Quantum Chaos for point scatterers on flat tori

Abstract

This survey article deals with a delta potential - also known as a point scatterer - on flat 2D and 3D tori. We introduce the main conjectures regarding the spectral and wave function statistics of this model in the so- called weak and strong coupling regimes. We report on recent progress as well as a number of open problems in this field.

13 pages, 1 figure, added some references and further explanations, Phil. Trans. R. Soc. A to appear

References in corpus (2)

• Statistics of wave functions for a point scatterer on the torus
• The trace formula for a point scatterer on a compact hyperbolic surface

Cited by in corpus (5)

• Dirac cones for point scatterers on a honeycomb lattice
• Scarred eigenstates for arithmetic toral point scatterers
• Multifractal eigenfunctions for a singular quantum billiard
• Localization of low-energy eigenfunctions in Seba billiards
• Eigenvalues of Šeba billiards with localization of low-energy eigenfunctions