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

TL;DR

This paper establishes dispersive decay bounds for the SSH model on the half-line, analyzing how energy spreads over time using oscillatory integral techniques and accounting for boundary-induced singularities.

Contribution

It introduces novel dispersive decay estimates for the SSH model on the half-line, with explicit dependence of constants on Hamiltonian parameters.

Findings

Proves dispersive time-decay estimates for the SSH model.

Analyzes the impact of boundary conditions on the propagator.

Provides explicit parameter dependence of decay constants.

Abstract

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.