On the Deviations from Ohm's Law at High Current Densities

The deviations from Ohm's law at high current densities are calculated on the basis of the wave-mechanical theory of conductivity. A current density of ${10}^9$ amp./${\mathrm{cm}}^2$ causes a 1 percent deviation only. No observable deviations are to be expected at the experimental current densities available at present (${10}^6$ amp./${\mathrm{cm}}^2$). This is in agreement with the experiments of Barlow, neither does it contradict those of Bridgman, if the effects found by him are due to secondary factors. The method used consists in the actual solving of the fundamental equation for conductivity in a higher approximation. It is proved that in the Lorentz model (fixed metal ions) the fundamental equation is not soluble in the second approximation in the field strength. A solution in this approximation can be obtained only by assuming inelastic collisions between the electrons and the metal ions. The analogy between the distribution function containing the influence of the electric field and a distribution function found by Pidduck for the motion of ions in gases is pointed out. A generalization of the present theory is indicated by taking into account the influence of the external field on the lattice waves.