Semiclassical quantization and spectral limits of h-pseudodifferential and Berezin-Toeplitz operators

Abstract

We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the spectrum of the associated classical system. This gives a quick alternative solution to the isospectrality problem for quantum toric systems. If the operators are uniformly bounded, the convergence is uniform. Analogous results hold for non-commuting operators.

27 pages, 3 figures

References in corpus (1)

• Toeplitz operators on symplectic manifolds

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