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- W755089441 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 Schrodinger 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 ThueDisciplines Mathematics Comments Presented at the Nebraska Conference for Undergraduate Women in Mathematics on February 1, 2014. This conference proceeding is available at Fisher Digital Publications: http://fisherpub.sjfc.edu/undergraduate_ext_pub/4 Asymptotic Spectral Properties of the Schrodinger Operator With Thue-Morse Potential Research supported by William Clark Ohio University • Rachael Kline St. John Fisher College • Michaela Stone Louisiana State University Advisors: May Mei and Andrew Zemke This work was supported by NSF grant DMS-0739338. Cornell University Department of Mathematics Summer Math Institute Why do we care? Historical background The Thue-Morse sequence Modeling quasicrystals 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 Schrodinger 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 Schrodinger Operator with Thue-Morse Potential Introduction" @default.
- W755089441 created "2016-06-24" @default.
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- W755089441 date "2014-01-01" @default.
- W755089441 modified "2023-09-27" @default.
- W755089441 title "Asymptotic Spectral Properties of the Schrödinger Operator With Thue-Morse Potential" @default.
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