43 citations · 172 across the 24 of their papers we have counts for
18 papers · 1 filter
Tunneling on graphs: an approach "a la Helffer-Sjoestrand"
Y. Colin de Verdiere
We revisit a paper of Li-Gabor-Yau on quantum tunneling on graphs using the approach of Helffer-Sjoestrand for the study of tunneling for Schroedinger operators on manifolds.
Spectral theory of pseudo-differential operators of degree 0 and application to forced linear waves
Yves Colin de Verdìère
We extend the results of our paper "Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0" written with Laure Saint-Raymond to the case of forced linear wa…
Attractors for two dimensional waves with homogeneous Hamiltonians of degree 0
Yves Colin de Verdìère, Laure Saint-Raymond, Yves Colin Deverdì
The density stratification in an incompressible fluid is responsible for the propagation of internal waves. In domains with topography, these waves exhibit interesting features. In…
The action of pseudo-differential operators on functions harmonic outside a smooth hyper-surface
Louis Boutet De Monvel, Yves Colin De Verdière
We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a…
Scattering theory for graphs isomorphic to a homogeneous tree at infinity
Yves Colin De Verdière, Francoise Truc
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scat…
Magnetic interpretation of the nodal defect on graphs
Yves Colin De Verdière
In this note, we present a natural proof of a recent and surprising result of Gregory Berkolaiko (arXiv 1110.5373) interpreting the "Courant nodal defect" of a Schrödinger operator…