We prove an analogue of Shnirelman, Zelditch and Colin de Verdiè-re's quantum ergodicity
Theorems in a case where there is no underlying classical ergodicity. The system we …

Whereas much work in the mathematical literature on quantum chaos has focused on
phenomena such as quantum ergodicity and scarring, relatively little is known at the …

We consider the Laplacian with a delta potential (a “point scatterer”) on an irrational torus,
where the square of the side ratio is diophantine. The eigenfunctions fall into two classes …

We investigate eigenfunctions of the Laplacian perturbed by a delta potential on the
standard tori R^ d/2 π Z^ d R d/2 π Z d in dimensions d= 2, 3 d= 2, 3. Despite quantum …

While quantum multifractality has been widely studied in the physics literature and is by now
well understood from the point of view of physics, there is little work on this subject in the …

We consider momentum push-forwards of measures arising as quantum limits
(semiclassical measures) of eigenfunctions of a point scatterer on the standard flat torus …

We consider the Laplacian with a delta potential (a" point scatterer") on an irrational torus,
where the square of the side ratio is diophantine. The eigenfunctions fall into two classes---" …

We show that arithmetic toral point scatterers in dimension three (“Šeba billiards on R 3/Z 3”)
exhibit strong level repulsion between the set of “new” eigenvalues. More precisely, let Λ:={λ …

We consider the Laplacian with a delta potential (also known as a “point scatterer”, or “Fermi
pseudopotential”) on an irrational torus, where the square of the side ratio is diophantine …

In the first part of this thesis, we derive comparison formulas relating the zeta-regularized
determinant of an arbitrary self-adjoint extension of the Laplace operator with domain …