Physica E 12 (2002) 637–640 www.elsevier.com/locate/physe Current correlations and quantum localization in a random or homogeneous magnetic eld I.V. Gornyi a;b; 1 , A.D. Mirlin a;b;*; 2 ,P.W ole a;b a Institutf ur Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany b Institutf ur Theorie der Kondensierten Materie, Universit at Karlsruhe, Postfach 6980, 76128 Karlsruhe, Germany Abstract We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic eld. Our result is universal, i.e. it does not depend on the type (random potential or random magnetic eld) or correlation length of disorder. Performing a closely connected analysis of the quantum correction to the conductivity in one-loop order, we show that it is non-divergent, in contrast to recent claims in the literature. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 72.15.Rn; 72.10.-d; 73.20.Fz; 73.23.-b Keywords: Current correlations; Localization; Random magnetic eld 1. Introduction The quantum coherence is well known to play a central role in the physics of mesoscopic systems. It induces, in particular, long-range spatial correlations of local densities of states and eigenfunction ampli- tudes. The long-range character of these correlations is due to the existence of massless modes, diusons and Cooperons. This leads also to strong mesoscopic uctuations of global quantities, such as the conduc- tance or the inverse participation ratio. In this paper, * Corresponding author. Tel.: +49-721-6083368; fax: +49-721- 698150. E-mail address: mirlin@tkm.physik.uni-karlsruhe.de (A.D. Mirlin). 1 Also at A.F. Ioe Physico-Technical Institute, 194021 St. Petersburg, Russia. 2 Also at Petersburg Nuclear Physics Institute, 188350 St. Pe- tersburg, Russia. we calculate the correlation function of local equilib- rium current densities of electrons subject to a (possi- bly smooth) random potential (RP) or random mag- netic eld (RMF). Non-zero local currents exist in a system if the time reversal invariance is broken by a magnetic eld, either uniform or spatially uctuating. We will demonstrate that the result is independent of the type of disorder and has a rather universal char- acter. We perform a closely connected analysis of the quantum correction to the conductivity in one-loop or- der and prove that it is non-divergent, irrespective of the type (RP or RMF) and the correlation length of disorder, in contrast to claims in the literature con- cerning delocalization in the RMF problem [1,2]. 2. Current correlations We consider the correlation function of local current densities j  (r;E) at equilibrium in 2D (we set ˝ =1 1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII:S1386-9477(01)00407-6