Theory of the universal and nonuniversal quantities of fluids at the critical point

We show that the hierarchical reference theory is an accurate global theory of fluids at least above the critical temperatureT _c. The hierarchy is truncated at the first equation, the one connecting the free energy to the pair correlation function, with an Ornstein-Zernike ansatz. In this approximation the theory can be considered as a sophisticated generalization of the optimized random phase approximation which has genuine nonclassical critical exponents and for which scaling is satisfied. We study the system of hard spheres plus the Lennard-Jones attractive well and find a good agreement with measuredPVT, specific heat, correlation length, and structure factor in rare gases. The accuracy of the theory remains very good up to freezing density.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Density matrix of superfluid4He and temperature dependence of the static structure factor

We have computed properties of superfluid⁴He on the basis of a new density matrix which is based on a shadow wave function for the roton excitation. We deduce the separate contribution of kinetic and potential energy to a roton and find that a roton lowers the potential energy of the system. We find that S (k; T) and g(r; T) have an anomalous T dependence as found experimentally and the extra correlations present at finite T are induced by rotons. By computing the condensate fraction n₀(T) we find that the Cummings et al relation between g(r; T) and n₀(T) is violated and that it leads to a value of n₀(T) larger of the true one.     

Excitations in Two-Dimensional 4He

We present the study of the ground state and of the low-energy excited states of liquid⁴He in two dimensions (2D) within the Variational Monte Carlo method. As trial wave function a shadow wave function is used. The energies of the maxon and of the roton are close together at the equilibrium density ρ_eq due to the low value of ρ_eq in 2D but at higher densities a well developed roton minimum is present. The short range backflow effects are stronger in 2D than in 3D and close to freezing the roton energy is about 5 K. This value is close to the lowest branch of excitations found from inelastic neutron scattering from thin⁴He film on graphite and interpreted as due to layer rotons. Some strong similarities between the 2D and 3D case are present: the maxon energy close to freezing is about twice the roton energy, the relative strength of the single roton peak in the dynamical structure factor is essentially density independent and very close in value to the 3D case, there is a similar shift between the wave vectors of the roton and of the position of the main maximum of the static structure factor.     

Many-body theories of condensed phases of 4He and normal 3He

An introduction is given to the microscopic theories of liquid and solid ⁴He and of ³He in the normal liquid phase. The emphasis is on the variational theory of the ground state and of the excited states of the system. The role of two body, three body and higher order correlations is discussed also in relation to the recently introduced shadow wave function.     

Fluctuations and BEC at the Free Surface of 4He

There is some theoretical evidence that full Bose–Einstein condensation (BEC) is achieved at the free surface of superfluid ⁴ He where the density is small. We present new variational results of the BEC and of the density fluctuation spectrum in the surface region of a slab of ⁴ He. We use both a standard wave function (wf) with bulk correlations and one body shape terms and a novel shadow wave function with a glue term (G-SWF). This last one describes the self- binding of ⁴ He only via interparticle correlations. In both cases we find that BEC increases from the bulk like value well inside the slab to a much larger value in the surface region but a striking different behavior is found in the low density region. With a standard wf the BEC reaches essentially 100% in the surface region. With the G-SWF the condensate only increases up to about 51%. Further out of the surface the condensate decreases and correspondingly there is an enhanced population of small momentum states. This different behavior is correlated with the presence in the G-SWF of enhanced density fluctuations in the surface region due to the zero point motion of ripplons. This enhancement is absent in the case of a standard wf.     

Microscopic theory of the liquid-solid interface of4He

Based on the shadow wave function we have developed the first microscopic theory of the interface between a quantum liquid and solid. We overcome the difficulties present in other variational theories because no a priori equilibrium positions for the atoms have to be assumed and localization of particles is exclusively due to interparticle correlations. We find that the crystalline order parameters vary smoothly over the interface and the interface itself is mobile. We have extended the previous work (Phys. Rev. Lett. 72, 2589 (1994)) to the {111} interface of a fcc crystal of⁴He. The interfacial energy is 0.16 K/Ų, the width of the interface is about 15 Å and the local density has a dip on the liquid side.     

Zero-Point Vacancies in Quantum Solids

A Jastrow wave function (JWF) and a shadow wave function (SWF) describe a quantum solid with Bose–Einstein condensate; i.e. a supersolid. It is known that both JWF and SWF describe a quantum solid with also a finite equilibrium concentration of vacancies x _v . We outline a route for estimating x _v by exploiting the existing formal equivalence between the absolute square of the ground state wave function and the Boltzmann weight of a classical solid. We compute x _v for the quantum solids described by JWF and SWF employing very accurate numerical techniques. For JWF we find a very small value for the zero point vacancy concentration, x _v =(1.4±0.1)×10^?6. For SWF, which presently gives the best variational energy of solid ⁴He, we find the significantly larger value x _v =(1.4±0.1)×10^?3 at a density close to melting. We also study two and three vacancies with SWF. We find that there is a strong short range attraction but the vacancies do not form a bound state, at variance with the exact finite temperature PIMC results.