46 citations · 126 across the 26 of their papers we have counts for
34 papers
The Yang-Mills measure on surfaces via Morse theory
Reda Chhaibi, Nguyen Viet Dang, Yannick Guedes Bonthonneau +2
We introduce a Morse theoretical approach to the construction of the Yang--Mills measure on the space of connections of a compact Riemannian surface. This provides a direct continu…
On the Lebesgue Component of Semiclassical Measures for Abelian Quantum Actions
Gabriel Rivière, Lasse L. Wolf
For a large class of symplectic integer matrices, the action on the torus extends to a symplectic -action with . We apply this to the study of semiclassical…
Nonlinear chaotic Vlasov equations
Yann Chaubet, Daniel Han-Kwan, Gabriel Rivière
In this article, we study nonlinear Vlasov equations with a smooth interaction kernel on a compact manifold without boundary where the geodesic flow exhibits strong chaotic behavio…
Asymptotic regularity of sub-Riemannian eigenfunctions in dimension 3: the periodic case
Gabriel Rivière
On the unit tangent bundle of a compact Riemannian surface of constant nonzero curvature, we study semiclassical Schr{ö}dinger operators associated with the natural sub-Riemannian…
Quantum limits of perturbed sub-Riemannian contact Laplacians in dimension 3
Victor Arnaiz, Gabriel Rivière
On the unit tangent bundle of a compact Riemannian surface, we consider a natural sub-Riemannian Laplacian associated with the canonical contact structure. In the large eigenvalue…
Length orthospectrum and the correlation function on flat tori
Nguyen Viet Dang, Matthieu Léautaud, Gabriel Rivière
This note presents some of the results obtained in arXiv:2207.05410 and it has beenthe object of a talk of the second author during the Journées "Équations auxDérivées Partielles"…
Length orthospectrum of convex bodies on flat tori
Nguyen Viet Dang, Matthieu Léautaud, Gabriel Rivière
In analogy with the study of Pollicott-Ruelle resonances on negatively curved manifolds, we define anisotropic Sobolev spaces that are well-adapted to the analysis of the geodesic…
Dynamics of nonlinear Klein-Gordon equations in low regularity on S^2
Joackim Bernier, Benoît Grébert, Gabriel Rivière
We describe the long time behavior of small non-smooth solutions to the nonlinear Klein-Gordon equations on the sphere S^2. More precisely, we prove that the low harmonic energies…
Local norms of Schr{ö}dinger eigenfunctions on
Gabriel Rivière
On the canonical -sphere and for Schr{ö}dinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for eve…
Poincar{é} series and linking of Legendrian knots
Nguyen Viet Dang, Gabriel Rivière
On a negatively curved surface, we show that the Poincar{é} series counting geodesic arcs orthogonal to some pair of closed geodesic curves has a meromorphic continuation to the wh…
Spectrum of a non-selfadjoint quantum star graph
Gabriel Riviere, Julien Royer
We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Ro…
Semiclassical behaviour of quantum eigenstates
Gabriel Rivière
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We…
Semiclassical asymptotics for nonselfadjoint harmonic oscillators
Victor Arnaiz, Gabriel Rivière
We consider nonselfadjoint perturbations of semiclassical harmonic oscillators. Under appropriate dynamical assumptions, we establish some spectral estimates such as upper bounds o…
Equidistribution of toral eigenfunctions along hypersurfaces
Hamid Hezari, Gabriel Riviere
We prove a new quantum variance estimate for toral eigenfunctions. As an application, we show that, given any orthonormal basis of toral eigenfunctions and any smooth embedded hype…
The quantum Loschmidt echo on flat tori
Gabriel Rivière, Henrik Ueberschaer
The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum system to perturbations of the Hamiltonian. In the case of the standard 2-torus, we derive some explicit…
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…
Spectral analysis of morse-smale flows ii: resonances and resonant states
Nguyen Viet Dang, Gabriel Riviere
The goal of the present work is to compute explicitely the correlation spectrum of a Morse-Smale flow in terms of the Lyapunov exponents of the Morse--Smale flow, the topology of t…
Topology of Pollicott-Ruelle resonant states
Nguyen Viet Dang, Gabriel Riviere
We prove that the twisted De Rham cohomology of a flat vector bundleover some smooth manifold is isomorphic to the cohomology of invariant Pollicott--Ruelleresonant states associat…
Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces
Nguyen Viet Dang, Gabriel Riviere
We prove the existence of a discrete correlation spectrum for Morse-Smale flows acting on smooth forms on a compact manifold. This is done by constructing spaces of currents with a…
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{…
Spectral analysis of morse-smale gradient flows
Nguyen Viet Dang, Gabriel Riviere
On a smooth, compact and oriented manifold without boundary, we give a complete description of the correlation function of a Morse-Smale gradient flow satisfying a certain nonreson…
Equidistribution of the conormal cycle of random nodal sets
Nguyen Viet Dang, Gabriel Riviere
We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifo…
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…
Quantitative equidistribution properties of toral eigenfunctions
Hamid Hezari, Gabriel Riviere
We prove quantitative equidistribution properties for orthonormal bases of eigenfunctions of the Laplacian on the rational -torus. We show that the rate of equidistribution of s…