An eigensystem approach to Anderson localization

作者：Elgart Alexander^*; Klein Abel

来源：Journal of Functional Analysis, 2016, 271(12): 3465-3512.

DOI：10.1016/j.jfa.2016.09.008

• Random Schrodinger operators
• Anderson localization
• Anderson model
• Multiscale analysis
• Level spacing
• Hall's Marriage Theorem

We introduce a new approach for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model at high disorder. In contrast to the usual strategy, we do not study finite volume Green's functions. Instead, we perform a multiscale analysis based on finite volume eigensystems (eigenvalues and eigenfunctions). Information about eigensystems at a given scale is used to derive information about eigensystems at larger scales. This eigensystem multiscale analysis treats all energies of the finite volume operator at the same time, establishing level spacing and localization of eigenfunctions in a fixed box with high probability. A new feature is the labeling of the eigenvalues and eigenfunctions by the sites of the box.

• 出版日期2016-12-15