Der AHP-Preis 2015 wurde an Ira Herbst und Juliane Rama für ihre Arbeit
"Instability for Pre-existing Resonances under a small constant Electric Field"
verliehen. (Dieser Preis wird jedes Jahr für den bemerkenswertesten Artikel in der Zeitschrift Annales Henri Poincaré verliehen.)
We analyze a general class of self-adjoint difference operators <tex>H_\varepsilon = T_\varepsilon + V_\varepsilon</tex> on <tex>\ell^2(\varepsilon{\mathbf Z}^d)</tex>, where <tex>V_\varepsilon</tex> is a one-well potential and <tex>\varepsilon</tex> is a small parameter.
We construct a Finslerian distance d induced by<tex> H_\varepsilon</tex> and show that short integral curves are geodesics. Then we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by the Finsler distance to the well. This is analog to semiclassical Agmon estimates for Schrödinger operators.
