59 citations · 572 across the 34 of their papers we have counts for
38 papers
Quantum ergodicity and semiclassical measures: mathematical results
Stéphane Nonnenmacher
In this chapter we review some results describing the high-frequency eigenmodes of the Laplacian on compact manifolds, or Euclidean domains, for which the geodesic flow is chaotic.…
Resonances in hyperbolic dynamics
Stéphane Nonnenmacher
The study of wave propagation outside bounded obstacles uncovers the existence of resonances for the Laplace operator, which are complex-valued generalized eigenvalues, relevant to…
Control of eigenfunctions on surfaces of variable curvature
Semyon Dyatlov, Long Jin, Stéphane Nonnenmacher
We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov g…
Local eigenvalue statistics of one-dimensional random non-selfadjoint pseudo-differential operators
Stéphane Nonnenmacher, Martin Vogel
We consider a class of one-dimensional nonselfadjoint semiclassical pseudo-differential operators, subject to small random perturbations, and study the statistical properties of th…
Strong Scarring of Logarithmic Quasimodes
Suresh Eswarathasan, Stéphane Nonnenmacher
We consider a semiclassical (pseudo)differential operator on a compact surface , such that the Hamiltonian flow generated by its principal symbol admits a hyperbolic periodi…
Decay of correlations for normally hyperbolic trapping
Stephane Nonnenmacher, Maciej Zworski
We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normal hyperbolic trapping means that the trapped s…