Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets

Abstract

We construct quasimodes for non-selfadjoint semiclassical operators using propagation of Hagedorn wave-packets. Assuming that the imaginary part of the principal symbol of the operator is non-negative and vanishes on certain points of the phase-space satisfying a finite-type dynamical condition, we construct quasimodes that concentrate on these non-damped points. More generally, we apply this technique to construct quasimodes for non-selfadjoint semiclassical perturbations of the harmonic oscillator that concentrate on periodic orbits or invariant tori.