The semiclassical tool in mesoscopic physics
Abstract
Semiclassical methods are extremely valuable in the study of transport and thermodynamical properties of ballistic microstructures. By expressing the conductance in terms of classical trajectories, we demonstrate that quantum interference phenomena depend on the underlying classical dynamics of noninteracting electrons. In particular, we are able to calculate the characteristic length of the ballistic conductance fluctuations and the weak localization peak in the case of chaotic dynamics. Integrable cavities are not governed by single scales, but their nongeneric behavior can also be obtained from semiclassical expansions (over isolated trajectories or families of trajectories, depending on the system). The magnetic response of a microstructure is enhanced with respect to the bulk (Landau) susceptibility, and the semiclassical approach shows that this enhancement is the largest for integrable geometries, due to the existence of families of periodic orbits. We show how the semiclassical tool can be adapted to describe weak residual disorder, as well as the effects of electronelectron interactions. The interaction contribution to the magnetic susceptibility also depends on the nature of the classical dynamics of noninteracting electrons, and is parametrically larger in the case of integrable systems.
 Publication:

arXiv eprints
 Pub Date:
 December 1999
 arXiv:
 arXiv:condmat/9912038
 Bibcode:
 1999cond.mat.12038J
 Keywords:

 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Chaotic Dynamics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 Latex, Cimentovarenna style, 82 pages, 21 postscript figures