ASA 125th Meeting Ottawa 1993 May

2pPA3. Anderson localization in the time domain: Numerical studies of waves in two-dimensional disordered media.

Richard L. Weaver

Dept. of Theor. and Appl. Mech., Univ. of Illinois, Urbana, IL 61801

Experimental work in the time domain on Anderson localization and anomalous diffusion in dimensions greater than one is scant, being confined to some ultrasonic work by Weaver and, inasmuch as measurements of frequency--frequency intensity correlation functions imply measurements of time domain behavior, some microwave work by Genack and co-workers. Numerical work in the time domain is similarly poorly developed. No studies have been conducted with sufficient detail for determination of the effective transport behavior. This paper presents results obtained from new numerical experiments in an attempt to rectify this lack. A numerical model is introduced that allows the tracking of evolving wave energy density in a two-dimensional linear classical wave equation version of an Anderson model diagonally disordered Hamiltonian. The behavior of the evolving average wave energy density in effectively infinite large samples of this system (typically 300 sites by 100 sites) excited by tone burst line sources is presented and the results shown to collapse to an apparent single universal response function with interesting asymptotic character like exp(-r/(lambda)-r[sup 2]/4 (beta) t) where r is the distance from the source, (lambda) is the localization length, and (beta) is a constant not equal to the bare diffusivity. The effect of dissipation is also investigated, and, consistent with previous demonstrations, found to be trivial. [Work supported by NSF MSS-91-14360.]