Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations

This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between $10^{-1}$ and $10^2$ Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter $\Gamma \lesssim 3$ and degeneracy parameter $n_e \Lambda^3 \lesssim 10$. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Pade approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.Comment: RevTex file, 21 pages, 5 ps-figures include

Second virial coefficient for the Landau diamagnetism of a two component plasma

This paper investigates the density expansion of the thermodynamic properties of a two component plasma under the influence of a weak constant uniform magnetic field. We start with the fugacity expansion for the Helmholtz free energy. The leading terms with respect to the density are calculated by a perturbation expansion with respect to the magnetic field. We find a new magnetic virial function for a low density plasma which is exact in quadratic order with respect to the magnetic field. Using these results we compute the magnetization and the magnetic susceptibility.Comment: 16 pages, 4 figures, to appear in Phys.Rev.

Saito duality between Burnside rings for invertible polynomials

We give an equivariant version of the Saito duality which can be regarded as a Fourier transformation on Burnside rings. We show that (appropriately defined) reduced equivariant monodromy zeta functions of Berglund-H\"ubsch dual invertible polynomials are Saito dual to each other with respect to their groups of diagonal symmetries. Moreover we show that the relation between "geometric roots" of the monodromy zeta functions for some pairs of Berglund-H\"ubsch dual invertible polynomials described in a previous paper is a particular case of this duality.Comment: 12 pages; the main result has been improve

On a Newton filtration for functions on a curve singularity

In a previous paper, there was defined a multi-index filtration on the ring of functions on a hypersurface singularity corresponding to its Newton diagram generalizing (for a curve singularity) the divisorial one. Its Poincar\'e series was computed for plane curve singularities non-degenerate with respect to their Newton diagrams. Here we use another technique to compute the Poincar\'e series for plane curve singularities without the assumption that they are non-degenerate with respect to their Newton diagrams. We show that the Poincar\'e series only depends on the Newton diagram and not on the defining equation.Comment: 11 page