Infinite Charge Research Articles

Infinite charge mobility in muscovite at 300 K

Evidence is presented for infinite charge mobility in natural crystals of muscovite mica at room temperature. Muscovite has a basic layered structure containing a flat monatomic sheet of potassium sandwiched between mirror silicate layers. It is an excellent electrical insulator. Studies of defects in muscovite crystals indicated that positive charge could propagate over great distances along atomic chains in the potassium sheets in the absence of an applied electric potential. The charge moved in association with anharmonic lattice excitations that moved at about sonic speed and created by nuclear recoil of the radioactive isotope 40K. This was verified by measuring currents passing through crystals when irradiated with energetic alpha particles at room temperature. The charge propagated more than 1000 times the range of the alpha particles of average energy and 250 times the range of channelling particles of maximum energy. The range is limited only by size of the crystal.

A Vlasov-Poisson plasma with unbounded mass and velocities confined in a cylinder by a magnetic mirror

We study the time evolution of a single species positive plasma, confined in a cylinder and having infinite charge. We extend the result of a previous work by the same authors, for a plasma density having compact support in the velocities, to the case of a density having unbounded support and gaussian decay in the velocities.

Stress Wave Interaction Between Two Adjacent Blast Holes

Rock fragmentation by blasting is determined by the level and state of stress in the rock mass subjected to blasting. With the application of electronic detonators, some researchers stated that it is possible to achieve improved fragmentation through stress wave superposition with very short delay times. This hypothesis was studied through theoretical analysis in the paper. First, the stress in rock mass induced by a single-hole shot was analyzed with the assumptions of infinite velocity of detonation and infinite charge length. Based on the stress analysis of a single-hole shot, the stress history and tensile stress distribution between two adjacent holes were presented for cases of simultaneous initiation and 1 ms delayed initiation via stress superposition. The results indicated that the stress wave interaction is local around the collision point. Then, the tensile stress distribution at the extended line of two adjacent blast holes was analyzed for a case of 2 ms delay. The analytical results showed that the tensile stress on the extended line increases due to the stress wave superposition under the assumption that the influence of neighboring blast hole on the stress wave propagation can be neglected. However, the numerical results indicated that this assumption is unreasonable and yields contrary results. The feasibility of improving fragmentation via stress wave interaction with precise initiation was also discussed. The analysis in this paper does not support that the interaction of stress waves improves the fragmentation.

Kohn-Sham kinetic energy density in the nuclear and asymptotic regions: Deviations from the von Weizsäcker behavior and applications to density functionals

We show that the Kohn-Sham positive-definite kinetic energy (KE) density significantly differs from the von Weizs\"acker (VW) one at the nuclear cusp as well as in the asymptotic region. At the nuclear cusp, the VW functional is shown to be linear and the contribution of p-type orbitals to the KE density is theoretically derived and numerically demonstrated in the limit of infinite nuclear charge, as well in the semiclassical limit of neutral large atoms. In the latter case, it reaches 12 of the KE density. In the asymptotic region we find new exact constraints for meta Generalized Gradient Approximation (meta-GGA) exchange functionals: with an exchange enhancement factor proportional to $\sqrt{\alpha}$, where $\alpha$ is the common meta-GGA ingredient, both the exchange energy density and the potential are proportional to the exact ones. In addition, this describes exactly the large-gradient limit of quasi-two dimensional systems.

Modified Slater exchange potential with correct uniform electron gas limit

Bulat and Levy recently deduced an expansion for the exact-exchange potential whose leading term is Slater’s averaged exchange-charge potential modified through the inclusion of orbital eigenvalues. When used as a stand-alone approximation to the exact-exchange potential, this leading term is much more accurate than Slater’s original. We give an alternative derivation of this term and show that, unlike the Slater potential, it correctly reduces to the Dirac exchange potential (i.e., the local density approximation) for a uniform electron gas, provided that the zero-energy reference of orbital eigenvalues is chosen as the Fermi level of the system. The orbital-energy-modified Slater potential should also recover the Dirac exchange potential for neutral atoms in the limit of infinite nuclear charge, but in practice converges to this limit very slowly on account of extreme sensitivity to the choice of zero-energy reference around the Fermi level.

The Screened Poisson–Vlasov System with Infinite Charge and Vanishing Screening

The Vlasov equation may be used to model the dynamics of a collisionless plasma. We consider a situation where the plasma has unbounded support and the charge density does not decay as |x|→ ∞. The electric field is computed from the screened Poisson equation, whose fundamental solution decays exponentially as |x|→ ∞ and hence gives a convergent integral despite the lack of decay of the charge density. The limit as the screening is removed is studied in one space dimension. It is shown that if some assumptions on the initial conditions hold, then the limit in question exists (but is not uniform) and the problem satisfied by the limit is identified.

On the monodromy problem for the four-punctured sphere

We consider the monodromy problem for the four-punctured sphere in which the character of one composite monodromy is fixed, by looking at the expansion of the accessory parameter in the modulus x directly, without taking the limit of the quantum conformal blocks for an infinite central charge. The integrals that appear in the expansion of the Volterra equation involve products of two hypergeometric functions to first order and up to four hypergeometric functions to second order. It is shown that all such integrals can be computed analytically. We give the complete analytical evaluation of the accessory parameter to first and second order in the modulus. The results agree with the evaluation obtained by assuming the exponentiation hypothesis of the quantum conformal blocks in the limit of infinite central charge. Extension to higher orders is discussed.

On a Magnetically Confined Plasma with Infinite Charge

We consider a one-species plasma moving in an infinite cylinder, in which it is confined by means of a magnetic field diverging on the walls of the cylinder. It is assumed that initially the particles have bounded velocities and are distributed according to a density which is bounded, without any decreasing at infinity. The mutual interaction is of Yukawa type, i.e., Coulomb at short distance and exponentially decreasing at infinity. We prove the global in time existence and uniqueness of the time evolution of the plasma and its confinement.

Modeling the transition from ohmic to space charge limited current in organic semiconductors

This paper presents a model for charge transport in organic and polymeric diodes that provides a physical explanation of the transition from ohmic to space-charge limited current (SCLC) regimes. The proposed model is based on two established models: a unified model for the injection and transport of charge in organic diodes, including a proper boundary condition for the free charge density at the metal–organic interface; and a temperature and electric-field dependent mobility model. The model reproduces published experimental current–voltage characteristics (for different temperatures and device lengths). The modeling results highlight the importance of the boundary condition at the interface that is used to explain different trends and their transitions in the current–voltage characteristics: linear, quadratic and a higher than quadratic trend at high electric fields. The model uses a finite charge at the interface to eliminate any dependence of the parameters of the mobility model with the length of the organic layer. Importantly, this result differs from others that consider an infinite charge at the interface, and make use of a length-dependent mobility, or other more complex models that incorporate a dependence with the free charge density in order to avoid such a dependence with the device length.

The calculation of the electrostatic potential of infinite charge distributions

We discuss some interesting aspects in the calculation of the electrostatic potential of charge distributions extending to infinity. The presentation is suitable for the advanced undergraduate level.

Gauss's law, infinite homogenous charge distributions and Helmholtz theorem

We rediscuss the validity of Gauss's law in the case of homogenous discrete and continuous charge distributions fulfilling all space.

Dissipative superfluid dynamics from gravity

Charged asymptotically AdS 5 black branes are sometimes unstable to the condensation of charged scalar fields. For fields of infinite charge and squared mass −4 Herzog was able to analytically determine the phase transition temperature and compute the endpoint of this instability in the neighborhood of the phase transition. We generalize Herzog’s construction by perturbing away from infinite charge in an expansion in inverse charge and use the solutions so obtained as input for the fluid gravity map. Our tube wise construction of patched up locally hairy black brane solutions yields a one to one map from the space of solutions of superfluid dynamics to the long wavelength solutions of the Einstein Maxwell system. We obtain explicit expressions for the metric, gauge field and scalar field dual to an arbitrary superfluid flow at first order in the derivative expansion. Our construction allows us to read off the the leading dissipative corrections to the perfect superfluid stress tensor, current and Josephson equations. A general framework for dissipative superfluid dynamics was worked out by Landau and Lifshitz for zero superfluid velocity and generalized to nonzero fluid velocity by Clark and Putterman. Our gravitational results do not fit into the 13 parameter Clark-Putterman framework. Purely within fluid dynamics we present a consistent new generalization of Clark and Putterman’s equations to a set of superfluid equations parameterized by 14 dissipative parameters. The results of our gravitational calculation fit perfectly into this enlarged framework. In particular we compute all the dissipative constants for the gravitational superfluid.

Particlelike solutions to classical noncommutative gauge theory

We construct perturbative static solutions to the classical field equations of noncommutative $U(1)$ gauge theory for the three cases: (a) space-time noncommutativity, (b) space-space noncommutativity, and (c) both (a) and (b). The solutions tend to the Coulomb solution at spatial infinity and are valid for intermediate values of the radial coordinate $r$. They yield a self-charge inside a sphere of radius $r$ centered about the origin which increases with decreasing $r$ for case (a), and decreases with decreasing $r$ for case (b). For case (a) this may mean that the exact solution screens an infinite charge at the origin, while for case (b) it is plausible that the charge density is well behaved at the origin, as happens in Born-Infeld electrodynamics. For both cases (a) and (b) the self-energy in the intermediate region grows faster as $r$ tends to the origin than that of the Coulomb solution. It then appears that the divergence of the classical self-energy is more severe in the noncommutative theory than it is in the corresponding commutative theory. We compute the lowest order effects of these solutions on the hydrogen atom spectrum and use them to put experimental bounds on the space-time and space-space noncommutative scales. For the former we get a significant improvement over previous bounds. We find that cases (a) and (b) have different experimental signatures.

Equilibrium points of logarithmic potentials induced by positive charge distributions. I. Generalized de Bruijn-Springer relations

A notion of weighted multivariate majorization is defined as a preorder on sequences of vectors in Euclidean space induced by the Choquet ordering for atomic probability measures. We characterize this preorder both in terms of stochastic matrices and convex functions and use it to describe the distribution of equilibrium points of logarithmic potentials generated by discrete planar charge configurations. In the case ofnnpositive charges we prove that the equilibrium points satisfy(n2)\binom {n}{2}weighted majorization relations and are uniquely determined byn−1n-1such relations. It is further shown that the Hausdorff geometry of the equilibrium points and the charged particles is controlled by the weighted standard deviation of the latter. By using finite-rank perturbations of compact normal Hilbert space operators we establish similar relations for infinite charge distributions. We also discuss a hierarchy of weighted de Bruijn-Springer relations and inertia laws, the existence of zeros of Borel series with positivel1l^1-coefficients, and an operator version of the Clunie-Eremenko-Rossi conjecture.

High-density limit of the Perdew-Burke-Ernzerhof generalized gradient approximation and related density functionals

We point out a simplifying but mildly inconsistent assumption of the Perdew-Burke-Ernzerhof (PBE) correlation functional, which should be corrected when evaluating the high-density limit of the PBE energy for nonsinglet systems under uniform density scaling. The discussion also concerns high-density limits of all density functionals that use PBE as an ingredient, including the Tao-Perdew-Staroverov-Scuseria (TPSS) approximation. We revisit the nonrelativistic correlation energies of isoelectronic atomic ions in the limit of infinite nuclear charge and explain small discrepancies between the PBE and TPSS values of these limits existing in the literature.

Coulomb problem for vector bosons

The Coulomb problem for vector bosons W{sup {+-}} incorporates a well-known difficulty; the charge of the boson localized in a close vicinity of the attractive Coulomb center proves to be infinite. The paradox is shown to be resolved by the QED vacuum polarization, which brings in a strong effective repulsion that eradicates the infinite charge of the boson on the Coulomb center. This property allows one to define the Coulomb problem for vector bosons properly.

COULOMB PROBLEM FOR VECTOR BOSONS IN STANDARD MODEL

The Coulomb problem for vector bosons W± propagating in an attractive Coulomb field incorporates a known difficulty, i.e. the total charge of the boson localized on the Coulomb center turns out to be infinite. This difficulty is shown to be resolved by the QED vacuum polarization, which brings in a strong effective repulsion and eradicates the infinite charge of the boson on the Coulomb center. The effect makes the Coulomb problem for vector bosons well defined and consistent with the Standard Model.

Aspects of WZW models at critical level

AbstractWe consider non‐compact WZW models at critical level (equal to the dual Coxeter number) as tensionless limits of gravitational backgrounds in string theory. Special emphasis is placed on the Euclidean black hole coset SL(2,R)k/U(1) when k = 2. In this limit gravity decouples in the form of a Liouville field with infinite background charge and the world‐sheet symmetry of the model becomes a truncated version of W∞ without Virasoro generator. This is regarded as manifestation of Langlands duality for the SL(2,R)k current algebra that relates small with large values of the level in the two extreme limits. However, the physical interpretation of the SL(2,R)k/U(1) coset model below the self‐dual value k = 3 remains elusive including the non‐conformal theory at k = 2.

Saturation of Electrostatic Potential: Exactly Solvable 2D Coulomb Models

We test the concepts of renormalized charge and potential saturation, introduced within the framework of highly asymmetric Coulomb mixtures, on exactly solvable Coulomb models. The object of study is the average electrostatic potential induced by a unique “guest” charge immersed in a classical electrolyte, the whole system being in thermal equilibrium at some inverse temperature β. The guest charge is considered to be either an infinite hard wall carrying a uniform surface charge or a charged colloidal particle. The systems are treated as two-dimensional; the electrolyte is modelled by a symmetric two-component plasma (TCP) of point-like ±e charges with logarithmic Coulomb interactions. Two cases are solved exactly: the Debye–Hückel limit β e2→ 0 and the Thirring free-fermion point β e2=2. The results at the free-fermion point can be summarized as follows: (i) The induced electrostatic potential exhibits the asymptotic behavior, at large distances from the guest charge, whose form is different from that obtained in the Debye–Hückel (linear Poisson–Boltzmann) theory. This means that the concept of renormalized charge, developed within the nonlinear Poisson–Boltzmann (PB) theory to describe the screening effect of the electrolyte cloud, fails at the free-fermion point. (ii) In the limit of an infinite bare charge, the induced electrostatic potential saturates at a finite value in every point of the electrolyte region. This fact confirms the previously proposed hypothesis of potential saturation.

Binding energy for hydrogen-like atoms in the Nelson model without cutoffs

In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge Ze, Z > 0 , fixed at the origin and an electron of mass m and charge e. This system forms a bound state with binding energy E bin = me 4 Z 2 / 8 π 2 to leading order in e. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that E bin = me 4 Z 2 / 8 π 2 + c 0 e 6 + O ( e 7 ln e ) with explicit coefficient c 0 and independent of the ultraviolet cutoff. c 0 can be computed by perturbation theory, which however is only formal since for the Nelson Hamiltonian the smallest eigenvalue sits exactly at the bottom of the continuous spectrum.