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Spectral monodromy of small non-selfadjoint quantum perturbations of completely integrable Hamiltonians (1701.01998v1)
Published 8 Jan 2017 in math.AP
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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