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Asymptotically Valid Approximation
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analytic analytically continued approximate solution approximation methods asymptotic form Balescu Boltzmann Boltzmann constant Boltzmann equation Born approximation calculation Chapter co-plane collision integral complex conjugate correlation energy ECorr correlation function defining integral equation diagrams dielectric functions distribution function electron gas electron plasma equation of motion equation V.l-5 equations III.2-1 equilibrium exchange effects exchange factor exchange potential exchangeless dielectric constant expressed in terms external charge Fermions g-bond GR(A GR(D GR(E Hamiltonian Hartree-Fock Hartree-Fock approximation Hence homogeneous system Hubbard dielectric constant inhomogeneous interaction energy interaction potential inverse Laplace transformation kinetic equation last term line integration long-time behavior lower-half momenta obtain one-particle distribution one-particle energy p,p+k p'+k p*-summation p+k+k particle exchange particle of momentum Phys pole potential energy potential v(k quantum mechanical random-phase approximation RPA reads readsi replace rewritten right-hand side second term solve Statistical Mechanics ternary correlation tion total energy upper-half yields zero temperature