Séminaire de EDP - Physique Mathématique

We consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates of the essential and discrete spectra. In particular, we give sufficient conditions ensuring that the discrete spectrum is non-empty. This is a joint work with Julien Royer from Toulouse III University and Nicolas Raymond from Angers University.

We shall describe a parametrix of the evolution semigroup associated to the Fokker-Planck equation by mean of a Fourier integral operator with complex phase. Although FIO with complex phase might look frightening to non experts, our approach is very elementary and requires no background in microlocal analysis. This talk will be based on ongoing discussions with Paul Alphonse, Matthieu Leautaud and Xue-Ping Wang.