  The dynamics of the annihilation of a vortex-antivortex pair is investigated.
The pair is activated magnetically during the run of a simulated hysteresis
loop on a square mesoscopic superconducting cylinder with an antidot inserted
at its center. We study the nucleation of vortices and antivortices by first
increasing the magnetic field, applied parallel to the axis of the sample, from
zero until the first vortex is created. A further increase of the field pulls
the vortex in, until it reaches the antidot. As the polarity of the field is
reversed, an antivortex enters the scene, travels toward the center of the
sample and eventually the pair is annihilated. Depending on the sample size,
its temperature, and Ginzburg-Landau parameter, the vortex-antivortex encounter
takes place at the antidot or at the superconducting sea around it. The
position and velocity of the vortex and antivortex singularities were evaluated
as a function of time. The current density, magnetization and order parameter
topology were also calculated.
