64 citations · 121 across the 23 of their papers we have counts for
15 papers · 1 filter
The semiclassical structure of the scattering matrix for a manifold with infinite cylindrical end
T. J. Christiansen, A. Uribe
We study the microlocal properties of the scattering matrix associated to the semiclassical Schrödinger operator on a Riemannian manifold with an infinite cylindrical…
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…
Szegö Limit Theorems for Singular Berezin-Toeplitz Operators
Salvador Pérez-Esteva, Alejandro Uribe
We consider Berezin-Toeplitz operators whose multipliers are compactly supported densities carried by a submanifold of . We compute asymptotically the moments of th…
Spectral properties of semi-classical Toeplitz operators
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
The main results of this paper are an asymptotic expansion in powers of for the spectral measure of a semi-classical Toeplitz operator, , and an equivari…
Canonical forms for perturbations of the harmonic oscillator
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff ca…
Band invariants for perturbations of the harmonic oscillator
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
We study the direct and inverse spectral problems for semiclassical operators of the form $S = S_0 +\h^2V$, where $S_0 = \frac 12 \Bigl(-\h^2Δ_{\bbR^n} + |x|^2\Bigr)$ is the harmon…
A semiclassical heat trace expansion for the perturbed harmonic oscillator
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
In this paper we study a semiclassical heat trace expansion for perturbations of the harmonic oscillator, by adapting to the semiclassical setting techniques developed by Hitrik an…
Quantum cutting and a Szegö limit theorem
G. Hernández-Dueñas, A. Uribe
Given a representation of the circle group by semiclassical Fourier integral operators, we construct an algebra of semiclassical pseudodifferential operators that are a quantum ana…
Geodesics on weighted projective spaces
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can "hear" the weights of a weighted projective space.
The spectral density function of a toric variety
D. Burns, V. Guillemin, A. Uribe
For a Kahler manifold (X, ω) with a holomorphic line bundle L and metric h such that the Chern form of L is ω, the spectral measures are the measures μ_N = \sum |s_{N,i}|^2 ν, wher…
"Bottom of the well" semi-classical trace invariants
V. Guillemin, T. Paul, A. Uribe
Let be an h-admissible pseudodifferential operator whose principal symbol, , has a unique non-degenerate global minimum. We give a simple proof that the semi-classical…
Some inverse spectral results for semi-classical Schrödinger operators
V. Guillemin, A. Uribe
We consider a semi-classical Schrödinger operator, -h^2Δ+ V(x). Assuming that the potential admits a unique global minimum and that the eigenvalues of the Hessian are linearly inde…
The semiclassical structure of low-energy states in the presence of a magnetic field
David Borthwick, Alejandro Uribe
We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of t…
On the pseudospectra of Berezin-Toeplitz operators
David Borthwick, Alejandro Uribe
We estimate the norm of the resolvent of non-selfadjoint Berezin Toeplitz operators in the semi-classical limit, under various assumptions on the Poisson bracket of the real and im…
The spectral density function for the Laplacian on high tensor powers of a line bundle
David Borthwick, Alejandro Uribe
For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Gui…