Spectral problems in open quantum chaos

This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic. We will focus on the distribution of quantum resonances, and the structure of the corresponding metastable states. Our study includes the toy model of open quantum maps, as well as the recent quantum monodromy operator method.Comment: Compared with the previous version, misprints and typos have been corrected, and the bibliography update