In: Micro Electro Mechanical Systems Editor: B. Ekwall and M. Cronquist ISBN: 978-1-60876-474-7 c  2010 Nova Science Publishers, Inc. Chapter 12 BALLISTIC T RANSPORT THROUGH QUANTUM WIRES AND R INGS Vassilios Vargiamidis 1∗ and Vassilios Fessatidis 2† 1 Department of Physics, Aristotle University, GR-54124 Thessaloniki, Greece 2 Department of Physics, Fordham University, Bronx, NY 10458, USA Abstract Phase-coherent electron transport through quasi-one-dimensional systems has de- veloped into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on ballistic conduction through quantum wires (or constrictions) and one-dimensional open rings. In quantum wires the electron con- ductance versus Fermi energy is quantized as a consequence of the reduced dimen- sionality and the subsequent quantization of transverse momentum. The presence of scatterers in otherwise “clean” wires can strongly suppress the quantum conductance, and can generate sharp resonances (which are due to quasibound states) if the scatter- ing potential is attractive. These resonances can be of the Fano or Breit-Wigner type, depending on the size or/and strength of the scattering potential. Thermal effects are also considered. The scattering approach is briefly discussed in order to derive the Landauer formula, which is the basic tool for calculating the conductance of a meso- scopic sample. Scattering theory in ballistic quantum wires is formulated in terms of the Lippmann-Schwinger equation while the Feshbach coupled-channel theory is em- ployed in order to treat Fano resonances. The occurrence of Fano resonances in strictly one-dimensional mesoscopic open rings is discussed in the last part of this review. PACS number: 72.10.Fk; 73.63.Nm 1. Introduction Since the 1980s advances in the growth techniques and new electronic materials developed therefrom have provided almost defect-free electronic devices, which have dimensions in one or more directions on the quantum scale [1]. New quantum regimes governing such ∗ Email address: vargiam@physics.auth.gr † Email address: fessatidis@fordham.edu