Analysis Seminar

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Quantum Complete Integrability

Speaker: Laurent Stolovitch, University of Nice

Location: Warren Weaver Hall 1302

Date: Thursday, April 9, 2015, 11 a.m.

Synopsis:

We consider families of commuting quantum Hamiltonian which are pertubations of constant Hamiltonians on a torus, which may have a dense pure point spectrum. We show that some of these families are unitary equivalent to a quantum Birkhoff normal form. As a consequence, we show that the Rayleigh-Schrödinger series are convergent in a neighborhood of each eigenvalue of the unperturbed Hamiltonians and that the spectrum of the perturbation is pure point. The results are uniform in the Planck constant. This a joint work with Thierry Paul.