  In this paper, we introduce a conduction model of Fermi particles on a finite
sample, and investigate the asymptotic behavior of stationary current for large
sample size. In our model a sample is described by a one-dimensional finite
lattice on which Fermi particles injected at both ends move under various
potentials and noise from the environment. We obtain a simple current formula.
The formula has broad applicability and is used to study various potentials.
When the noise is absent, it provides the asymptotic behavior of the current in
terms of a transfer matrix. In particular, for dynamically defined potential
cases, a relation between exponential decay of the current and the Lyapunov
exponent of a relevant transfer matrix is obtained. For example, it is shown
that the current decays exponentially for the Anderson model. On the other
hand, when the noise exists but the potential does not, an explicit form of the
current is obtained, which scales as 1/N for large sample size N. Moreover, we
provide an extension to higher dimensional systems. For a three-dimensional
case, it is shown that the current increases in proportion to cross section and
decreases in inverse proportion to the length of the sample.
