Kapitza Dynamics as a New Stabilization Mechanism for Heavy Tetraquarks

We investigate a Kapitza-inspired mechanism in which rapid oscillations in the heavy-quark interaction generate an effective short-range repulsive term in the diquark--antidiquark potential. The resulting $1/r^{4}$ contribution prevents collapse at short distances and produces a stable minimum in the effective potential. Within a diquark--antidiquark picture, we construct a modified Cornell-type potential and analyze the spectrum of heavy tetraquarks using a Gaussian variational method. We compute the binding energies, wave functions, radii, and mass spectra of charm and bottom tetraquarks, including the $X(3872)$, $T_{bb}$, and fully heavy $bb\bar{b}\bar{b}$ states. The model reproduces the mass of the $X(3872)$ and predicts a deeply bound $T_{bb}$ state consistent with lattice QCD. The fully heavy $bb\bar{b}\bar{b}$ mass also agrees with recent lattice determinations. Our results indicate that the Kapitza mechanism provides a natural and robust stabilization effect in multiquark systems and offers a unified description of molecular-like and compact tetraquark configurations.