23 research outputs found
THERMODYNAMIC FUNCTIONS OF A PARTIALLY DEGENERATE, FULLY IONIZED GAS
The formalism of Glassgold, Heckrotte, and Watson for the expansion of the quantum-mechanical grand partition function has been applied to a gas of point charges. The theory was extended to a multicomponent gas of fermions and bosons, and the ring diagrams were summed to give an approximate expression for the equation of state valid for the entire temperature range. The near-classical limit (high-temperature and low-density so that the gas is only slightly degenerate) is discussed in detail, and useful formulas for numerical computation of pressure and internal energy are derived from the general ring approximation to the equation of state. By expanding the chemical potential in powers of the coupling constant e/sup 2/, it is possible to eliminate the parametric dependence of pressure and density on the chemical potential and obtain the pressure as a function of density. The classical-limit Debye-Huckel results are obtained when h approaches 0. A general form of the screening length is obtained with the effective screening charge as z/sub i/e THETA /sub i/, where THETA /sub i/ is a measure of the degeneracy of the particle species i. The contribution to the pressure from the simplest exchange interaction valid for all temperatares is evaluated exactly. The temperature and density range for which the nearclassical- limit formulas are valid is discussed. (auth
Dislocation-Mediated Melting: The One-Component Plasma Limit
The melting parameter of a classical one-component plasma is
estimated using a relation between melting temperature, density, shear modulus,
and crystal coordination number that follows from our model of
dislocation-mediated melting. We obtain in good agreement
with the results of numerous Monte-Carlo calculations.Comment: 8 pages, LaTe
Bose-Einstein condensation for interacting scalar fields in curved spacetime
We consider the model of self-interacting complex scalar fields with a rigid
gauge invariance under an arbitrary gauge group . In order to analyze the
phenomenon of Bose-Einstein condensation finite temperature and the possibility
of a finite background charge is included. Different approaches to derive the
relevant high-temperature behaviour of the theory are presented.Comment: 28 pages, LaTe
Horizons, Constraints, and Black Hole Entropy
Black hole entropy appears to be ``universal''--many independent
calculations, involving models with very different microscopic degrees of
freedom, all yield the same density of states. I discuss the proposal that this
universality comes from the behavior of the underlying symmetries of the
classical theory. To impose the condition that a black hole be present, we must
partially break the classical symmetries of general relativity, and the
resulting Goldstone boson-like degrees of freedom may account for the
Bekenstein-Hawking entropy. In particular, I demonstrate that the imposition of
a ``stretched horizon'' constraint modifies the algebra of symmetries at the
horizon, allowing the use of standard conformal field theory techniques to
determine the asymptotic density of states. The results reproduce the
Bekenstein-Hawking entropy without any need for detailed assumptions about the
microscopic theory.Comment: 16 pages, talk given at the "Peyresq Physics 10 Meeting on Micro and
Macro structures of spacetime
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Statistical mechanics of dense plasmas: numerical simulation and theory
Recent Monte Carlo calculations from Paris and from Livermore for dense one and two component plasmas have led to systematic and accurate results for the thermodynamic properties of dense Coulombic fluids. This talk will summarize the results of these numerical experiments, and the simple analytic expressions for the equation of state and other thermodynamic functions that have been obtained. The thermal energy for the one component plasma has a simple power law dependence on temperature that is identical to Monte Carlo results on strongly coupled fluids governed by l/r/sup n/ potentials. A universal model for fluids governed by simple repulsive forces is suggested. For two component plasmas the ion-sphere model is shown to accurately reproduce the Monte Carlo data for the static portion of the energy. Electron screening is included using the Lindhard dielectric function and linear response theory. Free energy expressions have been constructed for one and two component plasmas that allow easy computation of all thermodynamic functions
Equilibrium statistical mechanics of strongly coupled plasmas by numerical simulation
Numerical experiments using the Monte Carlo method have led to systematic and accurate results for the thermodynamic properties of strongly coupled one-component plasmas and mixtures of two nuclear components. These talks are intended to summarize the results of Monte Carlo simulations from Paris and from Livermore. Simple analytic expressions for the equation of state and other thermodynamic functions have been obtained in which there is a clear distinction between a lattice-like static portion and a thermal portion. The thermal energy for the one-component plasma has a simple power dependence on temperature, (kT)/sup /sup 3///sub 4//, that is identical to Monte Carlo results obtained for strongly coupled fluids governed by repulsive l/r/sup n/ potentials. For two-component plasmas the ion-sphere model is shown to accurately represent the static portion of the energy. Electron screening is included in the Monte Carlo simulations using linear response theory and the Lindhard dielectric function. Free energy expressions have been constructed for one and two component plasmas that allow easy computation of all thermodynamic functions
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Equation of state of strongly coupled plasma mixtures
Thermodynamic properties of strongly coupled (high density) plasmas of mixtures of light elements have been obtained by Monte Carlo simulations. For an assumed uniform charge background the equation of state of ionic mixtures is a simple extension of the one-component plasma EOS. More realistic electron screening effects are treated in linear response theory and with an appropriate electron dielectric function. Results have been obtained for the ionic pair distribution functions, and for the electric microfield distribution
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QUANTUM MECHANICAL TREATMENT OF CLOSE COLLISIONS IN PLASMA TRANSPORT THEORY
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Equation of State of Classical Systems of Charged Particles
Recent developments in the classical theory of fully ionized gases and strong electrolyte solutions are reviewed, and are used to discuss the equation of state at high temperatures and low densities. The pressure is calculated using the ring-integral approximation, and quantitative estimates of higher correction terms are given. The effect of short range repulsive forces is shown by comparing the results with two kinds of potential functions hard spheres of diameter a, and soft'' spheres for which the short range potential cancels the Coulomb potential at the origin, and decreases exponentially with distance. It is found that the use of either type of potential extends the range of validity of the ring-integral approximation to considerably higher densities and lower temperatures. Since there is little difference in the results for the hard spheres and the soft spheres in this range, the latter system is investigated more extensively since it is more, easily handled by analytical methods. The expressions derived for the free energy of a system of charged particles can also be used in ionization equilibrium calculations, and the effect of electrostatic interactions on the equilibrium concentrations of various kinds of ions is indicated. 60 references. (auth