Quantum Variational Principle of Irreversible Processes in a Magnetic field

Masakazu Ichiyanagi

Masumi Hattori, Huzio Nakano

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.

Stig Stenholm

Masakazu Ichiyanagi

A method is proposed for investigating nonequilibrium processes in an arbitrary system under an action of external perturbations. We formulate a new quantum mechanical variation principle, which is valid beyond linear irreversible processes. The definition of our variation functional is made on the basis of our recognition of the importance of a change in the internal energy of the system. In this article, we go beyond the theory of Nakano by developing our new variation principle in the framework of the closed-time-path method by Schwinger. The relationship of the thermodynamical stability criterion to the exact solution of transport problems is discussed.

Boris B. Kadomtsev

A.P. Grécos, I. Prigogine