Monte Carlo analysis of an interatomic potential for He

Abstract

By means of a Quadratic Diffusion Monte Carlo method we have performed a comparative analysis between the Aziz potential and a revised version of it. The results demonstrate that the new potential produces a better description of the equation of state for liquid 4 He. In spite of the improvement in the description of derivative magnitudes of the energy, as the pressure or the compressibility, the energy per particle which comes from this new potential is lower than the experimental one. The inclusion of three-body interactions, which give a repulsive contribution to the potential energy, makes it feasible that the calculated energy comes close to the experimental result.

Condensate Fraction in Liquid 4He at Zero Temperature

“…4, we also compare our estimates for n 0 with the experimental ones 6 and with the ones obtained in previous numerical simulations. [9][10][11]13 It is easy to notice that our results provide an excellent description of the experimental dependence of the condensate fraction as a function of pressure in all the range of stability of the liquid phase of 4 He, improving previous calculations which focus especially on the equilibrium density and do not explore in detail the physically interesting pressure range where the experimental data can be measured. Notice that the experimental value of n 0 at zero pressure reported in the more recent experiment 6 is slightly smaller (7.01 ± 0.75%), but still statistically compatible within the error bars, than the previous one by the same team.…”

“…At the equilibrium density of liquid 4 4 He at zero temperature as a function of pressure p in the region of stability of liquid phase. Our PIGS results (black squares) are compared with the experimental ones (red diamonds) 6 and previous theoretical calculations, obtained with Diffusion Monte Carlo (green up triangles), 10 Diffusion Euler Monte Carlo (violet left triangles), 11 Reptation Quantum Monte Carlo (blue circle) 13 and PIMC at T = 1 K. 9 The dashed line represents the curve obtained fitting our results with the equation…”

“…Diffusion Monte Carlo technique, for instance, has provided estimations of n 0 in liquid 4 He on a wide range of pressures. [10][11][12] This method, however, suffers from the choice of a variational ansatz necessary for the importance sampling whose influence on ρ 1 (r) cannot be completely removed. Reptation Quantum Monte Carlo (RQMC) has also been used for this purpose, 13 but the calculated value of n 0 at SVP lies somewhat below the recent PIMC value 9 at T = 1 K noted above.…”

Phase Diagrams of 4He on Flat and Curved Environments

“…The DMC algorithm is nowadays a standard tool that provides exact results when solving the N -body Schrödinger equation for boson systems within some statistical errors. It does so by the introduction of an importance sampling strategy through a guiding wave function Ψ [15]. For the liquid phases studied in this work we have used…”

Quantum Halo States in Helium Tetramers

“…Furthermore, we test their halo nature. In the next Section, we introduce the diffusion Monte Carlo method (DMC) 31 and discuss the trial wave functions used for importance sampling. After results are discussed and compared with other theoretical works, we comprise a summary of the work and an account of the main conclusions.…”