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

Álvaro Pelayo, Leonid Polterovich, San Vũ Ngọc

Research output: Contribution to journalArticlepeer-review

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, then the convergence is uniform. Analogous results hold for non-commuting operators.

Original languageEnglish
Pages (from-to)676-696
Number of pages21
JournalProceedings of the London Mathematical Society
Volume109
Issue number3
DOIs
StatePublished - 1 Jan 2014

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