71 citations · 188 across the 19 of their papers we have counts for
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Concentration of Quasimodes for Perturbed Harmonic Oscillators
Víctor Arnaiz, Fabricio Macià
In this work, concentration properties of quasimodes for perturbed semiclassical harmonic oscillators are studied. The starting point of this research comes from the fact that, in…
The Born approximation in the three-dimensional Calderón problem II: Numerical reconstruction in the radial case
Juan A. Barceló, Carlos Castro, Fabricio Macià +1
In this work we illustrate a number of properties of the Born approximation in the three-dimensional Calderón inverse conductivity problem by numerical experiments. The results are…
The Born approximation in the three-dimensional Calderón problem
Juan A. Barceló, Carlos Castro, Fabricio Macià +1
Uniqueness and reconstruction in the three-dimensional Calderón inverse conductivity problem can be reduced to the study of the inverse boundary problem for Schrödinger operators $…
Observability results related to fractional Schrödinger operators
Fabricio Macià
We establish observability inequalities for various problems involving fractional Schrödinger operators , , on a compact Riemannian manifold. Observability from…
Effective mass theorems with Bloch modes crossings
Victor Chabu, Clotilde Fermanian Kammerer, Fabricio Macià
We study a Schr{ö}dinger equation modeling the dynamics of an electron in a crystal in the asymptotic regime of small wavelength comparable to the characteristic scale of the cryst…
Localization and delocalization of eigenmodes of Harmonic Oscillators
Víctor Arnaiz, Fabricio Macià
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequenci…
Semiclassical analysis of dispersion phenomena
Victor Chabu, Clotilde Fermanian-Kammerer, Fabricio Macià
Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schr{ö}dinger-type equation in R d. We describe quanti…
Wigner measures and effective mass theorems
Victor Chabu, Clotilde Fermanian-Kammerer, Fabricio Macià
We study a semi-classical Schr{ö}dinger equation which describes the dynamics of an electron in a crystal in the presence of impurities. It is well-known that under suitable assump…
Two-microlocal regularity of quasimodes on the torus
Fabricio Macià, Gabriel Rivière
We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schrödinger equation on two-dimensional flat tori. This is achieved by perfor…
Observability and quantum limits for the Schrödinger equation on the sphere
Fabricio Macià, Gabriel Riviere
In this note, we describe our recent results on semiclassical measures for the Schr{ö}dinger evolution on Zoll manifolds. We focus on the particular case of eigenmodes of the Schr{…
Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds
Fabricio Macià, Gabriel Rivière
We study the long time dynamics of the Schrödinger equation on Zoll manifolds. We establish criteria under which the solutions of the Schrödinger equation can or cannot concentrate…
Delocalization of quasimodes on the disk
Nalini Anantharaman, Matthieu Léautaud, Fabricio Macià
This note deals with semiclassical measures associated to {(sufficiently accurate)} quasimodes for the Laplace-Dirichlet operator on the disk. In this time-independent set-…
Wigner measures and observability for the Schrödinger equation on the disk
Nalini Anantharaman, Matthieu Léautaud, Fabricio Macià
We analyse the structure of semiclassical and microlocal Wigner measures for solutions to the linear Schrödinger equation on the disk, with Dirichlet boundary conditions. Our appro…
Kinetic theory and numerical simulations of two-species coagulation
Carlos Escudero, Fabricio Macia, Raul Toral +1
In this work we study the stochastic process of two-species coagulation. This process consists in the aggregation dynamics taking place in a ring. Particles and clusters of particl…
Semiclassical Completely Integrable Systems : Long-Time Dynamics And Observability Via Two-Microlocal Wigner Measures
Nalini Anantharaman, Clotilde Fermanian Kammerer, Fabricio Macià
We look at the long-time behaviour of solutions to a semi-classical Schrödinger equation on the torus. We consider time scales which go to infinity when the semi-classical paramete…
Long-time dynamics of completely integrable Schrödinger flows on the torus
Nalini Anantharaman, Clotilde Fermanian-Kammerer, Fabricio Macià
In this article, we are concerned with long-time behaviour of solutions to a semi-classical Schrödinger-type equation on the torus. We consider time scales which go to infinity whe…
Uniform estimates for the solutions of the Schrödinger equation on the torus and regularity of semiclassical measures
Tayeb Aïssiou, Dmitry Jakobson, Fabricio Macià
We establish uniform bounds for the solutions of the Schrödinger equation on arithmetic flat tori, generalising earlier results by J. Bourgain. We also study the regular…
The dynamics of the Schrödinger flow from the point of view of semiclassical measures
Nalini Anantharaman, Fabricio Macia
On a compact Riemannian manifold, we study the various dynamical properties of the Schrödinger flow , through the notion of semiclassical measures and the quantum-clas…
Concentration of symmetric eigenfunctions
Daniel Azagra, Fabricio Macia
In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More preci…
High-frequency propagation for the Schroedinger equation on the torus
Fabricio Macia
The main objective of this paper is understanding the propagation laws obeyed by high-frequency limits of Wigner distributions associated to solutions to the Schroedinger equation…
Semiclassical measures and the Schroedinger flow on Riemannian manifolds
Fabricio Macia
In this article we study limits of Wigner distributions (the so-called semiclassical measures) corresponding to sequences of solutions to the semiclassical Schroedinger equation at…
Generalized motion of level sets by functions of their curvatures on Riemannian manifolds
D. Azagra, M. Jimenez-Sevilla, F. Macia
We consider the generalized evolution of compact level sets by functions of their normal vectors and second fundamental forms on a Riemannian manifold M. The level sets of a functi…