83 citations · 122 across the 12 of their papers we have counts for
16 papers
The Steklov spectrum of convex polygonal domains II: investigating spectral determination
Emily B. Dryden, Carolyn Gordon, Javier Moreno +2
The extent to which the geometry of an object is determined by some associated spectral data is a longstanding problem. We investigate this problem in the context of the Steklov sp…
Spectral cluster asymptotics of the Dirichlet to Neumann operator on the two-sphere
S. Pérez-Esteva, A. Uribe, C. Villegas-Blas
We study the spectrum of the Dirichlet to Neumann operator of the two-sphere associated to a Schrödinger operator in the unit ball. The spectrum forms clusters of size aro…
The Steklov spectrum of convex polygonal domains I: spectral finiteness
Emily B. Dryden, Carolyn Gordon, Javier Moreno +2
We explore the Steklov eigenvalue problem on convex polygons, focusing mainly on the inverse Steklov problem. Our primary finding reveals that, for almost all convex polygonal doma…
Longtime dynamics for the Landau Hamiltonian with a time dependent magnetic field
Dario Bambusi, Benoit Grébert, Alberto Maspero +2
We consider a modulated magnetic field, , perpendicular to a fixed plane, where is constant, and a periodic function on the…
Perturbations of the Landau Hamiltonian: Asymptotics of eigenvalue clusters
G. Hernandez-Duenas, S. Pérez-Esteva, A. Uribe +1
We consider the asymptotic behavior of the spectrum of the Landau Hamiltonian plus a rapidly decaying potential, as the magnetic field strength, , tends to infinity. After a sui…
On the pseudospectra of Schrödinger operators on Zoll manifolds
David Sher, Alejandro Uribe, Carlos Villegas-Blas
We consider non-self-adjoint Schrödinger operators where is the Laplace-Beltrami operator on a Zoll manifold and . We obtain asymptotic re…
Oscillation theory for the density of states of high dimensional random operators
Julian Grossmann, Hermann Schulz-Baldes, Carlos Villegas-Blas
Sturm-Liouville oscillation theory is studied for Jacobi operators with block entries given by covariant operators on an infinite dimensional Hilbert space. It is shown that the in…
Semiclassical Szegö limit of eigenvalue clusters for the hydrogen atom Zeeman Hamiltonian
Misael Avendano-Camacho, Peter D. Hislop, Carlos Villegas-Blas
We prove a limiting eigenvalue distribution theorem (LEDT) for suitably scaled eigenvalue clusters around the discrete negative eigenvalues of the hydrogen atom Hamiltonian formed…
Signatures for -hermitians and -unitaries on Krein spaces with Real structures
Hermann Schulz-Baldes, Carlos Villegas-Blas
For -hermitian operators on a Krein space satisfying an adequate Fredholm property, a global Krein signature is shown to be a homotopy invariant. It is argued…
Quantization of interface currents
Motoko Kotani, Hermann Schulz-Baldes, Carlos Villegas-Blas
At the interface of two two-dimensional quantum systems, there may exist interface currents similar to edge currents in quantum Hall systems. It is proved that these interface curr…
Krein signatures of transfer operators for half-space topological insulators
Hermann Schulz-Baldes, Carlos Villegas-Blas
We propose a complementary point of view on the topological invariants of two-dimensional tight-binding models restricted to half-spaces. The transfer operators for such systems ar…
Topological invariants of edge states for periodic two-dimensional models
Julio Cesar Avila, Hermann Schulz-Baldes, Carlos Villegas-Blas
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublatt…
Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian
Alexander Pushnitski, Georgi Raikov, Carlos Villegas-Blas
We consider the Landau Hamiltonian (i.e. the 2D Schroedinger operator with constant magnetic field) perturbed by an electric potential V which decays sufficiently fast at infinity.…
Semiclassical Szego limit of resonance clusters for the hydrogen atom Stark Hamiltonian
Peter D. Hislop, Carlos Villegas-Blas
We study the weighted averages of resonance clusters for the hydrogen atom with a Stark electric field in the weak field limit. We prove a semiclassical Szego-type theorem for reso…
On the energy exchange between resonant modes in nonlinear Schrödinger equations
Benoit Grebert, Carlos Villegas-Blas
We consider the nonlinear Schrödinger equation and we prove that the solution of this equation, with small initial…
A uniform quantum version of the Cherry theorem
Carlos Villegas Blas, Sandro Graffi
Consider in the operator family . is the quantum harmonic oscillator with diophantine frequency vector $\om$, a bounded pseudodiffe…