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Creators/Authors contains: "Faust, Matthew"

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  1. ; ; (, Journal of Mathematical Physics)
    We use Bézout’s theorem and Bernstein–Khovanskii–Kushnirenko theorem to analyze the level sets of the extrema of the spectral band functions of discrete periodic Schrödinger operators on Z2. These approaches improve upon previous results of Liu and Filonov–Kachkovskiy. 
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    Free, publicly-accessible full text available June 1, 2026
  2. ; (, Journal of Spectral Theory)
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  3. ; ; ; ; ; ; ; (, Journal of Mathematical Physics)
    Let Γ=q1Z⊕q2Z⊕⋯⊕qdZ, with qj∈Z+ for each j ∈ {1, …, d}, and denote by Δ the discrete Laplacian on ℓ2Zd. Using Macaulay2, we first numerically find complex-valued Γ-periodic potentials V:Zd→C such that the operators Δ + V and Δ are Floquet isospectral. We then use combinatorial methods to validate these numerical solutions. 
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