We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.

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弱相互作用费米气体的相关能

我们严格推导了费米气体在高密度和弱相互作用的定标范围内的相关能的前导顺序。结果验证了随机相位近似的预测。我们的证明从三个方面完善了集体玻化的方法。我们近似对角线化了一个有效的哈密顿量，描述了哈特里-福克状态附近的近似玻色子的集体激发，同时表明无间隙和非集体激发对基态能量的影响可忽略不计。