Equations for the Theory of Response and Transport in Statistical Mechanics

Abstract

Taking the viewpoint that a complete solution of the Liouville equation contains much more information than is necessary in response theory (wherein one is concerned with a particular response), projection techniques are employed to introduce a shortcut in the problem. The treatment supplements and completes the formalism initiated in a previous publication and yields a general equation which is more relevant to response theory in the usual sense. The most natural application is to the theory of transport. The general transport equation is analyzed in the context of electrical conduction. Meaningful similarities to the simple classical Drude model of conduction are exhibited; the relationship of this exact formalism to the Kubo theory of linear response is shown, an exact solution for a step-function stimulus and approximation procedures which go beyond the linear regime are presented, and an expression for the electrical resistivity is explicitly calculated thus making contact with an earlier paper by Kenkre and Dresden. The response equation is also analyzed in the context of electric and magnetic polarization.