Quantum-mechanical perturbations giving rise to a statistical transport equation

Abstract

The quantum-mechanical theory of the transport equation is reconsidered for the case of transport processes produced by a small perturbation. On the basis of the most common applications of the equation to crystals (heat conduction, etc.) a characteristic property of the perturbation is recognized as being responsible for the appearance of dissipative effects in the time evolution of the system. With the help of this property a greatly improved derivation of the transport equation is obtained. It avoids the repeated use of a random phase assumption after each of a long succession of short time intervals, a common drawback of the conventional derivations. The validity of the transport equation is established without a priori statistical hypothesis for two special classes of initial states. It is also derived for arbitrary initial states with the help of a random phase assumption concerning the initial state alone.