  Transport through semiconductor nanostructures is a quantum-coherent process.
This paper focuses on systems in which the electron's dynamics is ballistic and
the transport is dominated by the scattering from structure boundaries.
Opposite to the well-known case of the nuclear reactions, the potentials
defining semiconductor structures are nonspherically symmetric and the
asymptotic motion of the electrons is determined by the different potential
levels in the contacts. For this special type of potential the mathematical
foundations for the scattering theoretical description of the transport
phenomena are presented. The transport properties of the system are then
derived from the scattering matrix using the Landauer-Buttiker formalism. A
rigorous analysis of the analytical properties of the S matrix leads to the
most general resonant line shape described by a Fano function with a complex
asymmetry parameter. On this basis the resonant and nonresonant contributions
to the conductance and capacitance of the system are identified.

Mesoscale and Nanoscale Physics