4 papers
Metastable diffusions with degenerate drifts
Marouane Assal, Jean-Francois Bony, Laurent Michel
We study the spectrum of the semiclassical Witten Laplacian associated to a smooth function on . We assume that is a confining Morse--Bott function.…
Resolvent estimates and resonance free domains for Schrödinger operators with matrix-valued potentials
Marouane Assal
We establish semiclassical resolvent estimates for Schrödinger operators with long-range matrix-valued potentials. As an application we prove resonance free domains both in trappin…
Eigenvalue splitting for a system of Schrödinger operators with an energy-level crossing
Marouane Assal, Setsuro Fujiié
We study the asymptotic distribution of the eigenvalues of a one-dimensional two-by-two semiclassical system of coupled Schrödinger operators in the presence of two potential wells…
Semiclassical Trace Formula and Spectral Shift Function for Systems via a Stationary Approach
Marouane Assal, Mouez Dimassi, Setsuro Fujiié
We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of -pseudodifferential operators, and apply it to the study of the spectra…