Behavior of Reduced Density Matrices of the Ideal Fermi Gas

概要

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The behavior of the one-particle reduced density matrix ρ^<(1)>(r) and the two-particle distribution function ρ^<(2)>(r) of the ideal Fermi gas are investigated for various limiting cases. These cases are classified by the relative magnitude of the following parameters ; the distance r, the thermal wave length λ_T and an "effective length" R_0=(6π^2ρ/2S+a)^<-1/3>, where ρ is the density and S is spin. At T=0, R_0^<-1> is reduced to the Fermi wave number k_0 and the obtained long distance behaviors are well known ; for instance, R_0^<-2>r^<-4>[1+cos(2k_0r)] for ρ^<(2)>(r), whereas for T≠0, this well-known behavior is shown to be valid only when r is smaller than λ_T and the asymptotic behavior is found to be λ_T^<-4>r^<-2>[1+cos(2k_0r)]exp(1ar/λ_T), where a is a constant. This is a sum of terms which shows exponential decay and oscillatory exponential decay, respectively. An explicit form of the three-particle distribution function ρ^<(3)>(r_<12>,r_<23>,r_6lt;31>) of the ideal Fermi gas is also given and its behaviors are discussed.
理論物理学刊行会の論文
1970-03-25