This line of research, supervised by J.-B. Bru, is a notoriously difficult subject. These methods are based on results of the monograph written by Bru-Pedra (Memoirs of the AMS, July 2013), which gives a first answer to an old open problem first addressed by Ginibre in 1968. This line of research also includes studies of quantum dynamics and transport properties in random media. The latter is a challenging issue in Random Schrödinger Operators. Cf. an application for a "proyectos de I.D. Excelencia" (PI: J.-B. Bru) recently submitted. It is strongly associated with the Mathematical Physics Department of the University of Sâo Paulo via Walter de Siqueira Pedra and Brazilian financial supports.

Moreover, quantum systems are of high interest of this research line both for the challenging future application of quantum technologies related to simulations of Dirac equation, through the recently established connection between L. Vega's group (N. Arrizabalaga and A. Mas) with the one directed by Ikerbasque Professor E. Solano, and for the statistical analysis of Bose-Einstein condensation in trapped gas within the hydrodynamic formulation of the so-called Gross-Pitaevskii theory, thanks to the connection of G. Pagnini with Ikerbasque Professor M. Modugno (Department of Theoretical Physics and History of Science, UPV/EHU, Bilbao) and with M. Escobedo.