Dispersive decay bounds for the SSH model on the half-line

We study the Schr\"odinger flow for the SSH model, a class of self-adjoint discrete dimer lattice Hamiltonians on the half-line. Using oscillatory integral techniques, we prove dispersive time-decay estimates, which quantify the spreading of energy throughout the lattice for a localized initial condition. Furthermore, we determine precise dependence of the constants in the decay rates on the parameters of the Hamiltonian. The analysis is complicated by the fact that as a consequence of the boundary condition, the expression for the propagator contains oscillatory integrals with nonintegrable singularities.