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DOCTORANDO: Víctor Arnaiz Solórzano (UAM-ICMAT).

TÍTULO: Semiclassical measures and asymptotic distribution of eigenvalues for quantum KAM systems.

ABSTRACT: This thesis addresses the study of the Schrödinger dynamics in the semiclassical regime, that is, when the wave length of the solutions is comparable with a scale of size h > 0 with respect to the metric size. This parameter h is sometimes identified with the normalized Planck constant. The correspondence principle establishes that the asymptotic behavior of these solutions, as h tends to zero, should be governed by the underlying classical (Hamiltonian) dynamics. The rigorous study of this phenomenon is called semiclassical analysis and has been widely developed during the last decades, covering numerous problems of linear and nonlinear PDEs. Motivated by some previous results of Fabricio Macià and Gabriel Rivière on the dynamics of the Schrödinger equation on Zoll manifolds, via the study of the so called semiclassical measures, I will present some new contributions to the understanding of the semiclassical asymptotics for small perturbations of completely-integrable systems, both in the selfadjoint and non-selfadjoint cases.

After the defense session, we will enjoy some chosen red wines, along with some delicious sheep cheeses from the Burgos region, among other traditional foods and liquors.

ADVISORS: Fabricio Macià (UPM) and Keith Rogers (ICMAT).

FECHA Y LUGAR: Martes, 18 de diciembre, 11:30. Aula Naranja (ICMAT).
Location FECHA Y LUGAR: Martes, 18 de diciembre, 11:30. Aula Naranja (ICMAT).