Quantum transport theory based on the equilibrium density projection technique

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Abstract
We introduce a projection technique, called the equilibrium density projection technique, which involves two schemes: the ensemble average projection scheme and the combined projection scheme. Using this technique directly on the Liouville equation, we derive the linear-nonlinear response formula. We also expand the scattering factors to a continued-fraction representation to avoid the danger of divergence, and expand again the continued-fraction representation formula in a series form. Finally, we introduce a simple example for the linear response term and compare the two schemes.