We investigate the phenomenon of quantum depinning of vortices in high
resistivity amorphous thin films and in high temperature superconduct
ors for the situation of weak collective pinning. Fluctuations of the
vortex system produce a smoothing of the pinning potential and thereby
a strong renormalization of the critical current density j(c)(T)propo
rtional to(1+[u(2)]/xi(2))(-kappa), With large exponents kappa(2D)=5/2
and kappa(3D)=11/2 for the regimes where the collective pinning invol
ves two- and three-dimensional bundles of vortices. We determine the m
ean squared displacement amplitude [u(2)] within a quantum statistical
ensemble for the cases of a dissipative vortex dynamics (amorphous ma
terial) and for a Hamiltonian dynamics dominated by the Hall force (ox
ide superconductors) and present results for the renormalized critical
current density j(c)(T).