7 papers
Semiclassical resolvent bounds for weakly decaying potentials
Jeffrey Galkowski, Jacob Shapiro
In this note, we prove weighted resolvent estimates for the semiclassical Schrödinger operator , . The potential $…
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…
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…
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…
The Topology of Mobility-Gapped Insulators
Jacob Shapiro
Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete sp…
Strongly Disordered Floquet Topological Systems
Jacob Shapiro, Clément Tauber
We study the strong disorder regime of Floquet topological systems in dimension two, that describe independent electrons on a lattice subject to a periodic driving. In the spectrum…