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Physical review. B, Condensed matter

4He/H2 binary clusters: A path-integral Monte Carlo study

M. C. Gordillo

Published Sep 1, 1999• 24 citations
Publisher

Abstract

The structure and thermodynamic properties of the ${}^{4}{\mathrm{H}\mathrm{e}/\mathrm{H}}_{2}$ binary clusters are studied by path-integral Monte Carlo simulations. It has been found that, despite their lower mass, the ${\mathrm{H}}_{2}$ molecules form a subcluster of their own at the center of the system. When the number of helium atoms increases for a fixed number of hydrogen molecules, those inner clusters get compressed but retain their original form. The fraction of ${\mathrm{H}}_{2}$ in the superfluid state decreases with the subcluster compression, but remains finite for small ${\mathrm{H}}_{2}$ concentrations.

DOI
10.1103/physrevb.60.6790

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The structure and thermodynamic properties of the 4He/H2{}^{4}{\mathrm{H}\mathrm{e}/\mathrm{H}}_{2}4He/H2​ binary clusters are studied by path-integral Monte Carlo simulations. It has been found that, despite their lower mass, the H2{\mathrm{H}}_{2}H2​ molecules form a subcluster of their own at the center of the system. When the number of helium atoms increases for a fixed number of hydrogen molecules, those inner clusters get compressed but retain their original form. The fraction of H2{\mathrm{H}}_{2}H2​ in the superfluid state decreases with the subcluster compression, but remains finite for small H2{\mathrm{H}}_{2}H2​ concentrations.
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.
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The interplay between magic number stabilities and superfluidity of small para-hydrogen clusters with sizes N=5N = 5N=5 to 40 and temperatures $0.5 K \leq T \leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo calculations. Clusters with N<26N < 26N<26 and T ≤1.5K\leq 1.5 K≤1.5K have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs (27,28)(27,28)(27,28), (30,31)(30,31)(30,31), and (35,36)(35,36)(35,36). For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.
Abstract Detailed numerical results obtained with state-of-the-art Quantum Monte Carlo (QMC) simulations are presented for the superfluid phase of 4 He at saturated vapor pressure. The aim of this contribution is that of providing reliable, up-to-date estimates for this archetypal superfluid, reflecting the methodological progress that has taken place over the past two decades. We simulate a system comprising 2,048 helium atoms, i.e., an order of magnitude greater in size than those for which results currently regarded as standard references were originally obtained. We offer revised estimates for energetic and structural properties, as well as for the ground state condensate fraction.
The effective moment of inertia of a CO impurity molecule in 4HeN and p-(H2)N solvent clusters initially increases with N but then commences a nonclassical decrease at N=4 (4He) or N=6 (p-H2). This suggests molecule-solvent decoupling and a transition to microscopic superfluidity. However, the quantum decoupling mechanism has not been elucidated. To understand the decoupling mechanism, a one-dimensional model is introduced in which the 4He atoms are confined to a ring. This model captures the physics and shows that decoupling happens primarily because of bosonic solvent-solvent repulsion. Quantum Monte Carlo and basis set calculations suggest that the system can be modeled as a stirred Tonks-Girardeau gas. This allows the N-particle time-dependent Schrödinger equation to be solved directly. Computations of the integrated particle current reveal a threshold for stirring and current generation, indicative of superfluidity.