Singular Bohr–Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case

Abstract

We state the Bohr–Sommerfeld conditions around a singular value of hyperbolic type of the principal symbol of a selfadjoint semiclassical Toeplitz operator on a compact connected Riemann surface. These conditions allow the description of the spectrum of the operator in a fixed-size neighborhood of the singularity. We provide numerical computations for three examples, each associated with a different topology.