Screened cluster EOS

Theory

Quick overview of the theoretical framework used to calculate the SC EOS

The H-He mixture is described as a non-relativistic gas made up of quantum point electrons, protons and He nuclei that interact solely via Coulomb interactions. The SC EOS is obtained by truncating, at some order, the expansion of the grand-potential in powers of particle fugacities. It becomes hence exact in the limit of small particle fugacities. Using the ring-polymer isomorphism, the partition function is first rewritten in terms of a classical gas of interacting ring-polymers (or loops), which are random closed paths with a typical extension given by the thermal de Broglie wave length. The grand-canonical partition function is then expanded in terms of cluster diagrams using Mayer diagrammatics. Systematic resummations are performed to account for screening effects; they give rise to the screened cluster diagrams. In the screened cluster EOS at 3rd order, all the SC diagrams involving at most 3 loops are computed exactly, either analytically or numerically with a path integral Monte Carlo algorithm.

Presentations

Slides of relevant talks
  1. Screened cluster equation of state for hydrogen-helium mixtures
    V. Ballenegger, International conference on Strongly Coupled Coulomb Systems (SCCS), 2017
  2. Equation of state of the H-He mixture under solar conditions
    V. Ballenegger, SOLARNET III / HELAS VII / SpaceInn Conference, 2015


For more information, see the published articles.