2 citations · 2 across the 8 of their papers we have counts for
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On Duclos-Exner's conjecture about waveguides in strong uniform magnetic fields
Enguerrand Bon-Lavigne, Loïc Le Treust, Nicolas Raymond +1
We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition ensuring the existence of the discrete spectrum…
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…
Absence of embedded eigenvalues for translationally invariant magnetic Laplacians
Nicolas Raymond, Julien Royer
Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum und…
Energy decay for the Klein-Gordon equation with highly oscillating damping
Julien Royer
We consider the free Klein-Gordon equation with periodic damping. We show on this simple model that if the usual geometric condition holds then the decay of the energy is uniform w…
Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation
Romain Joly, Julien Royer
We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly underst…
Semiclassical measure for the solution of the Helmholtz equation with an unbounded source
Julien Royer
We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of R^n. We prove that the solution has a unique semi-cla…