论文标题
离散磁随机schrödinger操作员的状态密度和离域的密度
Density of states and Delocalization for discrete magnetic random Schrödinger operators
论文作者
论文摘要
我们研究了正方形和蜂窝晶格上的离散磁随机schrödinger操作员。对于具有任何有理磁通量的六角形晶格上的非随机磁性算子，我们表明中间两个分散表面展示了狄拉克锥。然后，我们得出了蜂窝晶格上状态密度的渐近扩展，以进行任意有理磁通量的振荡。这使我们作为一种推论，可以严格研究量子厅效应，并结论靠近锥形点的动态界定。我们在$ \ mathbb z^2 $ lattice上获得离散的随机schrödinger运算符的结果相似，磁场较弱，靠近其光谱的底部和顶部。
We study discrete magnetic random Schrödinger operators on the square and honeycomb lattice. For the non-random magnetic operator on the hexagonal lattice with any rational magnetic flux, we show that the middle two dispersion surfaces exhibit Dirac cones. We then derive an asymptotic expansion for the density of states on the honeycomb lattice for oscillations of arbitrary rational magnetic flux. This allows us, as a corollary, to rigorously study the quantum Hall effect and conclude dynamical delocalization close to the conical point under disorder. We obtain similar results for the discrete random Schrödinger operator on the $\mathbb Z^2$-lattice with weak magnetic fields, close to the bottom and top of its spectrum.
