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Random phase approximation

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

In RPA, electrons are assumed to respond only to the total electric potential V(r) which is the sum of the external perturbing potential Vext(r) and a screening potential Vsc(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

εRPA(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].


  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).
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Random_phase_approximation". A list of authors is available in Wikipedia.
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