标题： 关于受周期性电势扰动的兰道哈密顿量的谱 $V\in H^s_{\mathrm {loc}}({\mathbb R}^2;{\mathbb R})$， $s > 0$ 显示英文标题

标题： On the spectrum of the Landau Hamiltonian perturbed by a periodic electric potential $V\in H^s_{\mathrm {loc}}({\mathbb R}^2;{\mathbb R})$, $s > 0$

摘要： 我们证明在Sobolev空间$H^s_{\Lambda }({\mathbb R}^2;{\mathbb R})$，$s > 0$中，对于具有给定周期格点$\Lambda $的周期函数，存在一个稠密的$G_{\delta }$-集${\mathcal O}$，使得当任何周期电势$V\in {\mathcal O}$对Landau哈密顿量$H_B + V$进行扰动时，对于所有具有有理通量的均匀磁场，其谱都是绝对连续的。 显示英文摘要

摘要： We prove that in a Sobolev space $H^s_{\Lambda }({\mathbb R}^2;{\mathbb R})$, $s > 0$, of periodic functions with a given period lattice $\Lambda $, there exists a dense $G_{\delta }$-set ${\mathcal O}$ such that the spectrum of the Landau Hamiltonian $H_B + V$ perturbed by any periodic electric potential $V\in {\mathcal O}$ is absolutely continuous for all homogeneous magnetic fields with a rational flux.