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3.3 Non-Equilibrium GREEN's Functions

In Section 3.2 the GREEN's function for a system under equilibrium at finite temperature has been introduced. In this section, a more general formalism for systems under non-equilibrium conditions at finite temperature is presented. First, the ensemble average of an operator under non-equilibrium is defined. Then the contour-ordered non-equilibrium GREEN's function (NEGF) formalism is introduced and the equation of motion for the GREEN's function is presented. Finally, it will be shown that a perturbation expansion similar to the equilibrium theory can be achieved.
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M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors