1999/06/29 by Tooru Taniguchi, Μ. Büttiker, Markus Buttiker · 132 citations
Computer Science · Mathematics · Physics and Astronomy · #Amplitude #Computer science #Condensed matter physics #Function (biology) #Geometry #Mathematics #Phase (matter) #Physics #Plane (geometry) #Quantum #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Quantum optics and atomic interactions #Scattering #Scattering amplitude #Scattering theory #Telecommunications #Transmission (telecommunications) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.60.13814
published in Physical review. B, Condensed matter 60(19), 13814-13823 (American Physical Society) · 12 pages, 12 figures
arxiv created 1999/06/29 · openalex publication_date 1999/11/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \ifmmode±\else\textpm\fi\ensuremathπ 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.