Physica D 168–169 (2002) 258–265 Effective eigenstates in a dynamical disordered tight-binding model A. Karina Chattah a,∗ , Manuel O. Cáceres b a Facultad de Matemática Astronom´ ıa y F´ ısica, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina b Centro Atómico Bariloche and Instituto Balseiro, CNEA and Universidad Nacional de Cuyo, Av. Bustillo Km 9.5, 8400 Bariloche, Argentina Abstract We study effective eigenstates—in mean value—for a 1D tight-binding (TB) Hamiltonian in the presence of diagonal dynamical disorder (DD). The averaged density of states (DOS) and localization length are shown as a function of the intensity of disorder and the correlation time of its temporal fluctuations. A delocalization electronic phenomenon is interpreted in terms of the localization length of the wave function, as a function of the time correlation of the DD. © 2002 Elsevier Science B.V. All rights reserved. PACS: 71.55; 02.50.Ey; 02.50.Wp; 05.30.-d Keywords: Tight-binding; Dynamical disorder; Kubo–Anderson process; Delocalization 1. Introduction In classical statistical mechanics the effects of dynamical disorder (DD) on the transport coefficient is well understood. A strong quenched disorder leads to sub-diffusion, but the presence of DD breaks down this classical localization, restoring a finite static conductivity [1–3]. The mathematical reason for this phenomenon is that DD in- troduces a shift in the generalized diffusion coefficient, which is ultimately the one responsible for reestablishing the analyticity at zero frequency. This shift is proportional to the inverse of the correlation time of the stochastic process which mimics the DD. This problem can be solved in a perturbative way, e.g. using the effective medium approxi- mation (EMA) [4] for dichotomic disorder. This approximate solution interpolates smoothly between static disorder and the limit of rapid temporal fluctuations, thus giving support to what physical intuition expects of the model. In quantum mechanics the conditions for localization are not as simple as in classical mechanics. The simplest model goes back to Anderson’s pioneer work, where a spinless non-interacting particle moving in a quenched random potential was studied. Since then, a lot of work has been done concerning transport in random media [5]. But the interesting quantum problem of DD was not studied until 1975 by Ovchinnikov and Érikhman [6], later on Madhukar and Post [7] reported an exact solution for the motion of a particle in a system with site diagonal and nearest-neighbor off-diagonal DD, using Gaussian white noises. Even when this result was of particular importance some doubts concerning the mobility were reported later [8,9]. This continuous quantum model was “exactly” solved ∗ Corresponding author. E-mail addresses: chattah@famaf.unc.edu.ar (A.K. Chattah), caceres@cab.cnea.gov.ar (M.O. C´ aceres). 0167-2789/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0167-2789(02)00514-6