Random phase approximation

From Wikipedia

The random phase approximation (RPA) is an approximation method in condensed matter physics and in nuclear physics. It was first introduced by David Bohm and David Pines as an important result in a series of seminal papers of 1952 and 1953.^[1][2][3] For decades physicists had been trying to incorporate the effect of microscopic quantum mechanical interactions between electrons in the theory of matter. Bohm and Pines' RPA accounts for the weak screened Coulomb interaction and is commonly used for describing the dynamic linear electronic response of electron systems.

In the RPA, electrons are assumed to respond only to the total electric potential V(r) which is the sum of the external perturbing potential V_ext(r) and a screening potential V_sc(r). The external perturbing potential is assumed to oscillate at a single frequency ω, so that the model yields via a self-consistent field (SCF) method ^[4] a dynamic dielectric function denoted by ε_RPA(k, ω).

The contribution to the dielectric function from the total electric potential is assumed to average out, so that only the potential at wave vector k contributes. This is what is meant by the random phase approximation. The resulting dielectric function, also called the Lindhard dielectric function,^[5][6] correctly predicts a number of properties of the electron gas, including plasmons.^[7]

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