Semiclassical inverse spectral theory for singularities of focus-focus type
Mathematical Physics
2015-06-15 v1 math.MP
Symplectic Geometry
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1302.2260,
title = {Semiclassical inverse spectral theory for singularities of focus-focus type},
author = {Álvaro Pelayo and San Vũ Ngoc},
journal= {arXiv preprint arXiv:1302.2260},
year = {2015}
}
Comments
14 pages, 2 figures