光滑函数有限阶零点的一个性质

一个函数在实数集上无限阶可导,这样的函数为实数集上的光滑函数.如果一个光滑函数f在x=a处函数值为零称x＝a是函数f的零点,如果该光滑函数在此点处还满足:直到n-1阶导数都为零,但n阶导数不为零,这个零点称为是n阶零点,本文中证明f与x-a的n次幂之比还是光滑函数.     

Exciton Excitations in a One－Dimensional Band Insulator with Hubbard Interactions

We study the properties of exciton excitations in the Hubbard model with alternating potential and dimerized hopping terms at half filling. With increasing Coulomb repulsive, we find that a spin triplet exciton band develops below the band gap. At certain critical interaction, the excitation gap of this exciton band vanishes and a new phase with a dimerized ground state emerges. The value of this critical Coulomb interaction is determined perturbatively.