About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Physica Scripta
Paper
Classical diffusion in a random environment and quantum mechanics with a random potential
Abstract
The problems of classical diffusion in a random environment and of quantum mechanics with a random potential are related by the transformation of the Fokker-Planck equation into the imaginary time SchrɆdinger equation. The hypothesis of dynamic scaling allows to connect the long-time properties of diffusion to the low-energy spectrum of the quantum problem. For the specific model where the drift force is a white noise, the anomalous sublinear diffusion found by Sinai is related to logarithmic anomalies in the inverse localization length and in the density of states. © 1988 IOP Publishing Ltd.