Random-walk model for equilibrium resistance fluctuations (Q1080556)

The Voss-Clarke relation between the fluctuations of the band-limited Johnson noise power and the nonequilibrium steady-state current fluctuations is investigated for a continuous time random walk (CTRW). The equivalence between the CTRW and a multistate trapping model (MSTM), as shown by \textit{K. W. Kehr} and \textit{J. W. Haus} [Physica A 93, 412 ff. (1978)] is exploited to calculate the higher-order current correlation functions using the Markovian property of the MSTM description. The Voss-Clarke relation is found to be obeyed provided the trapping and release times are long compared to the microscopic correlation time of a carrier in the conduction state. The equilibrium resistance fluctuations are shown to arise physically from equilibrium fluctuations in the number of carriers in the conduction state. It is suggested that the results obtained here should hold for more general trapping models under the same physical conditions.