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In the novel superfluid polar phase realized in liquid 3He in highlyanisotropic aerogels, a quantum transition to the polar-distorted A (PdA) phasemay occur at a low but finite pressure Pc(0). It is shown that a nontrivialquantum dynamics of the critical fluctuation of the PdA order is induced by thepresence of both the columnar-like impurity scattering leading to theAnderson's Theorem for the polar phase and the line node of the quasiparticlegap in the state, and that, in contrast to the situation of the normal to the Bphase transition in isotropic aerogels, a weakly divergent behavior of thecompressibility appears in the quantum critical region close to Pc(0).

Superfluid Quantum Criticality in Liquid 3He in Anisotropic Aerogel