Quantum Chaos for point scatterers on flat tori
Henrik Ueberschaer
TL;DR
This survey explores the spectral and wave function properties of point scatterers on flat tori, discussing conjectures, recent progress, and open problems in quantum chaos related to these models.
Contribution
It provides a comprehensive overview of conjectures, recent advances, and open questions in the study of quantum chaos for point scatterers on flat tori.
Findings
Discussion of main conjectures in spectral statistics
Summary of recent progress in weak and strong coupling regimes
Identification of open problems in the field
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.
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Taxonomy
TopicsQuantum chaos and dynamical systems