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In this paper, we introduce a conduction model of Fermi particles on a finitesample, and investigate the asymptotic behavior of stationary current for largesample size. In our model a sample is described by a one-dimensional finitelattice on which Fermi particles injected at both ends move under variouspotentials 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 interms of a transfer matrix. In particular, for dynamically defined potentialcases, a relation between exponential decay of the current and the Lyapunovexponent of a relevant transfer matrix is obtained. For example, it is shownthat the current decays exponentially for the Anderson model. On the otherhand, when the noise exists but the potential does not, an explicit form of thecurrent is obtained, which scales as 1/N for large sample size N. Moreover, weprovide an extension to higher dimensional systems. For a three-dimensionalcase, it is shown that the current increases in proportion to cross section anddecreases in inverse proportion to the length of the sample.

Asymptotic property of current for a conduction model of Fermi particles on finite lattice