G. V. Chester

A hard-sphere model of the helium film

A quantum hard-sphere system bounded by two parallel rigid walls is studied at absolute zero as a model of a helium film. A variational wave function is constructed which is of the Bijl-Dingle-Jastrow type modified by a one-body term which vanishes at the walls; Monte Carlo quadrature is used. We focus our attention particularly on the behavior of the single-particle density function and the condensed-state wave function, i.e., the order parameter. Both show significantly different behavior from that predicted by the Hartree theory. The healing length is calculated, we believe for the first time, and is rather small. The average condensate as a function of distance between two walls is also investigated. The calculation serves as a special probe for approximations to the ground-state wave function in a uniform system.

Vortex line in bulk4He

The core structure of a vortex in4He is still an open problem. Previous Monte Carlo variational computations have considered a vortex line in a small bucket so that the boundary conditions on the outer surface induce inhomogeneity in the system. We overcome this problem by considering 4 vortex lines of zero total vorticity in the simulation box and applying periodic boundary conditions. In this way we are essentially simulating an infinite array of vortices which is free of large scale flow. The first computation has been based on the Onsager-Feynman form of wave function. This gives an hollow core and the density dependence of the size of the core is studied. The case of a non-hollow core is under investigation. This is based on a shadow wave function for which the vorticity is distributed over a finite size.

DOES ANTISYMMETRY MATTER IN B.C.C. 3HE CRYSTALS

By comparing the results of both variational and exact Diffusion Monte Carlo (DMC) results for states of different symmetries we conclude that antisymmetry plays a fundamental role in stabilizing the b.c.c.3He crystal. We performed calculations for a system of 54 particles of mass 3 at density ρ = 0.02557 Å, just above the experimental freezing point. Symmetric (Jastrow and Shadow wave functions) and unsymmetrized wave functions (of the Nosanow-Jastrow type), fail to describe the system. In particular, a shadow wave function predicts a fluid as lowest energy state at the density considered, and this is confirmed by the computation of the exact symmetric ground state with DMC, which predicts an energy well below the experimental energy of the crystal. On the other hand, DMC calculations projecting the ground state in the space of the Nosanow–Jastrow functions, give an energy which is much above the experimental energy. The use of antisymmetric functions, and in particular of the recently introduced Fermionic Shadow Wave Function (FSWF), leads to the prediction that the b.c.c. crystal is the stable ground state. Antisymmetry plays therefore a fundamental role in this system. FSWF calculations also demonstrate the peculiar characteristics of this crystal (very low order parameter, a non Gaussian density profile around the lattice sites, and very wide vibrations of the atoms around the lattice sites, small dependence of the energy with respect to the magnetic order), which cannot be seen in the Nosanow framework.

A Schwinger variational method for the Bloch equation

A Schwinger variational principle has been derived for use in quantum, manybody systems at finite temperatures. The variational principle is a stationary expression for the density matrix which may be iterated to improve an approximate density matrix. It also can be used to find stationary expressions for observables. If an approximate, parametrized density matrix is used, the parameters are varied to find the regions where the variational principle is stationary. The variational density matrix obtained with the optimal parameters can be regarded as optimal for that observable. The method has been applied to two model problems, a particle in a box and two hard spheres at finite temperatures. The advantages and shortcomings of the method are discussed.

The binding of 3He impurities to a superfluid vortex

Abstract Using many-body wave functions we have calculated the binding energies of a 3 He impurity and a fictitious 4 He impurity to a superfluid vortex. We use both a shadow wave function with distributed vorticity, Ψ D , and the Onsagar–Feynman function with singular vorticity, Ψ O−F . For both wave functions there was no difference in the binding energies of the mass 3 and mass 4 impurities. The binding energy was independent of the density for Ψ D , but strongly density dependent for Ψ O−F . The value of 2.3 K for Ψ D , is somewhat smaller than the experimental estimate. Our results strongly suggest that the binding is due to the displacement of high-velocity 4 He atoms from the vortex core by the impurity.

Quantum Monte Carlo simulation of the second layer helium film on graphite

Abstract Greens function Monte Carlo and variational methods are used to study the properties of the second layer 4 He adsorbed on a smooth graphite substrate. Realistic He–He and He–carbon interactions are used in the simulation. The densities at which condensation and crystalization occur are determined and compared with experiment.

COMPARATIVE STUDY OF VACANCIES IN THE B.C.C. AND H.C.P. PHASES OF 4HE USING SHADOW WAVE FUNCTIONS

We use the shadow wave function formalism (SWF) to determine the energy of formation of single and double vacancies in4He crystals at T=0 K. Data is presented for both the bcc and hcp phases. The activation energy for single vacancies in bcc4He was found to be 6.7±3.9 K, about 43% of that in the hcp4He, 15.6±3.9 K. By determining the occupation of the Voronoi regions of the crystal sites, we determined the location of vacancies in the crystal and studied the relaxation of the neighboring atoms. We also present data on the correlations between vacancies, and between vacancies and3He impurities. Following the position of the vacancy through successive configurations we observed the motion of the vacancy as seen in our Monte Carlo simulations. On the shorter Monte Carlo time scales, greater vacancy motion was observed in the bcc phase than in the hcp phase.

Variational Study of a 3He Impurity Near a 4He Vortex Core

We have carried out variational calculations of the properties of a quantum vortex line4He using a shadow wave-function, which generates a distributed vorticity. Based on these calculations we present a microscopic of study the binding of a single3He to the vortex using both the Lekner-Feynman formalism and a correlated variational wave-function. Both approaches predict that the impurity should be bound. Lekner-Feynman model, however, does not appear to describe correctly some of the correlation effects within the vortex core. To remedy this defect, we propose a variational wave-function, and a preliminary calculation based on it predicts a binding energy in agreement with experiment.

Variational study of vacancies in solid4He

We present results of accurate Variational Monte Carlo simulations of a f.c.c.4He crystal with a vacancy atT=0. Calculations are based on the Shadow Wave Function sheme, in which the vacancy can move through the crystal and noa priori equilibrium positions for the atoms are assumed. this is the first microscopic calculation giving a realistic value for the energy of a vacancy, in the range 15–38K depending on the density of the solid. Results on the mobility of the vacancy are presented.

An improved shadow wavefunction for bulk He-4

Abstract We report ground state liquid and solid phase variational results for two forms of shadow wavefunction which contain an attractive pseudo-potential for the shadow particles. These results show a substantial improvement over those of the original shadow wavefunction. They yield a good equation of state and melting-freezing transition.