Physica E 6 (2000) 742–745 www.elsevier.nl/locate/physe Semiclassical transport in a random magnetic eld F. Evers a ; * , A.D. Mirlin a ; 1 , D.G. Polyakov b; 2 , J. Wilke a , P. W  ole a a Institut f ur Theorie de Kondensierten Materie, Universit at Karlsruhe, Engesser Strasse 7, 76128 Karlsruhe, Germany b Institut f ur Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany Abstract We present a theoretical description of the semiclassical kinetics of two-dimensional fermions in a smoothly varying random magnetic eld (RMF), with emphasis on the composite-fermion (CF) approach to the half-lled Landau level. We demonstrate that the Drude picture of the CF kinetics is only marginally valid at  = 1 2 and becomes totally inadequate already at a small deviation from half-lling. We show that the non-Markovian character of the transport leads to a strong positive magnetoresistance  xx at small  - 1 2 . At larger deviations from  = 1 2 , the positive magnetoresistance is followed by a sharp fallo of xx (“adiabatic localization”). We show that the AC conductivity xx (!) in the long-range RMF exhibits distinct non-Drude features. In particular, it has a sharp kink [xx (!) - xx (0) ˙ |!|] at zero ! and falls o exponentially at higher !. ? 2000 Elsevier Science B.V. All rights reserved. PACS: 73.40.-c; 73.50.Jt; 05.60.+w Keywords: Quantum Hall eect; Composite fermions; Localization There has been much recent interest in the transport properties of two-dimensional (2D) particles moving in a spatially random magnetic eld (RMF) B(r). This interest has been largely motivated by the fractional quantum Hall experiments near half-lling — these probe a disordered composite-fermion (CF) metal [1–3] subject to a ctitious RMF — and also by experiments with real RMFs in semiconductor het- * Corresponding author. Tel.: +49-721-608-7007; fax: +49-721-698150. E-mail address: fevers@tkm.physik.uni.karlsruhe.de (F. Evers) 1 Also at Petersburg Nuclear Physics Institute, 188350 St. Pe- tersburg, Russia. 2 Also at A.F. Ioe Physico-Technical Institute, 194021 St. Petersburg, Russia. erostructures with superconducting or ferromagnetic overlayers [4 –9]. The case of a long-range RMF is particularly interesting since the compressible state in a half-lled Landau level is observed in high-mobility samples where the correlation length of disorder is of the order of the large spacer width d (k F d ∼ 10, where k F is the Fermi wave vector). The purpose of this paper is to give a brief account of our recent results [10 –12] on the semiclassical (k F d1) kinetics of 2D fermions in a RMF, with particular emphasis on the resistivity in an external (homogeneous) magnetic eld  B = 〈B(r)〉 and= or at nite frequency !. Note that in the CF model a nite  B ˙  − 1 2 corresponds to a deviation from half lling  = 1 2 . Our study has found a variety of regimes with 1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII:S1386-9477(99)00193-9