It is found from a crystallization rate measurement of 4 He in silica-aerogels that crystals grow via thermal activation in a high-temperature creep region and via macroscopic quantum tunneling in a low-temperature avalanche region. Avalanche size distribution follows a power law in a 98% porosity aerogel and indicates that the system is in a selforganized critical state (SOC) in the growth regime via quantum tunneling. Temperature dependence of the exponent of the power law and the large-scale cutoff are also obtained. This is the first observation of SOC in macroscopic quantum tunneling phenomena.KEYWORDS: quantum solids, macroscopic quantum tunneling, self-organized critical state, aerogel Dynamics associated with the first order phase transition in the low temperature limit can be studied in condensed phases of 4 He. [1][2][3][4][5][6][7][8] At low enough temperatures, thermal fluctuation ceases and quantum phenomena emerge in the decay process of a metastable phase: 9) bubble cavitation and crystal nucleation from the superfluid liquid take place via macroscopic quantum tunneling to overcome the energy barrier. Although the quantum phenomena of the transitions have been studied extensively both in homogeneous and heterogeneous nucleation, the effect of disorder is not known well. Here, we report a novel result on crystallization of 4 He in silica-aerogels, which provide a spatial disorder for the transition. It is found that avalanche crystallization results from the macroscopic quantum tunneling and that the avalanche size distribution follows a power law indicating that the system in the quantum growth regime shows a selforganized criticality (SOC), similar dynamical phenomena known in classical systems such as growing sandpiles, fracture in disordered materials and so on. 10)Silica-aerogel consists of nanometer scale silica strands with a highly open structure [11][12][13] and provides a spatial disorder for various types of phase transition. [13][14][15][16][17][18][19][20][21] Since it is very transparent, one can visually observe the process of the first order phase transition within it. 17,18,20,21) 4 He has a nearly temperature-independent bulk melting pressure P m and crystallizes from the superfluid liquid down to 0 K. 22)The latent heat is negligible and liquid motion in the pores is very swift. The transport of heat and mass is not the limiting process of the crystallization. Therefore, the intrinsic effects of disorder on crystallization dynamics can be investigated.We used a 98% porosity aerogel made by the Halperin group at Northwestern University and a 96% porosity aerogel by Panasonic Corporation; here, we mainly report on the results of the former. The aerogel is grown in situ in a flat glass tube, and fills a space 10 mm in height, 8 mm in width and 1 mm in depth without a gap between the glass and the aerogel. The width of the glass wall is 1 mm. The bottom is glued to a glass plate and only the upper surface is open to have contact with outside bulk crystals. To make crystals at a const...

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