标题： 动态结构因子的任意阶奇频矩的动能贡献 显示英文标题

标题： Kinetic contribution to the arbitrary order odd frequency moments of the dynamic structure factor

摘要： 对于动态结构因子的奇数（任意阶）频率矩，通过一个有限求和得到了动能贡献的精确表达式，该求和涉及动量在精确动量分布上的偶数（所有较低阶）幂的平均值。 该推导针对非相互作用费米气体进行，并基于一个假设，即可以将费米分布上的平均值替换为精确分布上的平均值，从而推广到相互作用情况。 该表达式与已知结果（第一、第三频率矩）进行了验证，并进行了新的显式计算（第五、第七频率矩）。 显示英文摘要

摘要： An exact expression is derived for the kinetic contribution to the odd (arbitrary order) frequency moments of the dynamic structure factor via a finite summation that features averages of even (all lower orders) powers of the momentum over the exact momentum distribution. The derivation is carried out for the non-interacting Fermi gas and generalized to the interacting case based on the conjecture that averages over the Fermi distribution can be substituted with averages over the exact distribution. The expression is validated against known results (first, third frequency moments) and new explicit calculations (fifth, seventh frequency moments).