无规相近似的崩溃：壳模型的例子和反例
Collapse of the random phase approximation: examples and counter-examples from the shell model
摘要：
对多费米子问题的哈特里-福克近似可以打破精确的对称性，在某些情况下，通过改变相互作用中的一个参数，可以将哈特里-福克最小值从一个破缺态驱动到一个守恒态（在文献中也被称为"相变"）。当将随机相位近似（RPA）应用于Hartree-Fock波函数时，跃迁的阶数是很重要的：如果是一阶，RPA在整个跃迁过程中是稳定的，但是如果是二阶，RPA的振幅就会变大，导致非物理的结果。后者被称为爱国军的“占领”。虽然RPA中的一阶和二阶跃迁之间的差异是由Elderless首次指出的，但我们首次提出了一阶和二阶跃迁在统一模型（相互作用壳模型）中的非平凡例子，在那里我们可以与精确的数值结果进行比较。
英文摘要：
The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a ``phase transition'' in the literature). The order of the transition is important when one applies the random phase approximation (RPA) to the of the Hartree-Fock wavefunction: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as ``collapse'' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time non-trivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
