论文标题
正顺序函数的非线性schrödinger方程：I。基态的存在
The nonlinear Schrödinger equation for orthonormal functions: I. Existence of ground states
论文作者
论文摘要
我们研究了$ n $正交功能系统的非线性schrödinger方程。当非线性的指数$ p $不太大时，我们证明了所有$ n $的基础状态，而对于无限n_j $的无限序列$ n_j $倾向于在可能的整个可能的$ p $'s中，d \ geq1 $。这使我们能够证明，对于具有较大狄拉克交换常数的Kohn-Sham模型中的量子晶体，翻译对称性被打破。
We study the nonlinear Schrödinger equation for systems of $N$ orthonormal functions. We prove the existence of ground states for all $N$ when the exponent $p$ of the non linearity is not too large, and for an infinite sequence $N_j$ tending to infinity in the whole range of possible $p$'s, in dimensions $d\geq1$. This allows us to prove that translational symmetry is broken for a quantum crystal in the Kohn-Sham model with a large Dirac exchange constant.
