Semiclassical inverse spectral theory for singularities of focus-focus type

Abstract

We prove, assuming that the Bohr-Sommerfeld rules hold, that the joint spectrum near a focus-focus critical value of a quantum integrable system determines the classical Lagrangian foliation around the full focus-focus leaf. The result applies, for instance, to h-pseudodifferential operators, and to Berezin-Toeplitz operators on prequantizable compact symplectic manifolds.

14 pages, 2 figures

References in corpus (1)

• Semiclassical quantization and spectral limits of h-pseudodifferential and Berezin-Toeplitz operators

Cited by in corpus (1)

• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems