Path Integral Simulations of the Thermodynamic Properties of Quantum Dense Plasma

A novel path integral representation of the many-particle density operator is presented which makes direct Fermionic path integral Monte Carlo simulations feasible over a wide range of parameters. The method is applied to compute the energy of a dense hydrogen plasma in the region of intermediate coupling and degeneracy and is compared to analytical and experimental results. Many interesting phenomena in dense plasmas occur in situations where Coulomb and quantum effects are important simultaneously. Among the most promising theoretical approaches to these systems are path integral quantum Monte Carlo (PIMC) techniques. However, for Fermi systems, they are hampered by the so-called sign problem which lead to the incorporation of additional assumptions (restricted PIMC concept [1]). In this work we demonstrate that, for many current problems in dense warm plasmas (kBT > 0.1Ry), rigorous direct PIMC simulations can be carried out with acceptable efficiency. Here, we report results for the internal energy of partially ionized hydrogen over a broad range of coupling and degeneracy parameters, Γ = (4πne/3) e/4π 0kBT and χ = neλ 3 e [λe is the electron thermal wave length λe = 2π β/me]. Thermodynamic quantities are computed from the partition function which, for a binary mixture of Ne electrons and Ni protons is conveniently written as [2] Z(Ne, Ni, V, β) = Q(Ne, Ni, β) Ne!Ni! , Q(Ne, Ni, β) = ∑