Springer Online Journal Archives 1860-2000
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Abstract We investigate an autocorrelation function of a soluble three-dimensional system, namely the temporal coherence functionC E(t)∝〈E(0)E(t)〉 of the thermal radiation field in a cube-shaped cavity for the stochastic electrical fieldE. In the thermodynamic limit,C E(t) relaxes exponentially at intermediate times, but a “long-tail” behaviourC 0(t)=At−4 withA〈0 is predominant for long times. In the case of a finite, but not too small, cavity lengthL obeyingΛ=hc/k BT≲L and at timest withct≲L, C E(t) is described by an asymptotic expansion in powers ofL −1 using generalized Riemann zeta functions. Surface-and shape-effects enhance the long-tail. In the case of very small cavities withL«Λ, we calculate an expansion ofC E(t) in terms of exp(−L −1) and cosines. An oscillatory, but not strictly periodic, long-time behaviour is observed in this case.
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