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Pseudointegrable Andreev billiard

Jan Wiersig

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Abstract

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric barrier billiard, is discussed. Numerical evidence is presented indicating that the Poincaré map is typically weak mixing on the invariant sets. This link between these different classes of dynamical systems throws some light on the proximity effect in chaotic Andreev billiards.

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What this paper is about

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric barrier billiard, is discussed. Numerical evidence is presented indicating that the Poincaré map is typically weak mixing on the invariant sets. This link between these different classes of dynamical systems throws some light on the proximity effect in chaotic Andreev billiards.

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Available abstract

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric barrier billiard, is discussed. Numerical evidence is presented indicating that the Poincaré map is typically weak mixing on the invariant sets. This link between these different classes of dynamical systems throws some light on the proximity effect in chaotic Andreev billiards.

Key concepts: Dynamical billiards, Invariant (physics), Chaotic, Physics, Magnetic field, Andreev reflection, Polygon (computer graphics), Mixing (physics)

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