高斯随机势加宽的单朗道能级态密度的上界
Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials
摘要：
我们研究了欧氏平面R^2上的非相对论性带电粒子在垂直恒定磁场和R^2-齐次随机势作用下的情形，近似地将希尔伯特空间L^2（R^2）上相应的随机朗道哈密顿量限制在单个但任意的朗道能级的本征空间中。对于广泛的一类高斯随机势，我们严格证明了相关的限制积分态密度是绝对连续的勒贝格测度。我们构造明确的上界所产生的衍生物，限制态密度。因此，任何给定的能量几乎肯定不是限制随机朗道哈密顿量的本征值。
英文摘要：
We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian.
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