QUANTUM VARIATIONAL PRINCIPLE OF IRREVERSIBLE PROCESSES IN A MAGNETIC FIELD

Abstract

Quantum variational principle of irreversible processes is generalized to the systems under the uniform magnetic field. For the electron transport in impurity potentials as a typical example, contractions of the density matrix are performed without any approximation in two steps; first the off-diagonal part of the density matrix is eliminated and subsequently the even part with respect to time reversal. In consequence the maximum principle is derived for the odd part of the diagonal elements of the density matrix. This means the contraction of the density matrix brings about irreversibility. The variational principle is shown to be closely related to that for the conventional Boltzmann–Bloch equation and is regarded as its fundamental version. The dependences of the density matrix on the magnetic field and wave number are discussed.