Date of Completion

2014

Document Type

Thesis

Department

Department of Mathematics and Statistics

Faculty Advisor/Sponsor

Kenneth I. Golden

Keywords

plasma, fluctuation-dissipation, statistical mechanics, nonlinear, response theory

Abstract

Fluctuation-dissipation theorems (FDTs) link transport coefficients (density response functions, conductivities, electric susceptibilities, etc.) to equilibrium n-point correlation functions. Of special importance to us is the applications of the FDT to one component plasmas and binary ionic mixtures. When applied to such systems, the fluctuation-dissipation theorem provides invaluable insight into response functions and transport coefficients across the non-equilibrium spectrum. After an in-depth review of the FDT and linear response theory, we focus upon expanding the work of K.I. Golden and G. Kalman (J. Stat. Phys. 3, 87 (1972); Annals of Phys. 141, 160 (1982)) , which proposes a nonlinear response theory for magnetic field-free classical plasmas. We attempt to re-formulate the hierarchy of static fluctuation-dissipation relations in terms of external density response functions. This provides a systematic formalism for calculating higher order correlation functions in terms of lower-order ones. In future studies, we plan to derive relationships between the screened and external response functions in the RPA (or any suitable approximation method which takes account of particle correlation effects beyond the RPA). This will then provide insight into the hierarchy of static structure functions and their correlation functions.

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