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.     

Guest Charge and Potential Fluctuations in Two-Dimensional Classical Coulomb Systems

A known generalization of the Stillinger-Lovett sum rule for a guest charge immersed in a two-dimensional one-component plasma (the second moment of the screening cloud around this guest charge) is more simply retrieved, just by using the BGY hierarchy for a mixture of several species; the zeroth moment of the excess density around a guest charge immersed in a two-component plasma is also obtained. The moments of the electric potential are related to the excess chemical potential of a guest charge; explicit results are obtained in several special cases. Unité Mixte de Recherche No. 8627—CNRS.     

Pressures for a One-Component Plasma on a Pseudosphere

The classical (i.e., non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of constant negative curvature) is considered. In the case of a flat space, it is known that, for a one-component plasma, there are several reasonable definitions of the pressure, and that some of them are not equivalent to each other. In the present paper, this problem is revisited in the case of a pseudosphere. General relations between the different pressures are given. At one special temperature, the model is exactly solvable in the grand canonical ensemble. The grand potential and the one-body density are calculated in a disk, and the thermodynamic limit is investigated. The general relations between the different pressures are checked on the solvable model.     

Two-Dimensional Coulomb Systems in a Disk with Ideal Dielectric Boundaries

We study two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we consider the two-component plasma in detail. When the coulombic coupling constant =2 the model is exactly solvable. We compute the grand potential, densities and correlations. We show that the grand potential has a universal logarithmic finite-size correction as predicted in previous works. This logarithmic finite-size correction is also found in the free energy of another solvable model: the one-component plasma.     

Pressure and Maxwell Tensor in a Coulomb Fluid

The pressure in a classical Coulomb fluid at equilibrium is obtained from the Maxwell tensor at some point inside the fluid, by a suitable statistical average. For fluids in a Euclidean space, this is a fresh look at known results. But for fluids in a curved space, a case which is of some interest, these unambiguous results from the Maxwell tensor approach have not been obtained by other methods.     

A Coulomb Blockade in a Nanostructure Based on Single Intramolecular Charge Center

A novel technique for the production of metal electrodes of a nanotransistor with a nanogap less than 4 nm between them is developed on the basis of controlling the electromigration of previously suspended nanowires of the system. A method that allows the embedding of a molecule of Rh(III) terpyridine with aurophilic ligands between electrodes is elaborated, as well. The characteristics of electron transport through a system that consists of the specified molecule with a single-atom charge center indicate the correlated (single-electron) tunneling of electrons.     

Fluctuations of Induced Charge in Hemispherical Detectors

Detectors with hemispherical geometry are used to eliminate the contribution from the hole component to the signal of a detector based on a compound semiconductor operating at room temperature. In this work, the random process of charge induction on electrodes of a detector with hemispherical geometry is theoretically considered with allowance for capture of electrons by traps. Formulas are obtained for the first two moments of the distribution function for the induced charge on the detector electrodes. These formulas help analyze the contribution of the electron transport in detectors with hemispherical geometry.     

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N , the number of mobile particles of charge e. As expected, the distribution of N has, for large , a Gaussian form with a variance which grows only as ^||, where || is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^() decreases to an asymptotic value ^()^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length _L=2^/ associated with charge fluctuations behaves very differently from that of the Debye length, _D1/ , which it approaches as 0. The pair correlation function of the OCP is also studied.     

Long-Time Behavior for the Two-Dimensional Motion of a Disk in a Viscous Fluid

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier–Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive L ^p ?L ^q decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier–Stokes fluid-rigid disk system.     

Density Profiles in a Quantum Coulomb Fluid Near a Hard Wall

Journal of Statistical Physics - Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any...     

Charge screening in supercritical Coulomb fields and a lower bound for electron energy levels

We show that discontinuities in the vacuum polarisation give rise to charge screening effects which are large and result in a lower bound Δ with − m < Δ < m for the energy levels of an electron bound in a supercritical field.     

The Fluid of Primordial Fluctuations

We formulate a phenomenological model where theinflaton fluctuations are treated as a fluid. Byapplying the hydrodynamic equations to this fluid werecover the conventional result that relates thespectrum of density fluctuations in the inflaton fieldat reentering the horizon to the spectrum offluctuations at the time a scale leaves the horizon.Moreover, through the equivalent viscosity of the fluidwe obtain a Reynolds number that suggeststurbulent motion, which implies that mode–modecoupling in the inflaton field cannot be neglected. Forde Sitter inflation the resulting spectrum usingturbulence theory is scale invariant on all scales ofinterest. This suggests that the hypothesis of anextremely weakly coupled inflation could be relaxedwithout affecting the predictions of themodel.     

Charge oscillations in a double quantum dot in the Coulomb blockade regime

The two-electron dynamics in a symmetric double quantum dot placed in a onstant electric field is considered. It is shown that, despite the Coulomb blockade, interdot electron-density oscillations are possible. In these oscillations, a charge equal to the charge of a single electron is periodically transferred from one quantum dot to the other.     

Effect of Ergodic and Non-Ergodic Fluctuations on a Charge Diffusing in a Stochastic Magnetic Field

In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field where the sojourn time in one of the two states are distributed according to a given waiting-time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous-Time Random Walk models.     

Splitting of the Spectrum of Fermionic Excitations in a Topological Insulator by Charge Fluctuations

JETP Letters - It is shown that the intersite Coulomb interaction of electrons in a topological insulator leads to the splitting of the initial energy structure and to the induction of two bands of...