An Exact Dynamics of an Electron Gas at r_s≈3.5 and a Short-wavelength Limit(New Developments in Statistical Physics Similarities in Diversities,YITP Workshop)

Abstract

We show the exact dynamic structure factor S(κ, ω) of the many-electron system by calculating the relaxation function. Our S(κ, ω) is asymptotically exact as κ→∞ and at a particular metallic density r^*_s≈3.5. From the exact solution, we derive two static relations, x^2=3/5y, and x^2=3/16ω^2_ρ[1-g(0)] valid at r^*_s, where x and y are averages of the one-particle kinetic energy and its square, respectively. Our S(κ, ω) is compared with an experimental measurement for Li at κ=2.08κ_F.