Large-Distance Behavior of Particle Correlations in the Two-Dimensional Two-Component Plasma

The model under consideration is a two-dimensional two-component plasma, i.e., a continuous system of two species of pointlike particles of opposite charges ±1, interacting through the logarithmic Coulomb interaction. Using the exact results for the form-factors of an equivalent Euclidean sine-Gordon theory, we derive the large-distance behavior of the pair correlation functions between charged particles. This asymptotic behavior is checked on a few lower orders of its -expansion ( is the inverse temperature) around the Debye–Hückel limit 0, and at the free-fermion point =2 at which the collapse of positive-negative pairs of charges occurs.     

Renormalization of a Hard-Core Guest Charge Immersed in a Two-Dimensional Electrolyte

This paper is a continuation of a previous one [L. Šamaj, J. Stat. Phys. 120:125 (2005)] dealing with the renormalization of a guest charge immersed in a two-dimensional logarithmic Coulomb gas of pointlike ± unit charges, the latter system being in the stability-against-collapse regime of reduced inverse temperatures 0 ≤ β < 2. In the previous work, using a sine-Gordon representation of the Coulomb gas, an exact renormalized-charge formula was derived for the special case of the pointlike guest charge Q, in its stability regime β |Q| < 2. In the present paper, we extend the renormalized-charge treatment to the guest charge with a hard core of radius σ, which allows us to go beyond the stability border β|Q| = 2. In the limit of the hard-core radius much smaller than the correlation length of the Coulomb-gas species and at a strictly finite temperature, due to the counterion condensation in the extended region β|Q| > 2, the renormalized charge Q _ren turns out to be a periodic function of the bare charge Q with period 1. The renormalized charge therefore does not saturate at a specific finite value as |Q| →∞, but oscillates between two extreme values. In the high-temperature Poisson-Boltzmann scaling regime of limits β→ 0 and Q→∞ with the product β Q being finite, one reproduces the Manning-Oosawa type of counterion condensation with the uniform saturation of β Q _ren at the value 4/π in the region β|Q| ≥ 2. The obtained results disprove the “regularization hypothesis” of the previous work about the possibility of an analytic continuation of the formula for Q _ren from the stability region β |Q| < 2 to β |Q| ≥ 2.     

A Generalization of the Stillinger–Lovett Sum Rules for the Two-Dimensional Jellium

In the equilibrium statistical mechanics of classical Coulomb fluids, the long-range tail of the Coulomb potential gives rise to the Stillinger–Lovett sum rules for the charge correlation functions. For the jellium model of mobile particles of charge q immersed in a neutralizing background, the Stillinger–Lovett sum rules give the charge and second moment of the screening cloud around a particle of the jellium. In this paper, we generalize these sum rules to the screening cloud induced around a pointlike guest charge Zq immersed in the bulk interior of the 2D jellium with the coupling constant Γ=β q ² (β is the inverse temperature), in the whole region of the thermodynamic stability of the guest charge amplitude Z>−2/Γ. The derivation is based on a mapping technique of the 2D jellium at the coupling Γ = (even positive integer) onto a discrete 1D anticommuting-field theory; we assume that the final results remain valid for all real values of Γ corresponding to the fluid regime. The generalized sum rules reproduce for arbitrary coupling Γ the standard Z=1 and the trivial Z=0 results. They are also checked in the Debye–Hückel limit Γ→0 and at the free-fermion point Γ=2. The generalized second-moment sum rule provides some exact information about possible sign oscillations of the induced charge density in space.     

Variational extension of the mean spherical approximation to arbitrary dimensions

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limitT ΔS ^MSA /ΔE ^MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1. On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681.     

Phase behavior of three-component ionic fluids

We study the phase behavior of solutions consisting of positive and negative ions of valence z to which a third ionic species of valence Z>z is added. Using a discretized Debye-Hückel theory, we analyze the phase behavior of such systems for different values of the ratio . We find, for , a three-phase coexistence region and, for , a closed (reentrant) coexistence loop at high temperatures. We characterize the behavior of these ternary ionic mixtures as function of charge asymmetry and temperature, and show the complete phase diagrams for the experimentally relevant cases of and , corresponding to addition of divalent and trivalent ions to monovalent ionic fluids, respectively. Received 6 April 2000 and Received in final form 20 July 2000     

Coulomb pair density matrix I

The Coulomb pair density matrixG (r, r) for attractive and repulsive potentials is not only interesting for determining the two-particle effective potentials, but it is also essential in numerical studies of quantum systems. A high-temperature approximation is obtained for logG (r, r), in the form of simple integrals or series expansions; large-distance expansions are also given.     

Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, f (t) = f ₀exp - (t/τ)^β , with the exponent β increasing with the temperature. The relaxation time diverges as an Arrhenius law when T→ 0. Received 24 May 2001 and Received in final form 12 September 2001     

基于等离子体环境涨落的原子结构计算模型

本文将等离子体核聚变反应截面研究中利用等离子体环境涨落进行修正了的Debye-Hückel屏蔽势推广到计算等离子体中辐射离子束缚态的能级结构. 通过Tsallis参数q的变化,在等离子体辐射离子束缚态能级结构的计算中加入等离子体参数涨落的平均效应,即,等离子体动力学. 具体给出了利用修正的Debye-Hückel屏蔽势对类氦铝束缚态能级结构的计算结果. 结果表明基于这种修正的屏蔽势,自由电子的极化分布具有和线性Debye-Hückel屏蔽势不同的结构. 这种通过等离子体涨落分布对屏蔽势函数进 关键词： 等离子体中的原子结构 等离子体环境涨落 修正了的Debye-Hückel屏蔽势     

A renormalization group analysis of the Kosterlitz-Thouless phase

We consider a classical Coulomb gas with a short distance cutoff in two dimensions; equivalently a Sine-Gordon field theory. For low temperature β^-1 and low activityz the gas is in a multipole phase, the Kosterlitz-Thouless phase. For β>8π andz sufficiently small we give a complete renormalization group analysis for this phase and show that the flow of the effective measures is toward a free field (infrared asymptotic freedom). This should lead to control over the long distance behavior of the theory. Research supported by the Natural Sciences and Engineering Research Council     

Potential theory of strong electrolyte solutions using the Bogoliubov-Born-Green-Yvon integral equations

A potential analysis of strong electrolyte solutions is undertaken using the BBGY hierarchy of integral equations. An estimate for the fluctuation potential is found which implies damped oscillatory solutions of the Debye-Hückel potential for κa ? 1·720 (κ = Debye-Hückel constant, a = ionic diameter). The relation to the work of Martynov is also given.     

Asymptotic radial distribution function of a liquid

The large-distance asymptotic behavior of the radial distribution function is analyzed on the basis of the complete equation for this function. The asymptotic behavior is found for the case of a short-range force, a Coulomb force, and a Coulomb force with a solid core.Translated from Izvestiya VUZ. Fizika, No. 4, pp. 141–146, April, 1970.     

Renormalization Group Flow¶of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L&\darr; 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t→∞, to one of the countably infinite equilibrium solutions. The j ^th nontrivial equilibrium solution bifurcates from the trivial one at . These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature β >0. Gallavotti and Nicoló's conjecture on infinite sequence of “phases transitions” is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz–Thouless phases, at least in the hierarchical model we consider. Received: 29 November 1999 / Accepted: 13 January 2001     

Correlations in two-component log-gas systems

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a zero-density Kosterlitz-Thouless-type transition as the dimensionless coupling :=q ²/kT is varied through =2. In the charge-ordered system we use a perturbation technique to establish anO(1/r ⁴) decay of the two-body correlations in the high-temperature limit. For 2⁺, the low-fugacity expansion of the asymptotic charge-charge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations. In the system without charge ordering the two-body correlations exhibit anO(1/r ²) decay in the high-temperature limit, with a universal amplitude for the charge-charge correlation which is associated with the state being conductive. Low-fugacity expansions establish anO(1/r ) decay of the two-body correlations for 2<<4 and anO(1/r ⁴) decay for >4. For both systems we derive sum rules which relate the long-wavelength behaviour of the Fourier transform of the charge correlations to the dipole carried by the screening cloud surrounding two opposite internal charges. These sum rules are checked for specific solvable models. Our predictions for the Kosterlitz-Thouless transition and the large-distance behavior of the correlations should be valid at low densities. At higher densities, both systems might undergo a first-order liquid-gas transition analogous to the two-dimensional case.     

Weak Coupling and Continuous Limits for Repeated Quantum Interactions

We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three asymptotic regimes of the parameters λ and τ for which the effective evolution of observables on the small system becomes continuous over suitable macroscopic time scales T and whose generator can be computed: the weak coupling limit regime λ → 0, τ = 1, the regime τ → 0, λ²τ → 0 and the critical case λ²τ = 1, τ → 0. The first two regimes are perturbative in nature and the effective generators they determine is such that a non-trivial invariant sub-algebra of observables naturally emerges. The third asymptotic regime goes beyond the perturbative regime and provides an effective dynamics governed by a general Lindblad generator naturally constructed from the interaction Hamiltonian. Conversely, this result shows that one can attach to any Lindblad generator a repeated quantum interactions model whose asymptotic effective evolution is generated by this Lindblad operator.     

Thermodynamic properties of high temperature air in local thermodynamic equilibrium: II accurate analytical expression for electron molar fractions

An extremely accurate analytical expression for electron molar fractions in LTE air plasma in the temperature range 50–20 000 K and in the pressure range 10^-3 ÷ 10³ bar is reported. Results have been obtained by using self-consistent cutoff and inserting Debye-Hückel corrections.     

Coulomb excitation of 72 30Zn42

The reduced transition probability B(E2: 0₁ ⁺→ 2⁺) of ⁷²Zn has been measured for the first time by Coulomb excitation at intermediate energy. The result B(E2: 0₁ ⁺→ 2⁺) = 1740±210 e²fm⁴, corresponds to the deformation parameter β₂ of 0.23, in close agreement with expectations derived from the neighboring nucleus ⁷³Zn. A discussion of the evolution of the N = 40 sub-shell closure as a function of Z is presented. Received: 19 December 2001 / Accepted: 14 March 2002     

Global strings in extra dimensions: The full map of solutions,matter trapping,and the hierarchy problem

We consider (d ₀ + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d ₀ dimensions, endowed with a warp factor e ^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l _c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough distances l _c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane, where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems. The text was submitted by the authors in English.     

Field theoretical approach to inhomogeneous ionic systems: thermodynamic consistency with the contact theorem,Gibbs adsorption and surface tension

Using a statistical field approach we investigate the structure of an electrolyte solution in contact with a neutral impenetrable wall. The Hamiltonian contains the Coulomb interaction and the ideal entropy. At the level of the quadratic approximation, the Hamiltonian yields the Debye-Hückel theory in the bulk. Analytic expressions of the charge-charge and potential-potential inhomogeneous correlation functions are obtained. Exact asymptotic results for point ion charge correlation functions are obtained and the profile for the fluctuation of the electric potential is calculated. We also consider the term beyond the quadratic expansion of the ideal entropy in the Hamiltonian. With this term a higher order coupling between charge density and number density produces a non-trivial profile for the total ion density. This density profile is consistent with the contact theorem and the related surface tension calculated from the Gibbs adsorption isotherm.     

Triplet <Emphasis Type="Italic">p</Emphasis>-wave superconductivity in the low-density extended hubbard model with Coulomb repulsion

We analyze superconducting instabilities in 3D and 2D extended Hubbard model with Coulomb repulsion between electrons on neighboring sites in the limit of low electron density (n _el → 0) on simple cubic (square) lattice. We show that in a realistic strong-coupling case U ≫ V ≫ W (U and V are the onsite and the intersite Coulomb repulsions, respectively, and W the bandwidth) the main SC instability corresponds to the p-wave pairing and in the leading order is correctly described by the equations obtained earlier in the absence of the intersite Coulomb interaction V = 0.     

Asymptotic survival probability of random walks on a semi-infinite line

Symmetric and asymmetric random walks on a segment (−∞,T>0) of the real line are considered. There is a non-zero probability for the random walk to get absorbed at a site it visits. We derive for such random walks, expressions for survival probabilities in the asymptotic limit ofT→∞. An application of this asymptotic formulation to the problem of radiation transport through thick shields is presented.