On the problem of DC conductivity at T=0K in a one-dimensional system of finite length: calculation of the scattering rate in case of weak disorder

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Abstract
The theory of electronic conduction in a one-dimensional disordered system of finite length at T=0K is dealt with. Unlike other approaches in which only first-order electric field response is considered, the electric field is treated in full order. For the case of weak disorder, it is shown that the full-order inclusion of the electric field is essential to obtain a field-independent scattering rate and thus an ohmic relation between time-averaged current and field. This result is found, however, only for field values that are not too small, in which case the scattering rate is shown to agree, surprisingly, with the Golden Rule result. In addition, the existence of a very small critical field strength is discussed, below which the time-averaged current drops exponentially to zero with decreasing field.