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We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schrödinger equations with multiple moving potentials. By the discovery of a refined structure of the construction of distorted Fourier transforms adapted to the multi-potential framework, we remove the large-velocity separation assumption imposed in [8]. This work thus completes the full scattering theory and dispersive analysis for general one-dimensional charge transfer models. These dispersive estimates provide the foundation for analyzing asymptotic stability and collision phenomena for multi-solitons in a general setting.
We propose a modified definition of the jet charge, the "dynamic jet charge", where the constant jet momentum fraction weighting parameter, $κ$, in the standard jet charge definition is generalized to be a function of a dynamical property of the jet or the individual jet constituents. The dynamic jet charge can complement analyses based on the standard definition and give improved discrimination between quark and gluon initiated jets and between jets initiated by different quark flavors. We focus on the specific scenario where each hadron in the jet contributes to the dynamic jet charge with a $κ$-value dynamically determined by its jet momentum fraction. The corresponding dynamic jet charge distributions have qualitatively distinct features and are typically characterized by a multiple peak structure. For proton-proton collisions, compared to the standard jet charge, the dynamic jet charge gives significantly improved discrimination between quark and gluon initiated jets and comparable discrimination between $u$- and $d$-quark initiated jets. In Pythia simulations of heavy ion collisions, the dynamic jet charge is found to have higher jet discrimination power compared to the stand
We scrutinize the effect of polyvalent ions on polymer-DNA interactions. We extend a recently developed test charge theory to the case of a stiff polymer interacting with a DNA molecule in an electrolyte mixture. The theory accounts for one-loop level electrostatic correlation effects such as the ionic cloud deformation around the strongly charged DNA molecule as well as image-charge forces induced by the low DNA permittivity. Our model can reproduce and explain various characteristics of the experimental phase diagrams for polymer solutions. First, the addition of polyvalent cations to the electrolyte solution results in the attraction of the negatively charged polymer by the DNA molecule. The glue of the like-charge attraction is the enhanced shielding of the polymer charges by the dense counterion layer at the DNA surface. Secondly, through the shielding of the DNA-induced electrostatic potential, mono- and polyvalent cations of large concentration both suppress the like-charge attraction. Within the same formalism, we also predict a new opposite-charge repulsion effect between the DNA molecule and a positively charged polymer. In the presence of polyvalent anions such as sulfat
Predicting the rate for $μ\to e$ conversion in nuclei for a given set of effective operators mediating the violation of lepton flavor symmetry crucially depends on hadronic and nuclear matrix elements. In particular, the uncertainties inherent in this non-perturbative input limit the discriminating power that can be achieved among operators by studying different target isotopes. In order to quantify the associated uncertainties, as a first step, we go back to nuclear charge densities and propagate the uncertainties from electron scattering data for a range of isotopes relevant for $μ\to e$ conversion in nuclei, including $^{40,48}$Ca, $^{48,50}$Ti, and $^{27}$Al. We provide as central results Fourier-Bessel expansions of the corresponding charge distributions with complete covariance matrices, accounting for Coulomb-distortion effects in a self-consistent manner throughout the calculation. As an application, we evaluate the overlap integrals for $μ\to e$ conversion mediated by dipole operators. In combination with modern ab-initio methods, our results will allow for the evaluation of general $μ\to e$ conversion rates with quantified uncertainties.
In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge $Z_{cr}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, $Z_{cr,2e}=0.91085$ and $Z_{cr,3e}=2.009$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z-Z_{cr})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at $Z_{cr}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of 1/Z-expansion is briefly discussed.
We discuss the effect of a strong magnetic field on the chemical freezeout points in the ultrarelativistic heavy-ion collision. As a result of the inverse magnetic catalysis or the magnetic inhibition, the crossover onset to hot and dense matter out of quarks and gluons should be shifted to a lower temperature. To quantify this shift we employ the hadron resonance gas model and an empirical condition for the chemical freezeout. We point out that the charged particle abundances are significantly affected by the magnetic field so that the electric charge fluctuation is largely enhanced especially at high baryon density. The charge conservation partially cancels the enhancement but our calculation shows that the electric charge fluctuation and the charge chemical potential could serve as a magnetometer. We find that the fluctuation exhibits a crossover behavior rapidly increased for eB >~ (0.4GeV)^2, while the charge chemical potential has better sensitivity to the magnetic field.
We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.
The maximally symmetric D-branes of string theory on the non-simply connected Lie group SU(n)/Z_d are analysed using conformal field theory methods, and their charges are determined. Unlike the well understood case for simply connected groups, the charge equations do not determine the charges uniquely, and the charge group associated to these D-branes is therefore in general not cyclic. The precise structure of the charge group depends on some number theoretic properties of n, d, and the level of the underlying affine algebra k. The examples of SO(3)=SU(2)/Z_2 and SU(3)/Z_3 are worked out in detail, and the charge groups for SU(n)/Z_d at most levels k are determined explicitly.
We use the equations of motion of non-interacting electrons in a one-dimensional system to numerically study different aspects of charge pumping. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the Fourier transforms of the charge and energy currents in the leads. Our method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. Our results agree with Floquet and adiabatic scattering theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias.
The correlation between net baryon number and electric charge, $χ_{11}^{\rm BQ}$, can serve as a magnetometer of QCD. This is demonstrated by lattice QCD computations using the highly improved staggered quarks with physical pion mass of $M_π=135~$MeV on $N_τ=8$ and 12 lattices. We find that $χ_{11}^{\rm BQ}$ along the transition line starts to increase rapidly with magnetic field strength $eB\gtrsim 2M_π^2$ and by a factor 2 at $eB\simeq 8M_π^2$. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, $μ_{\rm Q}/μ_{\rm B}$, shows significant dependence on the magnetic field strength and varies from the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results can provide baselines for effective theory and model studies, and both $χ_{11}^{\rm BQ}$ and $μ_{\rm Q}/μ_{\rm B}$ could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model.
Non-empty space reading of Maxwell equations as local energy identities explains why a Coulomb field is carried rigidly by electrons in experiments. The analytical solution of the Poisson equation defines the sharp radial shape of charged elementary densities which are proportional to continuous densities of electric self-energy. Inward and outward longitudinal waves within the continuous electron reshape its radial energy structure in external fields. Both Coulomb field and radial charge densities are free from energy divergences. Non-empty space of electrically charged mass-energy can be described by complex analytical densities resulting in real values for volume mass integrals and in imaginary values for volume charge integrals. Imaginary electric charges in the Newton gravitational law comply with real Coulomb forces. Unification of forces through complex charges rids them of radiation self-acceleration.
We consider a massive Dirac neutrino electric charge and magnetic moment within the context of the standard model supplied with SU(2)-singlet right-handed neutrino in arbitrary R_ξgauge. Using the dimensional-regularization scheme we start with calculations of the one-loop contributions to the neutrino electromagnetic vertex function exactly accounting for the neutrino and other particles masses. We examine the decomposition of the massive neutrino electromagnetic vertex function and show that it contains only the four form factors. Then we get the closed integral expressions for different contributions to the neutrino electric charge and magnetic form factors. These calculations enable us to follow the neutrino and corresponding charged lepton masses and gauge-fixing parameters dependence. For several one-loop contributions to the neutrino charge and magnetic moment, that were calculated previously by the other authors with mistakes, we find the correct results. We show that the neutrino charge for massive neutrino is a gauge independent and vanishing value in the first two orders of the expansion over the neutrino mass parameter b. In the particular choice of the 't Hooft-Feynman
We show that (3+1)-dimensional topological phases of matter generically support loop excitations with topological degeneracy. The loops carry "Cheshire charge": topological charge that is not the integral of a locally-defined topological charge density. Cheshire charge has previously been discussed in non-Abelian gauge theories, but we show that it is a generic feature of all (3+1)-D topological phases (even those constructed from an Abelian gauge group). Indeed, Cheshire charge is closely related to non-trivial three-loop braiding. We use a dimensional reduction argument to compute the topological degeneracy of loop excitations in the (3+1)-dimensional topological phases associated with Dijkgraaf-Witten gauge theories. We explicitly construct membrane operators associated with such excitations in soluble microscopic lattice models in ${\mathbb{Z}_2}\times{\mathbb{Z}_2}$ Dijkgraaf-Witten phases and generalize this construction to arbitrary membrane-net models. We explain why these loop excitations are the objects in the braided fusion 2-category $Z(\mathbf{2Vect}_G^ω)$, thereby supporting the hypothesis that 2-categories are the correct mathematical framework for (3+1)-dimensional
The discoveries of GW 150914, GW 151226, and LVT 151012 suggest that double black hole (BH-BH) mergers are common in the universe. If at least one of the two merging black holes carries certain amount of charge, possibly retained by a rotating magnetosphere, the inspiral of a BH-BH system would drive a global magnetic dipole normal to the orbital plane. The rapidly evolving magnetic moment during the merging process would drive a Poynting flux with an increasing wind power. The magnetospheric activities during the final phase of the merger would make a fast radio burst (FRB) if the BH charge can be as large as a factor of $\hat q \sim (10^{-9}-10^{-8})$ of the critical charge $Q_c$ of the BH. At large radii, dissipation of the Poynting flux energy in the outflow would power a short duration high-energy transient, which would appear as a detectable short-duration gamma-ray burst (GRB) if the charge can be as large as $\hat q \sim (10^{-5}-10^{-4})$. The putative short GRB coincident with GW 150914 recorded by Fermi GBM may be interpreted with this model. Future joint GW/GRB/FRB searches would lead to a measurement or place a constraint on the charges carried by isolate black holes.
I propose the measurement of the $W^\pm h$ charge asymmetry as a consistency test for the Standard Model (SM) Higgs, which is sensitive to enhanced Yukawa couplings of the first and second generation quarks. I present a collider analysis for the charge asymmetry in the same-sign lepton final state, $p p \to W^\pm h \to (\ell^\pm ν) (\ell^\pm νjj)$, aimed at discovery significance for the SM $W^\pm h$ production mode in each charge channel with 300 fb$^{-1}$ of 14 TeV LHC data. Using this decay mode, I estimate the statistical precision on the charge asymmetry should reach 0.4\% with 3 ab$^{-1}$ luminosity, enabling a strong consistency test of the SM Higgs hypothesis. I also discuss direct and indirect constraints on light quark Yukawa couplings from direct and indirect probes of the Higgs width as well as Tevatron and Large Hadron Collider Higgs data. While the main effect from enhanced light quark Yukawa couplings is a rapid increase in the total Higgs width, such effects could be mitigated in a global fit to Higgs couplings, leaving the $W^\pm h$ charge asymmetry as a novel signature to test directly the Higgs couplings to light quarks.
Consider any 1-parameter family of initial data such that data with parameter value p > p* form black holes, and data with p < p* do not. As p -> p* from above ("critical collapse"), the black hole mass scales as M ~ (p-p*)^gamma, where the critical exponent gamma is the same for all such families of initial data. So far critical collapse has been investigated only for initial data with zero charge and zero angular momentum. Here we allow for U(1) charge. In scalar electrodynamics coupled to gravity, with action R + |(d + iqA) phi|^2 + F^2, we consider initial data with spherical symmetry and nonvanishing charge. From dimensional analysis and a previous calculation of Lyapunov exponents, we predict that in critical collapse the black hole mass scales as M ~ (p-p*)^gamma, and the black hole charge as Q ~ (p-p*)^delta, with gamma = 0.374 +- 0.001 (as for the real scalar field), and delta = 0.883 +- 0.007. We conjecture that, where there is no mass gap, this behavior generalizes to other charged matter models, with delta \ge 2 gamma. We suggest the existence of universality classes with respect to parameters such as q.
Electron spins in silicon quantum dots are promising qubits due to their long coherence times, scalable fabrication, and potential for all-electrical control. However, charge noise in the host semiconductor presents a major obstacle to achieving high-fidelity single- and two-qubit gates in these devices. In this work, we measure the charge-noise spectrum of a Si/SiGe singlet-triplet qubit over nearly 12 decades in frequency using a combination of methods, including dynamically-decoupled exchange oscillations with up to 512 π pulses during the qubit evolution. The charge noise is colored across the entire frequency range of our measurements, although the spectral exponent changes with frequency. Moreover, the charge-noise spectrum inferred from conductance measurements of a proximal sensor quantum dot agrees with that inferred from coherent oscillations of the singlet-triplet qubit, suggesting that simple transport measurements can accurately characterize the charge noise over a wide frequency range in Si/SiGe quantum dots.
In this contribution, we summarize our results concerning the observational constraints on the electric charge associated with the Galactic centre black hole - Sgr A*. According to the no-hair theorem, every astrophysical black hole, including supermassive black holes, is characterized by at most three classical, externally observable parameters - mass, spin, and the electric charge. While the mass and the spin have routinely been measured by several methods, the electric charge has usually been neglected, based on the arguments of efficient discharge in astrophysical plasmas. From a theoretical point of view, the black hole can attain charge due to the mass imbalance between protons and electrons in fully ionized plasmas, which yields about $\sim 10^8\,{\rm C}$ for Sgr A*. The second, induction mechanism concerns rotating Kerr black holes embedded in an external magnetic field, which leads to electric field generation due to the twisting of magnetic field lines. This electric field can be associated with the induced Wald charge, for which we calculate the upper limit of $\sim 10^{15}\,{\rm C}$ for Sgr A*. Although the maximum theoretical limit of $\sim 10^{15}\,{\rm C}$ is still 1
We investigate electron and ion surface states of a negatively charged dust particle in a gas discharge and identify the charge of the particle with the electron surface density bound in the polarization-induced short-range part of the particle potential. On that scale, ions do not affect the charge. They are trapped in the shallow states of the Coulomb tail of the potential and act only as screening charges. Using orbital-motion limited electron charging fluxes and the particle temperature as an adjustable parameter, we obtain excellent agreement with experimental data.
We report on the observation of a unique honeycomb charge ordering of the cleaved IrTe$_2$ surface by high-resolution scanning tunneling microscopy (STM) and spectroscopy (STS). IrTe$_2$ was recently established to exhibit intriguing stripe charge orderings. Here, we show that the stripe charge order coexists with a metastable honeycomb phase formed locally. The atomic and electronic structures of the honeycomb phase are consistent with the stripe phase indicating unambiguously its charge order nature. A simple model of the honeycomb structure is suggested based on the overlap of three degenerate stripe orders, which is analogous to the 3$q$ state description of a skyrmion. We suggest that the honeycomb charge order can be a route to an exotic Dirac electron system.