We study the elasticity of perfect 4 He at zero-temperature using the diffusion Monte Carlo method and a realistic semi-empirical pairwise potential to describe the He-He interactions. In particular, we calculate the value of the elastic constants of hcp helium {C ij } as a function of pressure up to ∼ 110 bar. It is found that the pressure dependence of all five non-zero {C ij } is linear and we provide an accurate parametrization of each of them. Our elastic constants results are compared to previous variational calculations and low-temperature measurements and in general we find notably good agreement among them. Furthermore, we report T = 0 results for the Grüneisen parameters, sound velocities and Debye temperature of hcp 4 He. This work represents the first of a series of computational studies aimed at thoroughly characterizing the response of solid helium to external stress-strain.
The changes that vacancies produce in the properties of hcp solid 4 He 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 4 He, even when the vacancy concentration is very small. We show that there is an onset temperature where the properties of incommensurate 4 He 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 4 He at zero temperature.
Equation of state of 4 He hcp crystals with vacancies is determined at zero temperature using the diffusion Monte Carlo technique, an exact ground-state zero-temperature method. This allows us to extract the formation enthalpy and isobaric formation energy of a single vacancy in otherwise perfect helium solid. Results are obtained for pressures up to 160 bar. The isobaric formation energy is found to reach a minimum near 57 bar where it is equal to 10.5Ϯ 1.2 K. At the same pressure, the vacancy formation volume exhibits a maximum and reaches the volume of the unit cell. This pressure coincides with the pressure interval over which a peak in the supersolid fraction of 4 He was observed in a recent experiment.
We study the elastic properties of incommensurate solid 4 He in the limit of zero temperature. Specifically, we calculate the pressure dependence of the five elastic constants (C 11 , C 12 , C 13 , C 33 , and C 44 ), longitudinal and transversal speeds of sound, and the T = 0 Debye temperature of incommensurate and commensurate hcp 4 He using the diffusion Monte Carlo method. Our results show that under compression, the commensurate crystal is globally stiffer than the incommensurate, however at pressures close to melting (i.e., P ∼ 25 bar) some of the elastic constants accounting for strain deformations of the hcp basal plane (C 12 and C 13 ) are slightly larger in the incommensurate solid. Also, we find that upon the introduction of tiny concentrations of point defects, the shear modulus of 4 He (C 44 ) undergoes a small reduction.
We report a quantum Monte Carlo calculation of the phase diagram of bosons
interacting with a repulsive inverse sixth power pair potential, a model for
assemblies of Rydberg atoms in the local van der Waals blockade regime. The
model can be parametrized in terms of just two parameters, the reduced density
and temperature. Solidification happens to the fcc phase. At zero temperature
the transition density is found with the diffusion Monte Carlo method at
density $\rho = 3.9 (\hbar^2/m C_6)^{3/4} $, where $C_6$ is the strength of the
interaction. The solidification curve at non-zero temperature is studied with
the path integral Monte Carlo approach and is compared with transitions in
corresponding harmonic and classical crystals. Relaxation mechanisms are
considered in relation to present experiments, especially pertaining to hopping
of the Rydberg excitation
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