Relatavistic Tunneling In Superposition

This presentation examines a relativistic generalization of quantum tunneling through a potential barrier and the role of quantum coherence. Specifically, we are interested in how nonclassical states of massive particles, moving close to the speed of light, incident on the potential barrier, modify the time the particle spends tunneling through the barrier. We sidestep a full quantum field-theoretic treatment in favor of a simpler quasi-relativistic approach. This allows us to evolve quantum states scattering off and through a potential barrier by numerically solving the Time-Dependent Schrödinger equation and applying Suzuki-Trotter approximation to obtain time of arrival probabilities, which exhibit quantum-relativistic interference effects.