  The frequency-dependent spectrum of current fluctuations through nano-scale
channels is studied using analytical and computational techniques. Using a
stochastic Nernst-Planck description and neglecting the interactions between
the ions inside the channel, an expression is derived for the current
fluctuations, assuming that the geometry of the channel can be incorporated
through the lower limits for various wave-vector modes. Since the resulting
expression turns out to be quite complex, a number of further approximations
are discussed such that relatively simple expressions can be used for practical
purposes. The analytical results are validated using Langevin dynamics
simulations.
