  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.
