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Singular Bohr-Sommerfeld conditions for 1D Toeplitz operators: hyperbolic case (1309.5322v1)
Published 20 Sep 2013 in math.SP, math-ph, math.AP, and math.MP
Abstract: In this article, we state the Bohr-Sommerfeld conditions around a singular value of hyperbolic type of the principal symbol of a self-adjoint semiclassical Toeplitz operator on a compact connected K\"{a}hler surface. These conditions allow the description of the spectrum of the operator in a fixed size neighbourhood of the singularity. We provide numerical computations for three examples, each associated to a different topology.