Spectral monodromy of small non-selfadjoint quantum perturbations of completely integrable Hamiltonians

Quang Sang Phan

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arXiv · 1701.01998

Spectral monodromy of small non-selfadjoint quantum perturbations of completely integrable Hamiltonians

Quang Sang Phan

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Abstract

We define a monodromy, directly from the spectrum of small non-selfadjoint perturbations of a selfadjoint semiclassical operator with two degrees of freedom, which is classically integrable. It is a combinatorial invariant that obstructs globally the existence of lattice structure of the spectrum, in the semiclassical limit. Moreover this spectral monodromy allows to recover a topological invariant (the classical monodromy) of the corresponding integrable system.

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Quang Sang Phan. 2017-01-08. Spectral monodromy of small non-selfadjoint quantum perturbations of completely integrable Hamiltonians. https://arxiv.org/abs/1701.01998

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