Generalized Nonlinear Fluctuation-Dissipation Relation for the One-Component Plasma

Abstract

We present a novel procedure leading to compact and tractable cubic \((p=3)\) and quartic \((p=4)\) scalar fluctuation-dissipation relations for the classical one-component plasma subjected to a weak external Coulombic perturbation; there is no external magnetic field. The ultimate goal here is to establish a generalized nonlinear fluctuation-dissipation relation in which a single \((p+1)\)-point dynamical structure function is expressed as a linear combination of pth-order external density response functions. When cast in this form, such an architecture, by definition, is invariant with respect to rotation on the (\(p+1\))-sided polygon formed by the wave vector-frequency arguments of the dynamical structure function. The application of this rotation symmetry to suppress unphysical isolated singularities is a basic ingredient of the derivation.