincides with the Wannier approximation up to the first order
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