Random Phase Approximation (Why they call it so?)

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"Random Phase Approximation" (Why they call it so?)


I'm wondering that why the scientists call this phenomena in many body physics "Random Phase Approximation". (Why Random? Why Phase?) It seems that when we want calculate a correlation function in quantum field theory, it leads to calculation of 4-particle or 6-particle green's function and we use mean field theory to calculate it and nothing more. so why we should call it random phase approximation (Why Random? Why Phase?) .

Thank you.


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From the original paper on RPA by Bohm and Pines, Phys. Rev. 82, 625, (1951):
Bohm and Pines said:
We distinguish between two kinds of response of the electrons to a wave. One of these is in phase with the wave, so that the phase difference between the particle response and the wave producing it is independent of the position of the particle. This is the response which contributes to the organized behavior of the system. The other response has a phase difference with the wave producing it which depends on the position of the particle. Because of the general random location of the particles, this second response tends to average out to zero when we consider a large number of electrons, and we shall neglect the contributions arising from this. This procedure we call the random phase approximation.”

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