Random Green matrices: From proximity resonances to Anderson localization

Instytut Fizyki, Polska Akademia Nauk, Aleja Lotniko´w 32/46, 02-668 Warszawa, Poland~Received 20 August 1999; published 6 January 2000!Universal properties of the spectra of certain matrices describing multiple elastic scattering of scalar wavesfrom a collection of randomly distributed point-like objects are discovered. The elements of these matrices areequal to the free-space Green’s function calculated for the differences between positions of any pair ofscatterers. A striking physical interpretation within Breit-Wigner’s model of the single scatterer is elaborated.Proximity resonances and Anderson localization are considered as two illustrative examples.PACS number~s!: 03.65.Nk, 41.20.Jb, 72.10.Fk, 72.15.Rn