9 citations · 29 across the 15 of their papers we have counts for
22 papers
An efficient Galerkin method for high-frequency scattering problems using Wilson bases
T. Chaumont-Frelet, M. Ingremeau, F. Proust
We propose a new Galerkin discretization scheme for wave scattering problems that is based on microlocalised basis functions. We show that the proposed method can be made uniformly…
Improved bounds for eigenfunctions under random perturbations in negative curvature
Maxime Ingremeau, Martin Vogel
It has been known since the work of Avakumovíc, Hörmander and Levitan that, on any compact smooth Riemannian manifold, if , then $\|ψ_λ\|_{L^\infty} \leq C λ^{\frac…
Emergence of Gaussian fields in noisy quantum chaotic dynamics
Maxime Ingremeau, Martin Vogel
We study the long time Schrödinger evolution of Lagrangian states on a compact Riemannian manifold of negative sectional curvature. We consider two models of semiclas…
Decay of coefficients and approximation rates in Gabor Gaussian frames
T. Chaumont-Frelet, M. Ingremeau
The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of t…
Efficient approximation of high-frequency Helmholtz solutions by Gaussian coherent states
T. Chaumont-Frelet, V. Dolean, M. Ingremeau
We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension $d…
A trace formula for scattering resonances of unbalanced quantum graphs
Maxime Ingremeau
Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of res…
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…
Scattering resonances of large weakly open quantum graphs
Maxime Ingremeau
In this paper, we consider a sequence of open quantum graphs, with uniformly bounded data, and we are interested in the asymptotic distribution of their scattering resonances. Supp…
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…
Local Weak Limits of Laplace Eigenfunctions
Maxime Ingremeau
In this paper, we introduce a new notion of convergence for the Laplace eigenfunctions in the semiclassical limit, the local weak convergence. This allows us to give a rigorous sta…
Semiclassical limits of distorted plane waves in chaotic scattering without a pressure condition
Maxime Ingremeau
In this paper, we study the semi-classical behavior of distorted plane waves, on manifolds that are Euclidean near infinity or hyperbolic near infinity, and of non-positive curvatu…
Sharp resolvent bounds and resonance-free regions
Maxime Ingremeau
In this note, we consider semiclassical scattering on a manifold which is Euclidean near infinity or asymptotically hyperbolic. We show that, if the cut-off resolvent satisfies pol…
Equidistribution of Phase Shifts in Obstacle Scattering
Jesse Gell-Redman, Maxime Ingremeau
For scattering off a smooth, strictly convex obstacle with positive curvature, we show that the eigenvalues of the scattering matrix -- the phase shifts --…
Lower bounds for the number of nodal domains for sums of two distorted plane waves in non-positive curvature
Maxime Ingremeau
In this paper, we will consider generalised eigenfunctions of the Laplacian on some surfaces of infinite area. We will be interested in lower bounds on the number of nodal domains…
The semi-classical scattering matrix from the point of view of Gaussian states
Maxime Ingremeau
In this note, we will consider semiclassical scattering for compactly supported non-trapping perturbations of the Laplacian on . We will define a family of Gaussian s…
Equidistribution of phase shifts in trapped scattering
Maxime Ingremeau
We prove an equidistribution result for the eigenvalues of the scattering matrix associated to an operator of the form , where is a comp…
Distorted plane waves on manifolds of nonpositive curvature
Maxime Ingremeau
We will consider the high frequency behaviour of distorted plane waves on manifolds of nonpositive curvature which are Euclidean or hyperbolic near infinity, under the assumption t…
Distorted plane waves in chaotic scattering
Maxime Ingremeau
Distorted plane waves, sometimes called Eisenstein functions, are a family of eigenfunctions of a Schrödinger operator that are not square integrable. More precisely, they can be w…