Statistical mechanics of simple coulomb systems

Baus, Marc; Hansen, Jean‐Pierre

doi:10.1016/0370-1573(80)90022-8

Cited by 749 publications

(496 citation statements)

References 92 publications

Supporting

Mentioning

484

Contrasting

Unclassified

Order By: Relevance

“…We work in one dimension because of the numerical feasibility of the study in this case: we measure directly the correlation between the positions of particles. In studies of the one component plasma, mentioned above [40], the appearance of multiple peaks in the correlation function is observed as the temperature is lowered. real-space mass variance for a large ensemble of configurations, which is not numerically feasible (for modest computational power) in three dimensions.…”

Section: Numerical Study In One Dimensionmentioning

confidence: 97%

“…The alternative starting point quite often used in cosmological NBS are "glassy" configurations, obtained by evolving gravity with a negative sign and a strong damping on the velocities [32,39]. Without the damping, this system is essentially just what is known as the "one component plasma" in statistical physics (for a review, see [40]). The small k behavior of the power spectrum is then expected to be P in (k) ∼ k 2 at small k 14 .…”

Section: F Glass Pre-initial Conditionsmentioning

confidence: 99%

See 1 more Smart Citation

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Joyce¹,

Marcos²

2007

Phys. Rev. D

View full text Add to dashboard Cite

The relation between the results of cosmological N-body simulations, and the continuum theoretical models they simulate, is currently not understood in a way which allows a quantification of N dependent effects. In this first of a series of papers on this issue, we consider the quantification of such effects in the initial conditions of such simulations. A general formalism developed in [1] allows us to write down an exact expression for the power spectrum of the point distributions generated by the standard algorithm for generating such initial conditions. Expanded perturbatively in the amplitude of the input (i.e. theoretical, continuum) power spectrum, we obtain at linear order the input power spectrum, plus two terms which arise from discreteness and contribute at large wavenumbers. For cosmological type power spectra, one obtains as expected, the input spectrum for wavenumbers k smaller than that characteristic of the discreteness. The comparison of real space correlation properties is more subtle because the discreteness corrections are not as strongly localised in real space. For cosmological type spectra the theoretical mass variance in spheres and two point correlation function are well approximated above a finite distance. For typical initial amplitudes this distance is a few times the inter-particle distance, but it diverges as this amplitude (or, equivalently, the initial red-shift of the cosmological simulation) goes to zero, at fixed particle density. We discuss briefly the physical significance of these discreteness terms in the initial conditions, in particular with respect to the definition of the continuum limit of N-body simulations.

show abstract

Section: Numerical Study In One Dimensionmentioning

confidence: 97%

Section: F Glass Pre-initial Conditionsmentioning

confidence: 99%

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Joyce¹,

Marcos²

2007

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…[17,11] for detailed reviews). All the thermodynamic functions of the OCP of classical ions in a uniform (rigid) electron background can be expressed as functions of the only parameter Γ i .…”

Section: Ocp Liquid Of Classical Ionsmentioning

confidence: 99%

Equation of state of fully ionized electron-ion plasmas

1998

View full text Add to dashboard Cite

Thermodynamic quantities of Coulomb plasmas consisting of point-like ions immersed in a compressible, polarizable electron background are calculated for ion charges Z = 1 to 26 and for a wide domain of plasma parameters ranging from the Debye-Hückel limit to the crystallization point and from the region of nondegenerate to fully degenerate nonrelativistic or relativistic electrons. The calculations are based on the linear-response theory for the electron-ion interaction, including the local-field corrections in the electronic dielectric function. The thermodynamic quantities are calculated in the framework of the N -body hypernetted-chain equations and fitted by analytic expressions. We present also accurate analytic approximations for the free energy of the ideal electron gas at arbitrary degeneracy and relativity and for the excess free energy of the one-component plasma of ions (OCP) derived from Monte Carlo simulations. The extension to multi-ionic mixtures is discussed within the framework of the linear mixing rule. These formulae provide a completely analytic, accurate description of the thermodynamic quantities of fully ionized electron-ion Coulomb plasmas, a useful tool for various applications from liquid state theory to dense stellar matter.

show abstract

“…The one component plasma (OCP) model is one of the basic models in the condensed matter physics [1,2]. Besides of its direct astrophysical applications [2], to model the ionized matter in white dwarfs [3], outer layers of neutron stars and interiors of heavy planets [4,5], OCP is widely used as a reference model for a variety of systems, ranging from alkali metals [6][7][8] to colloidal solutions [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…The OCP model is formulated as a system of point particles, interacting via the Coulombic potential, which move in a uniform neutralizing background [1,2]. All thermodynamic properties of the OCP depend only on the dimensionless plasma parameter Γ = l B /a c , where l B = e 2 /k B T is the Bjerrum length (e is the charge of the particles, k B is the Boltzmann's constant, T is the temperature) and a c = (3/4πρ) 1/3 is the ion-sphere radius with ρ = N/Ω being the concentration of particles (N is the number of particles, Ω is the volume of the system).…”

Section: Introductionmentioning

confidence: 99%

Accurate First‐Principle Equation of State for the One‐Component Plasma

Brilliantov

1998

Contrib. Plasma Phys.

View full text Add to dashboard Cite

Accurate "first-principle" expressions for the excess free energy F ex and internal energy U ex of the classical one-component plasma (OCP) are obtained.We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto the Ising-like Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of a reference system. We use the ideal gas as a reference system for which all the correlation functions are known. Explicit calculations are performed with the high-order terms in the Ising-like Hamiltonian omitted. For small values of the plasma parameter Γ the DebyeHuckel result for F ex and U ex is recovered. For Γ ≫ 1, these depend linearly on Γ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the obtained analytical expression.

show abstract

Statistical mechanics of simple coulomb systems

Cited by 749 publications

References 92 publications

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Quantification of discreteness effects in cosmologicalN-body simulations: Initial conditions

Equation of state of fully ionized electron-ion plasmas

Accurate First‐Principle Equation of State for the One‐Component Plasma

Contact Info

Product

Resources

About