Rotating Majorana zero modes in a disk geometry

We study the manipulation of Majorana zero modes in a thin disk made from $p$-wave superconductor order to understand their use as building block for topological quantum computers. analyze second-order corner that arise when an in-plane magnetic field is applied, and calculate dynamical evolution rotating field, with special emphasis on non-adiabatic effects. characterize phase transition between high-frequency near-adiabatic using Floquet analysis. show oscillations persist even adiabatic because frequency independent coupling excited states, which we have quantified numerically analytically. These results controlling rotation can be simple method avoid errors originated this thus increase robustness computation.