1302.2260 (Álvaro Pelayo et al.)

Semiclassical inverse spectral theory for singularities of focus-focus
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Álvaro Pelayo, San Vũ Ngoc

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.

View original: http://arxiv.org/abs/1302.2260