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Onset temperature of Bose-Einstein condensation in incommensurate solid 4He

The temperature dependence of the one-body density matrix in 4He crystals presenting vacancies is computed with Path Integral Monte Carlo. The main purpose of this study is to estimate the onset temperature T_0 of Bose-Einstein condensation in these systems. We see that T_0 depends on the vacancy concentration X_v of the simulated system, but not following the law $T_0 \sim X_v^{2/3}$ obtained assuming non-interacting vacancies. For the lowest X_v we have studied, that is X_v = 1/256, we get T_0 = (0.15 \pm 0.05) K, close to the temperatures at which a finite fraction of non-classical rotational inertia is experimentally observed. Below T_0, vacancies do not act as classical point defects becoming completely delocalized entities.