We report our results about the fluctuation effects on the surface static structure factor and on the local Bose-Einstein condensate (BEC) in the low density surface region of 4 He. This information has been obtained by a variational Monte Carlo calculation for a slab of 4 He modelled by a novel shadow wave function with a glue term (glue-SWF). This glue-SWF describes the self-binding of 4 He only via local interparticle correlations. BEC increases from the bulk-like value well inside the slab to a much larger value in the surface region (up to about 50%). Further out of the surface the condensate decreases and correspondingly there is an enhanced population of small momentum states. This is very different from the full BEC that was predicted using a simplified variational treatment of these 4 He systems. This different behaviour is correlated with the presence in the glue-SWF of enhanced density fluctuations in the surface region as shown by the behaviour of the static structure factor at small wave vector. This is interpreted as an effect due to the zero point motion of ripplons.
We report our results about the fluctuation effects on the surface static structure factor and on the local Bose-Einstein condensate (BEC) in the low density surface region of 4 He. This information has been obtained by a variational Monte Carlo calculation for a slab of 4 He modelled by a novel shadow wave function with a glue term (glue-SWF). This glue-SWF describes the self-binding of 4 He only via local interparticle correlations. BEC increases from the bulk-like value well inside the slab to a much larger value in the surface region (up to about 50%). Further out of the surface the condensate decreases and correspondingly there is an enhanced population of small momentum states. This is very different from the full BEC that was predicted using a simplified variational treatment of these 4 He systems. This different behaviour is correlated with the presence in the glue-SWF of enhanced density fluctuations in the surface region as shown by the behaviour of the static structure factor at small wave vector. This is interpreted as an effect due to the zero point motion of ripplons.
Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0:77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9, before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. A surface dispersion relation was calculated from imaginary-time density-density correlations. Similar calculations of the superfluid density throughout He-4 droplets doped with linear impurities (HCN)(sub n) are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the first solvation layer. This effective normal fluid exhibits temperature dependence similar to that of a two-dimensional helium system.
A path integral Monte Carlo method was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0.77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9 before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. Finally, a surface dispersion relation was calculated from imaginary-time density-density correlations.
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate fraction. This work will focus primarily on how phenomena such as superfluidity, Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous helium systems. Path Integral Monte Carlo is a powerful method for calculating the equilibrium properties of quantum systems at finite temperature. We have achieved linear scaling of computer time with number of particles through the use of neighbor lists, allowing us to simulate systems of several thousand atoms. We have derived a local superfluid estimator and used it to examine the microscopic superfluid response around a molecule rotating in a helium nanodroplet. We found that the first solvation layer is well-described by a two dimensional superfluid, with thermal excitations occuring at a lower temperature than in bulk helium. The effective moment of inertia of a linear impurity in a helium droplet is calculated, and compared with experimental scattering results. In addition, we calculated the vortex formation energy for both pure droplets and droplets doped with linear impurities, and found that the linear impurities had a negligible impact on the formation energy. A possible spectroscopic signature of vortices in doped helium droplets was suggested. After deriving a local estimator, we calculated the condensate fraction throughout the free helium surface of a semi-infinite slab. These results, along with densitydensity correlation functions, were used to characterize the surface excitations and calculate the extent to which ripplons are present. In addition, the ripplon dispersion relation was calculated using imaginary-time correlation functions, and found to be lll in good agreement with experimental results. Finally, we have calculated the Dey be-Waller factor in solid helium for a range of temperatures and densities, and compared the scaling behavior with the predictions of harmonic theory. The first non-Gaussian contribution to the density distribution was calculated.
We have computed the one-body density matrix ${\ensuremath{\rho}}_{1}$ in solid 4He at T=0K using the shadow wave-function (SWF) variational technique. The accuracy of the SWF has been tested with an exact projector method. We find that off-diagonal long-range order is present in ${\ensuremath{\rho}}_{1}$ for a perfect hcp and bcc solid 4He for a range of densities above the melting one, at least up to 54 bars. This is first microscopic indication that Bose Einstein condensation (BEC) is present in perfect solid 4He. At melting, the condensate fraction in the hcp solid is $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and it decreases by increasing the density. The key process giving rise to BEC is the formation of vacancy interstitial pairs. We also present values for Leggett's upper bound on the superfluid fraction deduced from the exact local density.
A trial wave function describing the ground state of a quantum system of N interacting bosons is written in the Jastrow form, a product of pair functions. With the interaction potential chosen to represent liquid He4, and with the parametrized form of the pair function chosen to include a long-range term which has been found necessary to represent the zero-point motion of the long-wavelength density oscillations, a variational calculation has been performed using a new approximate integral equation for the pair distribution function. This equation, which can also be used for classical fluids, is found to be more accurate for repulsive potentials than the Percus-Yevick equation and comparable to (but much simpler than) the Percus-Yevick 2 equation. The essential results are that including the zero-point motion in the wave function tends to lower the energy, raises the equilibrium density, corrects the behavior of the structure function and the momentum distribution of the particles in the low-wave-number region, and slightly decreases the Bose-Einstein condensate fraction. The value of the lower limit on the wavelength of the density oscillations was determined variationally to be about three interparticle spacings.
We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-superfluid phase transition point. We establish relations between basic thermodynamic functions: density, n(T,μ), superfluid density ns(T,μ), and condensate density, ncnd(T,μ). Being universal for all weakly interacting ∣ψ∣4 systems, these relations are obtained from Monte Carlo simulations of the classical ∣ψ∣4 model on a lattice. Comparing with the mean-field results yields a quantitative estimate of the fluctuation region size. Away from the fluctuation region, on the superfluid side, all the data perfectly agree with the predictions of the quasicondensate mean field theory.--This demonstrates that the only effect of the leading above-the-mean-field corrections in the condensate based treatments is to replace the condensate density with the quasicondensate one in all local thermodynamic relations. Surprisingly, we find that a significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.