Non-equilibrium thermo field dynamics and the transport of electrons in magnetic and electric fields

Abstract

The superoperator formalism of non-equilibrium Thermo Field Dynamics is extended to consider a system of electrons in contact with a thermal reservoir in a homogeneous crossed electric and magnetic field. Particular attention is paid to the role of gauge invariance. A brief overview of the development of a non-equilibrium, finite time, temperature dependent field theory is included, as well as an outline of the construction of the superoperator formalism of non-equilibrium thermo field dynamics. The relationship between the two point electron Green's functions and the probability distribution function appearing in the semi-classical Boltzmann equation is established. -- As an illustration of how the transport coefficients are found from the Boltzmann equation, the case of the Chamber's solution for the electrical conductivity is considered. The position dependence of the conductivity tensor in the presence of a domain wall is evaluated numerically, and the trends are verified analytically. -- Future extensions of the present work are discussed.