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