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Register a new userBose-Einstein Quantum Statistics and the Ground State of Solid 4He
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The ground state of solid $^4$He is studied using the diffusion Monte Carlo method and a new trial wave function able to describe the supersolid. The new wave function is symmetric under the exchange of particles and reproduces the experimental equation of state. Results for the one-body density matrix show the existence of off-diagonal long-range order with a very small condensate fraction $sim 10^{-4}$. The superfluid density of the commensurate system is below our resolution threshold, $rho_s/rho < 10^{-5}$. With a 1% concentration of vacancies the superfluid density is manifestly larger, $rho_s/rho=3.2(1) cdot 10^{-3}$.
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In a recent study we have reported a new type of trial wave function symmetric under the exchange of particles and which is able to describe a supersolid phase. In this work, we use the diffusion Monte Carlo method and this model wave function to study the properties of solid 4He in two- and quasi two-dimensional geometries. In the purely two-dimensional case, we obtain results for the total ground-state energy and freezing and melting densities which are in good agreement with previous exact Monte Carlo calculations performed with a slightly different interatomic potential model. We calculate the value of the zero-temperature superfluid fraction rho_{s} / rho of 2D solid 4He and find that it is negligible in all the considered cases, similarly to what is obtained in the perfect (free of defects) three-dimensional crystal using the same computational approach. Interestingly, by allowing the atoms to move locally in the perpendicular direction to the plane where they are confined to zero-point oscillations (quasi two-dimensional crystal) we observe the emergence of a finite superfluid density that coexists with the periodicity of the system.
Although solid helium-4 (4He) may be a supersolid it also exhibits many phenomena unexpected in that context. We studied relaxation dynamics in the resonance frequency f(T) and dissipation D(T) of a torsional oscillator containing solid 4He. With the appearance of the supersolid state, the relaxation times within f(T) and D(T) began to increase rapidly together. More importantly, the relaxation processes in both D(T) and a component of f(T) exhibited a complex synchronized ultraslow evolution towards equilibrium. Analysis using a generalized rotational susceptibility revealed that, while exhibiting these apparently glassy dynamics, the phenomena were quantitatively inconsistent with a simple excitation freeze-out transition because the variation in f was far too large. One possibility is that amorphous solid 4He represents a new form of supersolid in which dynamical excitations within the solid control the superfluid phase stiffness.
We study the zero-temperature equation of state (EOS) of solid 4He in the hexagonal closed packet (hcp) phase over the 0-57 GPa pressure range by means of the Diffusion Monte Carlo (DMC) method and the semi-empirical Aziz pair potential HFD-B(HE). In the low pressure regime (P ~ 0-1 GPa) we assess excellent agreement with experiments and we give an accurate description of the atomic kinetic energy, Lindemann ratio and Debye temperature over a wide range of molar volumes (22-6 cm^{3}/mol). However, on moving to higher pressures our calculated P-V curve presents an increasingly steeper slope which ultimately provides differences within ~40 % with respect to measurements. In order to account for many-body interactions arising in the crystal with compression which are not reproduced by our model, we perform additional electronic density-functional theory (DFT) calculations for correcting the computed DMC energies in a perturbative way. We explore both generalized gradient and local density approximations (GGA and LDA, respectively) for the electronic exchange-correlation potential. By proceeding in this manner, we show that discrepancies with respect to high pressure data are reduced to 5-10 % with few computational extra cost. Further comparison between our calculated EOSs and ab initio curves deduced for the perfect crystal and corrected for the zero-point motion of the atoms enforces the reliability of our approach.
The dynamics of 3He atoms in solid 4He have been investigated by measuring the NMR relaxation times T1, T2 in the region where a significant non-classical rotational inertia fraction (NCRIF) has been reported. For 3He concentrations x3 = 16 ppm and 24 ppm, changes are observed for both the spin-lattice relaxation time T1 and the spin-spin relaxation time T2 at the temperatures corresponding to the onset of NCRIF and, at lower temperatures, to the 3He-4He phase separation. The magnitudes of T1 and T2 at temperatures above the phase separation agree roughly with existing theory based on the tunneling of 3He impurities in the elastic strain field due to isotopic mismatch. However, a distinct peak in T1 and a less well-resolved feature in T2 are observed near the reported NCRIF onset temperature, in contrast to the temperature-independent relaxation times predicted by the tunneling theory.
The changes that vacancies produce in the properties of hcp solid 4He are studied by means of quantum Monte Carlo methods. Our results show that the introduction of vacancies produces significant changes in the behavior of solid 4He, even when the vacancy concentration is very small. We show that there is an onset temperature where the properties of incommensurate 4He change significantly. Below this temperature, we observe the emergence of off-diagonal long range order and a complete spatial delocalization of the vacancies. This temperature is quite close to the temperature where non-classical rotational inertia has been experimentally observed. Finally, we report results on the influence of vacancies in the elastic properties of hcp 4He at zero temperature.
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