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We investigate the effects of relatively rapid variations of the boundariesof an overmoded cavity on the stochastic properties of its interior acoustic orelectromagnetic field. For quasi-static variations, this field can berepresented as an ideal incoherent and statistically homogeneous isotropicrandom scalar or vector field, respectively. A physical model is constructedshowing that the field dynamics can be characterized as a generalized diffusionprocess. The Langevin--It\^{o} and Fokker--Planck equations are derived andtheir associated statistics and distributions for the complex analytic field,its magnitude and energy density are computed. The energy diffusion parameteris found to be proportional to the square of the ratio of the standarddeviation of the source field to the characteristic time constant of thedynamic process, but is independent of the initial energy density, to firstorder. The energy drift vanishes in the asymptotic limit. The time-energyprobability distribution is in general not separable, as a result ofnonstationarity. A general solution of the Fokker--Planck equation is obtainedin integral form, together with explicit closed-form solutions for severalasymptotic cases. The findings extend known results on statistics anddistributions of quasi-stationary ideal random fields (pure diffusions), whichare retrieved as special cases.

Nonstationary random acoustic and electromagnetic fields as wave diffusion processes