Application of the Dielectric Formulation to the Multi-Component, Many-Particle System with Coulomb Interaction

概要

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A multi-component, many-particle system with Coulomb interaction is described in terms of a generalized dielectric constant ε(q,ω) is calculated by the use of the equation-of-motion of a correlation function obtained within the random phase approximation (R.P.A.). For the Fermi, Bose, Bose and Bose, and Bose and Fermi systems, the ε(q,ω) obtained above leads directly to the result of Gell-Mann and Brueckner, Foldy, Bassichis, and Ginoza and Kanazawa. respectively. As for Fermi and Fermi system, it has two collective excitations : plasma wave and acoustic phonon wave. The letter is well-defined only for such a special choice of parameters specifying the system as ν<F_1> ≫ s > ν<F_2> and further, for the choice of parameters as ν<F_1 ≫ s ≫ν<F_2>, agrees with the acoustic phonon wave of an electron-ion system treated by the Thomas-Fermi approximation. For the parameters chosen otherwise, such a wave is unstable of does not exist. In the expressions of the conditions above, s is the velocity of acoustic phonon wave and ν<F_1> and ν<F_2> are Fermi velocities in one component and in the other, respectively. The above results show that in the weak coupling limit, the results obtained by treating Bose components consistently by the Bogoliubov method are equivalent to those obtained with the R.P.A.
理論物理学刊行会の論文
1974-12-25