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math.AP2019
Existence and asymptotics of nonlinear Helmholtz eigenfunctions
Jesse Gell-Redman, Andrew Hassell, Jacob Shapiro +1
We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form \begin{equation*} (Δ- λ^2) u = N[u], \end{equation*} wher…
math-ph2019
Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
Eli Fonseca, Jacob Shapiro, Ahmed Sheta +2
We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredho…
math.AP2019
Semiclassical Estimates for Scattering on the Real Line
Kiril Datchev, Jacob Shapiro
We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has…