Exact Calculation of the Fluctuation Spectrum for a Nonlinear Model System

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Abstract
Fluctuations in a circuit consisting of a diode and a condenser have been treated by means of approximate methods [C. T. J. Alkemade, Physica 24, 1029 (1958); N. G. van Kampen, ibid. 26, 585 (1960)]. In the present paper, exact eigenfunctions and eigenvalues of the master equation for this system are obtained, and the spectral density of the equilibrium fluctuations is calculated. The most striking result is that the spectrum of the eigenvalues (which are reciprocal relaxation times) has an accumulation point, corresponding to the average time interval between two successive electron transitions.