Asymptotic Spectral Properties of the Schrödinger Operator With Thue-Morse Potential

Authors

William Clark, Ohio University
Rachael Kline, St. John Fisher UniversityFollow
Michaela Stone, Louisiana State University

Document Type

Conference Proceeding

Publication Date

2-1-2014

Department

Mathematics

Abstract

The open problem

Study the Thue-Morse trace map; in particular, find the asymptotics of the Hausdorff dimension of the spectrum as the coupling constant tends to zero or infinity.

Our research

• We studied the dynamics of the Thue-Morse trace map.

• We developed MATLAB code to help approximate the box-counting dimension, thickness, and Hausdorff measure of the Schrödinger operator with Thue-Morse potential.

• We analysed the resulting data, which confirmed conjectures about the asymptotic behavior of the fractal dimensions of the operator. Asymptotic Spectral Properties of the Schr¨odinger Operator with Thue-

Comments

Presented at the Nebraska Conference for Undergraduate Women in Mathematics on February 1, 2014.

Publication Information

Clark, William; Kline, Rachael; and Stone, Michaela, "Asymptotic Spectral Properties of the Schrödinger Operator With Thue-Morse Potential" (2014). Undergraduate External Publications. Paper 4.
https://fisherpub.sjf.edu/undergraduate_ext_pub/4

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