Journal of Mathematical Physics

Classical Green's Functions in Response Theory

John C. Herzel

Published Mar 1, 1970• 3 citations

Abstract

The present paper is concerned with the retarded many-time thermodynamic Green's function method in classical statistical mechanics. In the formulation of the nonlinear response of a dynamical variable, unaveraged Green's functions are specified and used to discuss the physical meaning of many-time Poisson-bracket nests. Equilibrium ensemble averages of these Green's functions are relevant to the classical Kubo response theory, the latter of which is interpreted from the viewpoints of both the classical ``Heisenberg'' and ``Schrödinger'' pictures. A method for evaluating the many-time thermodynamic Green's functions based on their definition in terms of the resolvent operator is suggested and discussed in relation to the linear dielectric function and the anharmonic oscillator. The many-time Green's function equations of motion are shown to be equivalent to identities based on the resolvent operator. It is shown how microscopic equations of motion can be used to derive the Bogoliubov-Sadovnikov (B-S) hierarchy from the lowest-order many-time Green's function equation of motion.

DOI: 10.1063/1.1665204

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