Thermodynamic Properties of Correlated Strongly Degenerate Plasmas

An efficient numerical approach to equilibrium properties of strongly coupled systems which include a subsystem of fermionic quantum particles and a subsystem of classical particles is presented. It uses an improved path integral representation of the many-particle density operator and allows to describe situations of strong coupling and strong degeneracy, where analytical theories fail. A novel numerical method is developed, which allows to treat degenerate systems with full account of the spin scatistics. Numerical results for thermodynamic properties such as internal energy, pressure and pair correlation functions are presented over a wide range of degeneracy parameter.Comment: 8 pages, 4 figures, uses sprocl.sty (included) to be published in "Progress in Nonequilibrium Green's functions", M. Bonitz (Ed.), World Scientific 200

Strict derivation of angular-averaged Ewald potential

In this work we strictly derive an angular-averaged Ewald potential suitable for numerical simulations of disordered Coulomb systems. The potential was first introduced by E. Yakub and C. Ronchi without strict mathematical justification. Two methods are used to find the coefficients of the series expansion of the potential: based on the Euler-Maclaurin and Poisson summation formulas. The expressions for each coefficient is represented as a finite series containing derivatives of Jacobi theta functions. We also demonstrate the formal equivalence of the Poisson and Euler-Maclaurin summation formulas in the three-dimensional case. The effectiveness of the angular-averaged Ewald potential is shown by the example of calculating the Madelung constant for a number of crystal lattices

Exchange--correlation bound states of the triplet soft--sphere fermions by the path integral Monte Carlo simulations

Path integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin--resolved radial distribution functions of the strongly correlated soft--sphere quantum fermions. The obtained spin--resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr--Sommerfeld quantization condition applied to the potential of the mean force corresponding to the same--spin radial distribution functions allows to detect exchange--correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution.Comment: arXiv admin note: substantial text overlap with arXiv:2305.0760