Random phase approximation

Random phase approximation (RPA) is one of the most often used methods for describing the dynamic electronic response of systems.

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In 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 [1] a dynamic dielectric function

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 [2,3], correctly predicts a number of properties of the electron gas, including plasmons [4].

References

1. H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959).
2. J. Lindhard, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 28, 8 (1954).
3. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Thomson Learning, Toronto, 1976).
4. G. D. Mahan, Many-Particle Physics, 2nd ed. (Plenum Press, New York, 1990).