Thermal Fluctuations in a Nonlinear System

Abstract

As an example of a nonlinear system, an electric circuit containing a voltage-dependent resistance $R\left(V\right)\mathrm{}$ is studied. The resistance is in contact with a heat bath and generates current fluctuations. A general method is given to find the spectral density of these fluctuations. For two special forms of $R\left(V\right)\mathrm{}$, explicit results are obtained by means of a perturbation calculation. The result differs from the Nyquist formula mainly in that new terms appear, corresponding to relaxation times $\frac{1}{2}{R}_{0}C$, $\frac{1}{3}{R}_{0}C$, etc.