6 citations · 9 across the 2 of their papers we have counts for
7 papers
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…
How Lagrangian states evolve into random waves
Maxime Ingremeau, Alejandro Rivera
In this paper, we consider a compact manifold of negative curvature, and a family of semiclassical Lagrangian states on . For a wide…
Empirical spectral measures of quantum graphs in the Benjamini-Schramm limit
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graph…
Absolutely Continuous Spectrum for Quantum Trees
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling…
Quantum ergodicity for large equilateral quantum graphs
Maxime Ingremeau, Mostafa Sabri, Brian Winn
Consider a sequence of finite regular graphs (GN) converging, in the sense of Benjamini-Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral…
A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves
Maxime Ingremeau, Alejandro Rivera
This note deals with nodal domains of random monochromatic plane waves. It was shown by Nazarov and Sodin that the expected number of such nodal domains included in a disk of radiu…