  In the novel superfluid polar phase realized in liquid 3He in highly
anisotropic aerogels, a quantum transition to the polar-distorted A (PdA) phase
may occur at a low but finite pressure Pc(0). It is shown that a nontrivial
quantum dynamics of the critical fluctuation of the PdA order is induced by the
presence of both the columnar-like impurity scattering leading to the
Anderson's Theorem for the polar phase and the line node of the quasiparticle
gap in the state, and that, in contrast to the situation of the normal to the B
phase transition in isotropic aerogels, a weakly divergent behavior of the
compressibility appears in the quantum critical region close to Pc(0).
