Out of Equilibrium Majoranas in Interacting Kitaev Chains

We employ a time-dependent real-space local density-of-states method to study the movement and fusion of Majorana zero modes in the 1D interacting Kitaev model, based on the time evolution of many-body states. We analyze the dynamics and both fusion channels of Majoranas using time-dependent potentials, either creating {\it Walls} or {\it Wells}. % focusing on the local density-of-states and charge-density of fermions varying with time. For fast moving Majoranas, we unveil non-equilibrium signatures of the ``strong-zero mode'' operator (quasi parity degeneracy in the full spectrum) and its breakdown in the presence of repulsive Coulomb interactions. Focusing on forming a full electron after fusion, we also discuss upper and lower limits on the Majorana speed needed to reduce non-adiabatic effects and to avoid poisoning due to decoherence.