Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems

This article introduces the notion of good labellings for asymptotic lattices in order to study joint spectra quantum integrable systems from point view inverse spectral theory. As an application, we consider a new quantity system, rotation number. In case two degrees freedom, obtain constructive algorithm detection appropriate eigenvalues, which use prove that, semiclassical limit, number can be calculated on spectrum robust way, and converges well-known classical The general results are applied semitoric where formulas become particularly natural.