Path Integral Monte Carlo Simulation of the Low-Density Hydrogen Plasma

Restricted path integral Monte Carlo simulations are used to calculate the equilibrium properties of hydrogen in the density and temperature range of $9.83 \times 10^{-4}\rm \leq \rho \leq 0.153 \rm gcm^{-3}$ and $5000 \leq T \leq 250 000 \rm K$. We test the accuracy of the pair density matrix and analyze the dependence on the system size, on the time step of the path integral and on the type of nodal surface. We calculate the equation of state and compare with other models for hydrogen valid in this regime. Further, we characterize the state of hydrogen and describe the changes from a plasma to an atomic and molecular liquid by analyzing the pair correlation functions and estimating the number of atoms and molecules present.Comment: 12 pages, 21 figures, submitted for Phys. Rev.

Hydrogen-Helium Mixtures at High Pressure

The properties of hydrogen-helium mixtures at high pressure are crucial to address important questions about the interior of Giant planets e.g. whether Jupiter has a rocky core and did it emerge via core accretion? Using path integral Monte Carlo simulations, we study the properties of these mixtures as a function of temperature, density and composition. The equation of state is calculated and compared to chemical models. We probe the accuracy of the ideal mixing approximation commonly used in such models. Finally, we discuss the structure of the liquid in terms of pair correlation functions.Comment: Proceedings article of the 5th Conference on Cryocrystals and Quantum Crystals in Wroclaw, Poland, submitted to J. Low. Temp. Phys. (2004

Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen

A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by Gaussians with the mean, width and amplitude as variational parameters. The method is illustrated for the particle in an external field problem, the hydrogen molecule and dense hydrogen where the molecular, the dissociated and the plasma regime are described. Structural and thermodynamic properties (energy, equation of state and shock Hugoniot) are presented.Comment: 26 pages, 13 figures. submitted to Phys. Rev. E, October 199

Frontiers of the physics of dense plasmas and planetary interiors: experiments, theory, applications

Recent developments of dynamic x-ray characterization experiments of dense matter are reviewed, with particular emphasis on conditions relevant to interiors of terrestrial and gas giant planets. These studies include characterization of compressed states of matter in light elements by x-ray scattering and imaging of shocked iron by radiography. Several applications of this work are examined. These include the structure of massive "Super Earth" terrestrial planets around other stars, the 40 known extrasolar gas giants with measured masses and radii, and Jupiter itself, which serves as the benchmark for giant planets.Comment: Accepted to Physics of Plasmas special issue. Review from HEDP/HEDLA-08, April 12-15, 200

Mass-Radius Relationships for Solid Exoplanets

We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial-mass planets of all compositions we considered follow a generic functional form that is not a simple power law: $\log_{10} R_s = k_1 + 1/3 \log_{10}(M_s) - k_2 M_s^{k_3}$ for up to $M_p \approx 20 M_{\oplus}$, where $M_s$ and $R_s$ are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form $\rho = \rho_0 + c P^n$. We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found that: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with $\sim$~5% uncertainty water ice planets with $\gtrsim 25$ water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of "super Earths'' based on the clear distinction in radii between planets with significant gas envelopes and those without.Comment: ApJ, in press, 33 pages including 16 figure

The Equation of State and the Hugoniot of Laser Shock-Compressed Deuterium

The equation of state and the shock Hugoniot of deuterium are calculated using a first-principles approach, for the conditions of the recent shock experiments. We use density functional theory within a classical mapping of the quantum fluids [ Phys. Rev. Letters, {\bf 84}, 959 (2000) ]. The calculated Hugoniot is close to the Path-Integral Monte Carlo (PIMC) result. We also consider the {\it quasi-equilibrium} two-temperature case where the Deuterons are hotter than the electrons; the resulting quasi-equilibrium Hugoniot mimics the laser-shock data. The increased compressibility arises from hot $D^+-e$ pairs occuring close to the zero of the electron chemical potential.Comment: Four pages; One Revtex manuscript, two postscipt figures; submitted to PR

Path integral Monte Carlo simulation of charged particles in traps

This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as a small perturbation. For weakly coupled systems many efficient theoretical and computational techniques do exist. However, for strongly interacting systems such as nonideal gases or plasmas, strongly correlated electrons and so on, perturbation methods fail and alternative approaches are needed. Among them, an extremely successful one is the Monte Carlo (MC) method which we are going to consider in this chapter.Comment: 18 pages, based on talks on Hareaus school on computational methods, Greifswald, September 200

Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation

We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times of Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different confining potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail

Structural Phase Transition at High Temperatures in Solid Molecular Hydrogen and Deuterium

We study the effect of temperature up to 1000K on the structure of dense molecular para-hydrogen and ortho-deuterium, using the path-integral Monte Carlo method. We find a structural phase transition from orientationally disordered hexagonal close packed (hcp) to an orthorhombic structure of Cmca symmetry before melting. The transition is basically induced by thermal fluctuations, but quantum fluctuations of protons (deuterons) are important in determining the transition temperature through effectively hardening the intermolecular interaction. We estimate the phase line between hcp and Cmca phases as well as the melting line of the Cmca solid.Comment: 8 pages, 7 figures; accepted in Phys. Rev.

Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration

In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult life1, and are an important model for organ regeneration. Hair stem cells located in the follicle bulge2 are regulated by the surrounding microenvironment, or niche3. The activation of such stem cells is cyclic, involving periodic -catenin activity4, 5, 6, 7. In the adult mouse, regeneration occurs in waves in a follicle population, implying coordination among adjacent follicles and the extrafollicular environment. Here we show that unexpected periodic expression of bone morphogenetic protein 2 (Bmp2) and Bmp4 in the dermis regulates this process. This BMP cycle is out of phase with the WNT/-catenin cycle, thus dividing the conventional telogen into new functional phases: one refractory and the other competent for hair regeneration, characterized by high and low BMP signalling, respectively. Overexpression of noggin, a BMP antagonist, in mouse skin resulted in a markedly shortened refractory phase and faster propagation of the regenerative wave. Transplantation of skin from this mutant onto a wild-type host showed that follicles in donor and host can affect their cycling behaviours mutually, with the outcome depending on the equilibrium of BMP activity in the dermis. Administration of BMP4 protein caused the competent region to become refractory. These results show that BMPs may be the long-sought 'chalone' inhibitors of hair growth postulated by classical experiments. Taken together, results presented in this study provide an example of hierarchical regulation of local organ stem cell homeostasis by the inter-organ macroenvironment. The expression of Bmp2 in subcutaneous adipocytes indicates physiological integration between these two thermo-regulatory organs. Our findings have practical importance for studies using mouse skin as a model for carcinogenesis, intra-cutaneous drug delivery and stem cell engineering studies, because they highlight the acute need to differentiate supportive versus inhibitory regions in the host skin