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 difference operators <tex>H_\varepsilon = T_\varepsilon + V_\varepsilon</tex> acting on the square summable function on <tex>\varepsilon</tex><tex> Z^d</tex>, where <tex>V_\varepsilon</tex> is a multi-well potential and <tex>\varepsilon</tex> is a small parameter.
We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for <tex>H_\varepsilon</tex> as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrödinger operator (see Helffer-Sjöstrand (1982)), and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
