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

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 Kähler 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.

References in corpus (2)

• Toeplitz operators on symplectic manifolds
• Berezin-Toeplitz quantization for compact Kaehler manifolds. A Review of Results

Cited by in corpus (2)

• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems
• Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells