A study is made of the kinetic properties of the quantum systems formed in dilute solid mixtures of ³He in ⁴He at ultralow temperatures as a result of the first-order phase transition known as phase separation. The system is a crystalline matrix of almost pure ⁴He in which small solid inclusions of almost pure ³He are embidded. Data on the inclusion growth kinetics, which is gaverned by diffusion processes in the matrix, are obtained using precise pressure measurements at constant volume. It is shown that impurition quantum diffusion is the main process causing the inclusion growth at T > 100 mK. At lower temperatures a strong suppression of quantum diffusion is discovered. This suppression can be associated with the elastic strains induced by the large difference in molar volume between the matrix and inclusions. The magnetic relaxation processes in such two-phase crystals are also investigated using a pulsed NMR technique. The spin-lattice and spin-spin relaxation in the inclusions are found to be practically independent of temperature. This can be described by exchange processes associated with the ³He tunnel motion. The values of the relaxation times are in good agreement with the corresponding times for pure bulk ³He. In contrast with the case of pure solid ³He, the exchange plateau region extends down to low temperatures. The nuclear magnetic relaxation in the matrix can be described by the Torrey model, which is based on ³He -

⁴He tunnel exchange. The concentration dependence of the relaxation times coincides with that observed for homogeneous dilute mixtures of ³He in ⁴He.

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