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.     

Coulomb Systems at Low Density: A Review

Results on the correlations of low-density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system, Debye–Hückel screening, is compared and contrasted with the quantum case, where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye–Hückel screening is discussed.     

Screening of an Electric Field and the Quasi-Static Capacitance of an Induced Charge in Semiconductors with Hopping Conductivity

Expressions for the screening length of an external electrostatic field in a crystalline semiconductor are derived in the Debye–Hückel and Mott–Schottky approximations taking into account electron (hole) hopping via hydrogen-like donors (acceptors). The feasibility of determining the Debye–Hückel screening length from measurements of a quasi-static capacitance with low and high degrees of basic dopant compensation has been demonstrated even in a strong field, that is, in the Mott–Schottky approximation. To measure the capacitance, the electric signal frequency must be much less than the average frequency of electron hopping via donors.     

Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature.     

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.     

Charge Correlations in a Coulomb System Along a Plane Wall: A Relation Between Asymptotic Behavior and Dipole Moment

Classical Coulomb systems at equilibrium, bounded by a plane dielectric wall, are studied. A general two-point charge correlation function is considered. Valid for any fixed position of one of the points, a new relation is found between the algebraic tail of the correlation function along the wall and the dipole moment of that function. The relation is tested first in the weak-coupling (Debye–Hückel) limit, and afterwards, for the special case of a plain hard wall, on the exactly solvable two-dimensional two-component plasma at coupling =2, and on the two-dimensional one-component plasma at an arbitrary even integer .     

Anomalous Effects of “Guest” Charges Immersed in Electrolyte: Exact 2D Results

We study physical situations when one or two “guest” arbitrarily-chargedbreak particles are immersed in the bulk of a classical electrolyte modelled by a Coulomb gas of pm unit point-like charges, the whole system being in thermal equilibrium. The models are treated as two-dimensional with logarithmic pairwise interactions among charged constituents; the (dimensionless) inverse temperature beta is considered to be smaller than 2 in order to ensure the stability of the electrolyte against the collapse of positive-negative pairs of charges. Based on recent progress in the integrable (1+1)-dimensional sine-Gordon theory, exact formulas are derived for the chemical potential of one guest charge and for the asymptotic large-distance behavior of the effective interaction between two guest charges. The exact results imply, under certain circumstances, anomalous effects such as an effective attraction (repulsion) between like-charged (oppositely-charged) guest particles and the charge inversion in the electrolyte vicinity of a highly-charged guest particle. The adequacy of the concept of renormalized charge is confirmed in the whole stability region of inverse temperatures and the related saturation phenomenon is revised.     

Guest Charges in an Electrolyte: Renormalized Charge, Long- and Short-Distance Behavior of the Electric Potential and Density Profiles

We complement a recent exact study by L. Šamaj on the properties of a guest charge Q immersed in a two-dimensional electrolyte with charges +1/−1. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Šamaj’s previous work, exact results for arbitrary coulombic coupling β were obtained for a system where all the charges are points, provided β Q < 2 and β < 2. Here, we first focus on the mean field situation which we believe describes correctly the limit β→ 0 but β Q large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value β Q > 2. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Šamaj for the renormalized charge are not valid for β Q > 2, contrary to a hypothesis put forward by Šamaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough (β Q≥ 2−β). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning–Oosawa threshold β Q = 2.     

Charge Fluctuations in Finite Coulomb Systems

When described in a grand canonical ensemble, a finite Coulomb system exhibits charge fluctuations. These fluctuations are studied in the case of a classical (i.e., non-quantum) system with no macroscopic average charge. Assuming the validity of macroscopic electrostatics gives, on a three-dimensional finite large conductor of volume V, a mean square charge Q ² which goes as V ^1/3. More generally, in a short-circuited capacitor of capacitance C, made of two conductors, the mean square charge on one conductor is Q ²=TC, where T is the temperature and C the capacitance of the capacitor. The case of only one conductor in a grand canonical ensemble is obtained by removing the other conductor to infinity. The general formula is checked in the weak-coupling (Debye–Hückel) limit for a spherical capacitor. For two-dimensional Coulomb systems (with logarithmic interactions), there are exactly solvable models which reveal that, in some cases, macroscopic electrostatics is not applicable even for large conductors. This is when the charge fluctuations involve only a small number of particles. The mean square charge on one two-dimensional system alone, in the grand canonical ensemble, is expected to be, at most, one squared elementary charge.     

Debye-Hückel limit of quantum coulomb systems

In this paper, we consider charge symmetric quantum Coulomb systems with Boltzmann statistics. We prove that the theory of screening of Debye and Hückel is a combined classical and mean field limit of these quantum Coulomb systems.Supported by the Swiss National Foundation for Scientific Research     

Debye–Hückel Theory for Charged Aligned Needles and for Polyelectrolyte Solutions

We consider a simple extension of the familiar Debye–Hückel theory of electrolyte solutions (in which the ions are represented by spheres with embedded point charges) to study the thermodynamic properties and the phase diagram of ionic solutions in which the ions of at least one of the species are deformed into parallel and rigid needle-like ellipsoidal objects that have a continuous line of charge distribution along their axis of revolution. We examine two specific cases: (a) solutions comprising both cationic and anionic needles that are identical in every respect except for the charge sign, and (b) solutions in which only one ionic species is made up of parallel rigid needles while the other species is made up of point ions. The first system is the analog, for ionic needles, of the familiar restricted primitive model of electrolytes, while the second one is a very simple model for a polyelectrolyte solution. For both systems we investigate how the phase diagram is affected by the extent of deformation of the ions, as measured by the spatial spread of their charge distribution.     

The oscillator representation and the stability of three-body Coulomb systems

Within nonrelativistic quantum mechanics the Wick-ordering method, called the oscillator representation, is suggested for calculating the energy spectrum for a wide class of potentials allowing the existence of a bound state. As test cases, anharmonic (V(r)=r ²) and screened Coulomb potentials are considered. In particular, the method is applied to three-body Coulomb systems to obtain the dependence of the bound-state energy on the masses and charges of the particles. The calculations of the bound-state energies for the moleculesH ^–=(pee),H ₂ ⁺ =(ppe), (e ^–e^–e⁺) and (pp), (dd), (dt) prove the accuracy of the zeroth approximation to be better than one per cent. For the three-body Coulomb system with charges +, –, – and arbitrary masses the region of stability is determined. For the systems (pe ^–C⁺), (A ⁺e^–e⁺), and (pB ^–e^–) the critical masses are calculated to beM _c=1.945m_e,M _A=4.350m_e andM _B=1.575m_e. It turns out that the system (pe ^–e⁺) is unstable.     

TIGHT MACH-STYLE CONNECTION BETWEEN THE EINSTEIN MASS-ENERGY AND INERTIA-GRAVITY EQUIVALANCES. REMARKS ON A RECENT EXPERIMENT BY MIKHAILOV

Equivalence of the two famous Einstein equivalences is, U denoting the cosmological potential, expressed à la Mach as U=c ². The electrostatic analog is induction of an extra mass –c ^–2eV (esu) in an electron immersed in the constant Coulomb potential c=Q/R enclosed in a charged sphere. This effect has been evidenced in a recent experiment by Mikhailov.     

Solution of three-dimensional Faddeev equations for three-body Coulomb bound states

A new method of directly solving the three-dimensional Faddeev equations in the total-angular-momentum representation for the pure Coulomb bound-state problem is developed. The method is based on the tri-quintic Hermite spline expansion of the Faddeev components. The ground states of thee ^– e ^– e ⁺ system and thepp ^– mesic molecule are calculated.     

Faddeev calculation of energy states in two-electron atoms

The Faddeev equations are used to calculate the ground state as well as a few ortho- and para-excited states of e^–e⁺e^–, H^–, He, Li⁺ and Be⁺⁺ atoms. The Coulomb potential is represented in a separable form using the appropriate Coulombic Sturmians for both the attractive and repulsive interactions. Up to 36 Sturmians are employed in each interaction leading to the solution of a maximum of 56 coupled one-variable integral equations. Results are compared with data or predictions from variational calculations.     

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.     

Boundary G/G Theory and Topological Poisson–Lie Sigma Model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G ^* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.     

New fermions at e+e− colliders II. Signals and backgrounds

We discuss the production, at high-energye ⁺ e ^– linear colliders, of new heavy fermions predicted by extensions of the Standard Model. We analyze in great details the various signals and the corresponding backgrounds for both pair production and single production in association with ordinary fermions. Concentrating on new leptons, we use a model detector fore ⁺ e ^– collisions at a center of mass energy of 500 GeV, to illustrate the discovery potential of the next linear colliders.     

Doubly Excited <Superscript>1,3</Superscript><Emphasis Type="Italic">P</Emphasis><Superscript>e</Superscript> Resonance States of the Positronium Negative Ion with Coulomb and Screened Coulomb Potentials

We have investigated the doubly excited ^1,3 P ^e resonance states of positronium negative ion with Coulomb and screened Coulomb potentials using highly accurate correlated exponential wavefunctions. For Coulomb interaction, the stabilization and the complex-rotation methods are employed to extract resonance parameters (resonance positions and widths). We have obtained two ¹ P ^e resonances and three ³ P ^e resonances below the n = 3 Ps threshold. In addition to Feshbach resonances lying below n = 3 Ps threshold, we have calculated one ³ P ^e shape resonances lying above the Ps (n = 2) threshold. For screened Coulomb (Yukawa) interaction, we employ the stabilization method to extract resonance parameters as functions screening parameter. The resonance energies and widths for ^1,3 P ^e resonance states of Ps⁻ below the n = 3 Ps threshold for different screening parameters ranging from infinity (Coulomb case) to small values are reported, along with the Ps(3S) and Ps(3P) threshold energies. The screened Coulomb results for the ^1,3 P ^e resonance states are reported for the first time in the literature.     

The electrostatic persistence length of polymers beyond the OSF limit

We use large-scale Monte Carlo simulations to test scaling theories for the electrostatic persistence length l _e of isolated, uniformly charged polymers with Debye-Hückel intrachain interactions in the limit where the screening length κ^-1 exceeds the intrinsic persistence length of the chains. Our simulations cover a significantly larger part of the parameter space than previous studies. We observe no significant deviations from the prediction l _e∝κ^-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. A linear or sublinear dependence of the persistence length on the screening length can be ruled out. We show that previous results pointing into this direction are due to a combination of excluded-volume and finite chain length effects. The paper emphasizes the role of scaling arguments in the development of useful representations for experimental and simulation data. Received 12 February 2002