Mathematical Analysis and Quantum Transport

The project deals with quantum transport in mesoscopic systems. Physically these systems are realized in nanostructures. A general model represents it as an electron gas in a system consisting of a small sample and several large (infinite) reservoirs. Our focus is on the methods needed for a rigorous mathematical treatment of these systems to an extent where one can get quantitative statements on the systems. Thus mathematical analysis problems arising from such models will be studied in detail. Topics to be studied include memory effects in quantum transport and their connection with spontaneous pair creation, and effective non-linear models for quantum transport.

Danish Council for Independent Research. Grant ID DFF-4181-00042