Details

Autor(en) / Beteiligte

• Zakharov, Dmitry
• Zakharov, Vladimir
• Kielanowski, Piotr
• Odzijewicz, Anatol
• Previato, Emma

Titel

Non-periodic One-gap Potentials in Quantum Mechanics

Ist Teil von

• Geometric Methods in Physics XXXV, p.221-233

Ort / Verlag

Cham: Springer International Publishing

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We construct a broad class of bounded potentials of the one-dimensional Schrödinger operator that have the same spectral structure as periodic finite-gap potentials, but that are neither periodic nor quasi-periodic. Such potentials, which we call primitive, are non-uniquely parametrized by a pair of positive Hölder continuous functions defined on the allowed bands. Primitive potentials are constructed as solutions of a system of singular integral equations, which can be efficiently solved numerically. Simulations show that these potentials can have a disordered structure. Primitive potentials generate a broad class of bounded non-vanishing solutions of the KdV hierarchy, and we interpret them as an example of integrable turbulence in the framework of the KdV equation.