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The electric current is calculated in the linear response regime by solving the Smoluchowski equation. To maintain a stationary current one needs the steady state distribution which differs from the equilibrium one. Due to the presence of an arbitrary crystal potential the conventional Drude conductivity is modified. We derive an exact expression for the conductivity in one dimension. The coupling between the applied electric field and the crystal potential leads to a systematic deformation of the potential that contributes to the renormalization of the electric field inside the system. The corrections to the Drude conductivity are determined completely by the configurational part of the partition function. The activation energy for the conductivity process is expressed by a combination of the free energy of the underlying equilibrium system. In case of a tight binding potential the conductivity offers corrections depending on the amplitude of the potential. The probability distribution for the charge carriers depends significantly on the electric field. As a further application we discuss nano‐contacts with piecewise constant potentials. The corrections to the electric conductivity are determined by the potential height. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Exact expression for Drude conductivity in one‐dimension with an arbitrary potential