  Pauli crystals are ordered geometric structures that emerge in trapped
noninteracting fermionic systems due to their underlying Pauli repulsion. The
deformation of Pauli crystals - often called melting - has been recently
observed in experiments, but the mechanism that leads to it remains unclear. We
address this question by studying the melting dynamics of N=6 fermions as a
function of periodic driving and experimental imperfections in the trap
(anisotropy and anharmonicity) by employing a combination of numerical
simulations and Floquet theory. Surprisingly, we reveal that the melting of
Pauli crystals is not simply a direct consequence of an increase in system
energy, but is instead related to the trap geometry and the population of the
Floquet modes. We show that the melting is absent in traps without
imperfections and triggered only by a sufficiently large shaking amplitude in
traps with imperfections.
