Non-Hermitian approach of edge states and quantum transport in a magnetic field

Abstract: We develop a manifest non-Hermitian approach of spectral and transport properties of two- dimensional mesoscopic systems in strong magnetic field. The finite system to which several ter- minals are attached constitutes an open system that can be described by an effective Hamiltonian. The life time of the quantum states expressed by the energy imaginary part depends specifically on the lead-system coupling and makes the difference among three regimes: resonant, integer quan- tum Hall effect and superradiant. The discussion is carried on in terms of edge state life time in different gaps, channel formation, role of hybridization, transmission coefficients quantization. A toy model helps in understanding non-Hermitian aspects in open systems.