Unified formalism for excess current noise in random-walk models

Excess current noise in random-walk models with a frequency-independent conductivity is studied from a general point of view. By introducing a ``dynamical'' diffusion constant, it is shown that the current autocorrelation function in an external field probes the equilibrium dynamical diffusion-constant autocorrelation function. From this a number of results, previously shown for particular models, are derived. Also, it is shown that the external-field current autocorrelation function is proportional to the equilibrium autocorrelation function for the absolute value of the current. Thus, the excess-noise spectrum probes the equilibrium-speed autocorrelation function. In the treatment advanced here, the study of excess current noise in random-walk models reduces to a study of the stochastic point process constituted by the particle-jump times. This point process contains all information about the noise. As an illustration of the general theory, the continuous-time random-walk model is briefly reviewed and a simple derivation of the excess noise in the model is given. Finally, the role of Fermi statistics in models for 1/f noise is discussed. It is argued that number-fluctuation models, i.e., models with long trapping times, are incompatible with Fermi statistics. On the other hand, it is shown there is a peculiar ``single-particle'' 1/f noise which is due to Fermi statistics but has nothing to do with the observed 1/f current noise.