Bloch Oscillation and Landau-Zener Tunneling of a Periodically Kicked Dirac Particle

Abstract: We investigate the dynamics of a relativistic spin-$\frac{1}{2}$ particle governed by a one-dimensional time-periodic kicking Dirac equation. We observe distinct oscillatory behavior in the momentum space and quantum tunneling in the vicinity of zero momentum, which is found to be equivalent to the Bloch oscillations and Landau-Zener tunneling, i.e., Bloch-Landau-Zener (BLZ) dynamics in tilted bipartite lattices. Using the Floquet formalism, we derive an effective Hamiltonian that can accurately predict the oscillation period and amplitude. The tunneling probability has also been determined analytically. Our analysis extends to the influence of various parameters on dynamic behavior. We also discuss how relativistic effects and spin degrees of freedom impact quantum systems' transport properties and localization phenomena.