论文标题
磁性schrödinger操作员和景观功能
Magnetic Schrödinger operators and landscape functions
论文作者
论文摘要
我们研究了磁性schrödinger操作员低洼特征功能的定位属性$$ \ frac {1} {2} {2} {2} \ left（ - i \ nabla-a（x）\ right）^2 ϕ+ v（x）+ v（x）ϕ =λϕ，$ v：$ v：$ v：$ v：ω\ offerart $ em pecy＆extrow \ extrow \ ext and y math and and and and and and and and and and and and and and and and and and and and and。 $ a：ω\ rightarrow \ mathbb {r}^d $诱导磁场。我们扩展了Filoche-Mayboroda不平等，并证明了磁性环境中的精致不等式，可以预测低能特征函数的定位。即使在消失磁场的情况下，该结果也是新的。数值示例说明了结果。
We study localization properties of low-lying eigenfunctions of magnetic Schrödinger operators $$\frac{1}{2} \left(- i\nabla - A(x)\right)^2 ϕ+ V(x) ϕ= λϕ,$$ where $V:Ω\rightarrow \mathbb{R}_{\geq 0}$ is a given potential and $A:Ω\rightarrow \mathbb{R}^d$ induces a magnetic field. We extend the Filoche-Mayboroda inequality and prove a refined inequality in the magnetic setting which can predict the points where low-energy eigenfunctions are localized. This result is new even in the case of vanishing magnetic field. Numerical examples illustrate the results.
