91 citations · 323 across the 30 of their papers we have counts for
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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…
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…
Decay rates for the damped wave equation on the torus
Nalini Anantharaman, Matthieu Léautaud, Stéphane Nonnenmacher
We address the decay rates of the energy for the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link…
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…
A Haar component for quantum limits on locally symmetric spaces
Nalini Anantharaman, Lior Silberman
We prove lower bounds for the entropy of limit measures associated to non-degenerate sequences of eigenfunctions on locally symmetric spaces of non-positive curvature. In the case…
Dispersion and controllability for the Schrödinger equation on negatively curved manifolds
Nalini Anantharaman, Gabriel Riviere
We study the time-dependent Schrödinger equation on a compact riemannian manifold on which the geodesic flow has the Anosov property.…
Exponential decay for products of Fourier integral operators
Nalini Anantharaman
This text contains an alternative presentation, and in certain cases an improvement, of the "hyperbolic dispersive estimate" that was proved by Anantharaman and Nonnenmacher and us…