Path integral calculations of vacancies in solid Helium
We study properties of vacancies in solid 4He using Path Integral Monte Carlo. We find, in agreement with other calculations, that the energy to create a single vacancy is 11.5 K and is monotonic with the number of vacancies. If more then a few percent of the system becomes vacant, we find the system becomes unstable to melting. We show the number of exchanges in the system is increased by vacancies and how the underlying lattice is altered by the presence of a vacancy. We also examine the efficacy of using a tight binding Hamiltonian to describe the vacancy in the crystal, show that vacancies are attractive, and find values for the effective mass and inter-vacancy attraction.
Temperature Dependence of the Vacancy Formation Energy in Solid 4He
We studied the thermal effects on the behavior of incommensurate solid 4He at low temperatures using the path integral Monte Carlo method. Below a certain temperature, depending on the density and the structure of the crystal, the vacancies delocalize and a finite condensate fraction appears. We calculated the vacancy formation energy as a function of the temperature and observed a behavior compatible with a two-step structure, with a gap of few K appearing at the onset temperature of off-diagonal long-range order. Estimation of the energy cost of creating two vacancies seems to indicate an effective attractive interaction among the vacancies but the large error inherent to its numerical estimation precludes a definitive statement.
Momentum distribution in a Bose solid
The momentum distribution and possibility of Bose-Einstein condenstation in a Bose solid is discussed. It is shown that for a wide class of wave functions describing solids of general symmetries, Bose-Einstein condensation does not exist, provided the sum of certain normalized overlap intergrals is less than 1. The realistic parameters of solid $sup 4$He are such that the above condition is obeyed. (auth)