Schrödinger Operators with Thin Spectra

2020/07/02 by David Damanik, Jake Fillman, Damanik, David +1
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quasicrystal Structures and Properties #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2007.01402

openalex publication_date 2020/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The determination of the spectrum of a Schrödinger operator is a fundamental problem in mathematical quantum mechanics. We discuss a series of results showing that Schrödinger operators can exhibit spectra that are remarkably thin in the sense of Lebesgue measure and fractal dimensions. We begin with a brief discussion of results in the periodic theory, and then move to a discussion of aperiodic models with thin spectra.

Citations

• Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
• Schrödinger operators with dynamically defined potentials

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