Constructive methods for interacting fermions with applications to the microscopic theory of conductivity and superconductivity

Abstract

The algebraic formulation of quantum mechanics, based on the theory of C*- and von Neumann algebras, is a very fruitful mathematical framework for the study of quantum many-body problems. In this context, by considering interacting fermion systems on lattices, our aim is to prove the physical conjecture saying that interparticle interaction is one of the causes of resistivity. To achieve this, rigorous methods of constructive quantum field theory will be adapted and applied. Also the transition between ohmic and superconducting behavior will be investigated in this context. This project is related with the FAPESP projects 2013/13215-5 (finished) and 2016/02503-8 (ending at 11/2017). The visiting researcher, J.-B. Bru, is the main scientific collaborator of W. de Siqueira Pedra, the responsible for the project at the USP. For instance, from 2015 to 2017, J.-B. Bru and W. de Siqueira Pedra have published together 9 articles (7 in Q1 and 2 Q2) and submitted further 4 articles. Many scientific visits of both researcher, to Bilbao and São Paulo, have been necessary to achieve these results. The grant will make possible to gather them during one year at the department of mathematical physics of the institute of Physics (USP). This will strongly support their research production. The production of 3 to 5 (research) articles is expected during the stay. The four submitted papers mentioned above have been done in collaboration with PhD students from the USP. Several seminars as well as a lecture at graduate level will be additionally held at the USP, by J.-B. Bru, together with the preparation of lectures notes (150 pages) on constructive methods for interacting fermions. In fact, the presence of J.-B. Bru at the mathematical physics department will support, both scientifically and professionally, Master and PhD students of USP in the context of the institutional agreement ("Memorandum of Understanding") between the BCAM and the institute of physics of the USP. In particular, some of them may be hired for internships or as postdocs at BCAM. Note that J.-B. Bru and W. de Siqueira Pedra are also organizers of a satellite conference of the 2018 International Congress of Mathematicians (ICM 2018, Rio de Janeiro, Brazil) taking place during J.-B. Bru’s stay at the USP. This event is also supported by BCAM (5000 EUR). (AU)