We study the microlocal kernel of h-pseudodifferential operators Op h (p) − z, where z belongs to some neighborhood of size O(h) of a critical value of its principal symbol p0(x, ξ). We suppose that… (More)

We study the resonant set of a two-level Schrödinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real halfline.… (More)

For non-critical energies, the asymptotic behaviour of the scattering phase and of the time-delay are known to be described by a Weyl type formula and the BreitWigner formula respectively. We… (More)

We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance.… (More)

Bohr-Sommerfeld type quantization conditions of semiclassical eigenvalues for the non-selfadjoint Zakharov-Shabat operator on the unit circle are derived using an exact WKB method. The conditions are… (More)

We study the resonant set of a two-level Schrödinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real half-line.… (More)

We give a semiclassical expansion of the Schrödinger group in terms of the resonances created by a non-degenerate potential maximum. This formula implies that the imaginary part of the resonances… (More)