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math-ph2020
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…
math-ph2019
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…
math-ph2017
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…