平均场区费米气体关联能的最佳上界
Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime
摘要：
虽然哈特里-福克理论是相互作用费米子的基本近似，但由于多体关联，如何描述对它的修正一直不清楚。本文从平面波给出的Hartree-Fock态出发，引入了粒子-空穴对集体激发。这些对可以近似地用玻色子二次哈密顿量来描述。我们利用Bogoliubov理论构造了一个试探态，得到了一个严格的Gell-Mann-Brueckner型的基态能量上限。我们的结果证明了随机相位近似的平均场标度制度，排斥，经常相互作用势。
英文摘要：
While Hartree-Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree-Fock state given by plane waves and introduce collective particle-hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann-Brueckner-type upper bound to the ground state energy. Our result justifies the random phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.
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