Off-diagonal long-range order, pair distribution function, and structure factor of the ideal Fermi gas in D dimensions and Price's inequality.

Abstract

The one-particle density matrix in the coordinate representation is calculated for the ideal Fermi gas in general D dimensions and a slow decay form of off-diagonal long-range order (ODLRO) is demonstrated therein. The pair distribution function and the structure factor are deduced from the one-particle density matrix. Their deviations from the classical values are viewed as a measure of the quantum phase, manifesting the existence of ODLRO. An upper bound on the structure factor due to Price [Phys. Rev. 94, 257 (1954)] is tested with our general solution and is also applied to the interacting electron gas.