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

摘要

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 ωn and ω, respectively, the transient regime exhibits a set of transient harmonics oscillating at frequencies (ωn−ω) and (ωn+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.