 
Summary: Statistical characterization of random electrostatic potentials
M. Aldana, H. Larralde, and G. Marti´nezMekler
Centro de Ciencias Fi´sicas, UNAM, Apartado Postal 483, Cuernavaca, Morelos, CP 62251, Mexico
Received 14 January 2000
In this work we study statistical properties of random electrostatic potentials generated by one dimensional
lattices with random charges. We show that the resulting random potentials are correlated Gaussian processes,
satisfying the Lindeberg version of the central limit theorem, if certain restrictions are imposed on the indi
vidual potentials generated by the particles on the lattice. Since most of the pointparticle electrostatic poten
tials occurring in nature satisfy the Lindeberg condition, the correlation properties of the random potentials are
not arbitrary and must comply with the central limit theorem. Based on this theorem we can obtain explicit
expressions for these correlations. We thus are able to give a characterization of a broad class of potentials
yielding feasible physical scenarios. We illustrate some consequences of our findings by considering dynamical
properties of a test particle interacting with the lattice. We show how the long range correlations generate
statistical features in these properties, which are best exhibited when considering different length scales.
PACS number s : 05.40. a, 02.50.Ey
I. INTRODUCTION
Random potentials have long been an integral part of the
modeling of disordered systems 1 . They appear in the de
scription of localization phenomena, anomalous transport,
pinning, glassy states, intracellular transport, molecular
