Abstract
The class of random linear systems having stochastic Green’s functions whose moments are invariant under arbitrary uniform translations of all time variables is defined and investigated. It is pointed out that this class is very broad, including, for example, virtually all treatments of wave propagation through a random medium. Proceeding by analogy with quantum field theory the quantities 𝒢 and M, related to the first and second moments of the stochastic Green’s function, are defined. Various properties of 𝒢 and M (which in quantum field theory correspond respectively to a propagator and an elastic scattering amplitude) are discussed, and it is shown that they may be conveniently used to describe the principal physical effects induced by transmission through a randomly fluctuating system. Specific examples are given in which these quantities are explicitly calculated and used to illustrate the general results.
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