91 citations · 323 across the 30 of their papers we have counts for
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Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum…
Quantum ergodicity on large graphs
Nalini Anantharaman
We give three different proofs of the main result of Anantharaman-Le Masson, establishing quantum ergodicity -- a form of delocalization --for eigenfunctions of the laplacian on la…
Quantum ergodicity on large regular graphs
Nalini Anantharaman, Etienne Le Masson
We propose a version of the Quantum Ergodicity theorem on large regular graphs of fixed valency. This is a property of delocalization of "most" eigenfunctions. We consider expander…
Chaotic vibrations and strong scars
Nalini Anantharaman, Stéphane Nonnenmacher
This article aims at popularizing some aspects of "quantum chaos", in particular the study of eigenmodes of classically chaotic systems, in the semiclassical (or high frequency) li…
Entropy of eigenfunctions
Nalini Anantharaman, Herbert Koch, Stéphane Nonnenmacher
We study the high--energy limit for eigenfunctions of the laplacian, on a compact negatively curved manifold. We review the recent result of Anantharaman-Nonnenmacher giving a lowe…
Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
Nalini Anantharaman, Stéphane Nonnenmacher
We study the high-energy eigenfunctions of the Laplacian on a compact Riemannian manifold with Anosov geodesic flow. The localization of a semiclassical measure associated with a s…