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Rafael Tiedra

Spectral and scattering properties of quantum walks on homogenous trees of odd degree
Monday, 15 November, 2021 - 13:30
Résumé : 

For unitary operators U_0, U in Hilbert spaces H_0, H and identification operator J:H_0H, we present results on the derivation of a Mourre estimate for U starting from a Mourre estimate for U_0 and on the existence and completeness of the wave operators for the triple (U,U_0,J). As an application, we determine spectral and scattering properties of a class of anisotropic quantum walks on homogenous trees of odd degree with evolution operator U. In particular, we establish a Mourre estimate for U, obtain a class of locally U-smooth operators, and prove that the spectrum of U covers the whole unit circle and is purely absolutely continuous, outside possibly a finite set where U may have eigenvalues of finite multiplicity. We also show that (at least) three different choices of free evolution operators U_0 are possible for the proof of the existence and completeness of the wave operators.

Institution de l'orateur : 
Pontifical Catholic University of Chile
Thème de recherche : 
Physique mathématique
Salle : 
1, Tour Irma
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