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The superfluid transition in liquid 4He filled in Gelsil glass observed inrecent experiments is discussed in the framework of quantum critical phenomena.We show that quantum fluctuations of phase are indeed important at theexperimentally studied temperature range owing to the small pore size ofGelsil, in contrast to 4He filled in previously studied porous media such asVycor glass. As a consequence of an effective particle-hole symmetry, thequantum critical phenomena of the system are described by the 4D XYuniversality class, except at very low temperatures. The simple scaling agreeswith the experimental data remarkably well.

Quantum Critical Phenomena of 4He in Nanoporous Media