1999/12/02 by Rodolfo A. Jalabert, Jalabert, Rodolfo A. · 1 citation
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Quantum many-body systems #Quantum, superfluid, helium dynamics #chao-dyn #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.48550/arxiv.cond-mat/9912038
Latex, Cimento-varenna style, 82 pages, 21 postscript figures; lectures given in the CXLIII Course "New Directions in Quantum Chaos" on the International School of Physics "Enrico Fermi"; Varenna, Italy, July 1999; to be published in Proceedings
arxiv created 1999/12/02 · openalex publication_date 1999/12/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 non-interacting 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 non-generic 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 electron-electron interactions. The interaction contribution to the magnetic susceptibility also depends on the nature of the classical dynamics of non-interacting electrons, and is parametrically larger in the case of integrable systems.