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Creators/Authors contains: "Matos, Rodrigo"

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  1. ; ; (, Nonlinearity)
    Abstract This paper investigates uniqueness results for perturbed periodic Schrödinger operators on Z d . Specifically, we consider operators of the form H = − Δ + V + v , where Δ is the discrete Laplacian, V : Z d → R is a periodic potential, and v : Z d → C represents a decaying impurity. We establish quantitative conditions under which the equation − Δ u + V u + v u = λ u , for λ ∈ C , admits only the trivial solution u ≡ 0 . Key applications include the absence of embedded eigenvalues for operators with impurities decaying faster than any exponential function and the determination of sharp decay rates for eigenfunctions. Our findings extend previous works by providing precise decay conditions for impurities and analyzing different spectral regimes ofλ. 
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    Free, publicly-accessible full text available April 9, 2026
  2. ; ; ; ; ; ; ; (, 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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  3. ; ; (, Annales Henri Poincaré)
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  4. ; ; (, Journal of Functional Analysis)
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  5. (, Journal of Mathematical Physics)
    Localization results for a class of random Schrödinger operators within the Hartree–Fock approximation are proved in two regimes: Large disorder and weak disorder/extreme energies. A large disorder threshold λHF analogous to the threshold λAnd obtained in Schenker [Lett. Math. Phys. 105(1), 1–9 (2015)] is provided. We also show certain stability results for this large disorder threshold by giving examples of distributions for which λHF converges to λAnd, or to a number arbitrarily close to it, as the interaction strength tends to zero. 
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  6. ; ; (, Journal of Functional Analysis)
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  7. ; (, Communications in Mathematical Physics)
    null (Ed.)
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