DISPERSIVE DECAY ESTIMATES FOR DIRAC EQUATIONS WITH A DOMAIN WALL

Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at x = +∞ and x = -∞. This family of Hamiltonians arises in the theory of topologically protected states of one-dimensional quantum materials. For certain values of the phase-shift parameter, \tau, the Dirac Hamiltonian has a threshold resonance at the endpoint of its essential spectrum. Such resonances are known to influence the time-decay rate. Our main result explicitly displays the transition in time-decay rate as \tau varies between resonant and nonresonant values. Our results appear to be the first dispersive time-decay estimates for Dirac Hamiltonians which are not a relatively compact perturbation of a free Dirac operator.