Stark–Wannier ladders and cubic exponential sums


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Abstract

Given a one-dimensional Stark–Wannier operator, we study the reflection coefficient and its poles in the lower half of the complex plane far from the real axis. In particular, the reflection coefficient is described asymptotically in terms of regularized infinite cubic exponential sums.

About the authors

F. Klopp

Institut de Mathématiques de Jussieu—Paris Rive Gauche, Université Pierre et Marie Curie

Author for correspondence.
Email: frederic.klopp@imj-prg.fr
France, Paris

A. A. Fedotov

St. Petersburg State University

Email: frederic.klopp@imj-prg.fr
Russian Federation, St. Petersburg

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