摘要:

AbstractThe orbital magnetism of two‐dimensional electrons in mesoscopic samples is studied in models where the interaction between electrons is neglected. Various geometries are considered as there are disc, plaquette, bracelet with hard wall confinement and also a confinement with a parabolic potential. We calculate the average magnetic moment which means an average with respect to size fluctuations and de Haas‐van Alphen oscillations which arise in the case of a sharp Fermi cutoff. We see three distinct ranges in the magnetic field: (i) small field region where perturbation theory applies; (ii) moderate fields where edge currents play a prominent role; and (iii) the high field range with a Landau type susceptibility. In a quasiclassical picture, the electronic orbits are not qualitatively changed by a magnetic field in (i); skipping orbits are important in (ii); and in (iii), the cyclotron radius is smaller than the sample size. As a rule, we find an enhancement of the magnetic response which increases withkFL, that is, with sample size divided by the Fermi wave length. Also, we have found out that the quasiclassical approximation fails in the calculation of the magnetic properties; on the other hand, we have seen no essential differences between the canonical ensemble (fixed particle number) and the grand canonical ensemble (chemical potential given). In the case of plaquettes, in particular for samples in the form of squares, we have found agreement with experimental results by Lévy, Reich, Pfeiffer and

ISSN:0003-3804    

DOI:10.1002/andp.19975090702

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

摘要:

AbstractWe investigate two models for traffic flow with modified acceleration (‘slow‐to‐start’) rules. Even in the simplest casevmax= 1 these rules break the ‘particle‐hole’ symmetry of the model. We determine the fundamental diagram (flow‐density relationship) using the so‐called car‐oriented mean‐field approach (COMF) which yields the exact solution of the basic model withvmax= 1. Here we find that this is no longer true for the models with modified acceleration rules, but the results are still in good agreement with simulations. We also compare the effects of the two different slow‐to‐start rules and discuss their relevance for real traffic. In addition, in one of these models we find a new phase transition to

ISSN:0003-3804    

DOI:10.1002/andp.19975090703

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY

ISSN:0003-3804    

DOI:10.1002/andp.19975090701

出版商:WILEY‐VCH Verlag    

年代:1997

数据来源: WILEY