We investigate the spectrum and the dispersion relation of the Schrödinger operator with
point scatterers on a triangular lattice and a honeycomb lattice. We prove that the low-level …

The resonant spectrum of a thin plate driven with a mechanical oscillator is precisely
measured to distinguish modern Chladni figures (CFs) observed at the resonant frequencies …

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 prove that the eigenfunctions of quantum star graphs exhibit multifractal self-similar
structure in certain specified circumstances. In the semiclassical regime, when the spectral …

The coupling interaction between the driving source and the RLC network is explored and
characterized as the effective impedance. The mathematical form of the derived effective …

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 …

Waves in the plane, punctured by excision of a small disk with radius much smaller than the
wavelength, can be modified by being forced to vanish on the boundary of the disk. Such …

We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials
on a torus T^ d_L= R^ d/LZ^ d, in the thermodynamic limit L\to\infty, for dimension d= 2. The …

We study the Laplacian perturbed by two delta potentials on a two-dimensional flat torus.
There are two types of eigenfunctions for this operator: old, or unperturbed eigenfunctions …