Two-phase coexistence for hydrogen-helium mixtures

Abstract

We use our newly constructed quantum Gibbs ensemble Monte Carlo algorithm to perform computer experiments for the two phase coexistence of a hydrogen-helium mixture. Our results are in quantitative agreement with the experimental results of C. M. Sneed, W. B. Streett, R. E. Sonntag, and G. J. Van Wylen. The difference between our results and the experimental ones is in all cases less than 15% relative to the experiment, reducing to less than 5% in the low helium concentration phase. At the gravitational inversion between the vapor and the liquid phase, at low temperatures and high pressures, the quantum effects become relevant. At extremely low temperature and pressure the first component to show superfluidity is the helium in the vapor phase.

Jellium at finite temperature

“…Our algorithm briefly presented in the previous section is based on the worm algorithm of Boninsegni et al [39,56,[59][60][61]. This algorithm uses a menu of 9 moves.…”

Jellium at finite temperature using the restricted worm algorithm

“…Our algorithm, that we will call algorithm A, briefly presented in the previous section is based on the worm algorithm of Boninsegni et al 33,52,[55][56][57] . The algorithm of Boninsegni et al solves the path integral in the grand canonical ensemble and uses a menu of 9 moves.…”

Screened activity expansion for the grand-potential of a quantum plasma and how to derive approximate equations of state compatible with electroneutrality

“…[50,51]). For instance, in the case of the hydrogen plasma made with protons (α = 1) and electrons (α = 2), the zero-density limit of Z [1,1] gives rise to the bare partition function Z H of the hydrogen atom in the vacuum, which is close to the virial second-order function Q first introduced by Ebeling [15]. Similar partition functions Z H + 2 , Z H − and Z H 2 for ions and molecules can be defined.…”

“…The thermodynamic properties of hydrogen and helium gases enter as a basic and key ingredient in the study of the structure and evolution of dense astrophysical bodies like stars, brown dwarfs and giant planets, for these objects are mostly made of a mixture of H and He. Many works have been performed to determine the equation of state of H-He mixtures and also to address the related question of the helium solubility in hydrogen, which is important for a correct description of planetary interiors [1][2][3]. The hydrogen-helium mixture is fundamentally a quantum plasma made of electrons and nuclei interacting via the Coulomb potential.…”