Friedel phases and phases of transmission amplitudes in quantum scattering systems

Details Friedel phases and phases of transmission amplitudes in quantum scattering systems Friedel phases and phases of transmission amplitudes in quantum scattering systems

1999-06-29

arxiv.org/abs/cond-mat/9906431v1

Phys. Rev. B 60, 13814 (1999)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 12 figures

Scientific paper

10.1103/PhysRevB.60.13814

We illustrate the relation between the scattering phase appearing in the Friedel sum rule and the phase of the transmission amplitude for quantum scatterers connected to two one-dimensional leads. Transmission zero points cause abrupt phase changes $\pm\pi$ of the phase of the transmission amplitude. In contrast the Friedel phase is a continuous function of energy. We investigate these scattering phases for simple scattering problems and illustrate the behavior of these models by following the path of the transmission amplitude in the complex plane as a function of energy. We verify the Friedel sum rule for these models by direct calculation of the scattering phases and by direct calculation of the density of states.

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