Theoretical model of transient random fields based on the fluctuation-dissipation theorem

Abstract

In this paper, we calculate the transient field response of an electromagnetic mode inside a dynamic (mode-stirred) complex cavity. This is carried out on a physical basis through application of the theory of linear systems. The transition between equilibrium (stationary) states of the cavity is viewed as a non-equilibrium occurrence (event) for the partial/resultant field and is modeled by a second-order ordinary differential equation with time-dependent modal coefficients. On application of the fluctuation-dissipation theorem from statistical mechanics, it is possible to write this non-equilibrium evolution as a convolution integral of the linear response function of the cavity mode. A solution is found by using the Green's function technique. It is found that, besides the set of harmonics oscillating at natural and excitation frequencies ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> and ω, respectively, the transient regime exhibits a set of transient harmonics oscillating at frequencies (ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> -ω) and (ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> +ω). This intermediate set decays in accordance with modal damping and shows dependence on the initial time, exhibiting nonstationarity. Analytical results are of interest to mode-stirred reverberation chambers, random fields, as well as in other areas of physics and engineering involving dynamic cavities or random media.