Charge Renormalization Research Articles

Donnan equilibrium in charged slit-pores from a hybrid nonequilibrium molecular dynamics/Monte Carlo method with ions and solvent exchange.

Ion partitioning between different compartments (e.g., a porous material and a bulk solution reservoir), known as Donnan equilibrium, plays a fundamental role in various contexts such as energy, environment, or water treatment. The linearized Poisson-Boltzmann (PB) equation, capturing the thermal motion of the ions with mean-field electrostatic interactions, is practically useful to understand and predict ion partitioning, despite its limited applicability to conditions of low salt concentrations and surface charge densities. Here, we investigate the Donnan equilibrium of coarse-grained dilute electrolytes confined in charged slit-pores in equilibrium with a reservoir of ions and solvent. We introduce and use an extension to confined systems of a recently developed hybrid nonequilibrium molecular dynamics/grand canonical Monte Carlo simulation method ("H4D"), which enhances the efficiency of solvent and ion-pair exchange via a fourth spatial dimension. We show that the validity range of linearized PB theory to predict the Donnan equilibrium of dilute electrolytes can be extended to highly charged pores by simply considering renormalized surface charge densities. We compare with simulations of implicit solvent models of electrolytes and show that in the low salt concentrations and thin electric double layer limit considered here, an explicit solvent has a limited effect on the Donnan equilibrium and that the main limitations of the analytical predictions are not due to the breakdown of the mean-field description but rather to the charge renormalization approximation, because it only focuses on the behavior far from the surfaces.

Renormalization of spin-one asymptotic charges in AdSD

We study the renormalized action and the renormalized presymplectic potential for Maxwell fields on Anti de Sitter backgrounds of any dimensions. We then use these results to explicitly derive finite boundary charges for angle-dependent asymptotic symmetries. We consider both Poincaré and Bondi coordinates, the former allowing us to control the systematics for arbitrary D, the latter being better suited for a smooth flat limit.

Effective interactions, structure, and pressure in charge-stabilized colloidal suspensions: Critical assessment of charge renormalization methods.

Charge-stabilized colloidal suspensions display a rich variety of microstructural and thermodynamic properties, which are determined by electro-steric interactions between all ionic species. The large size asymmetry between molecular-scale microions and colloidal macroions allows the microion degrees of freedom to be integrated out, leading to an effective one-component model of microion-dressed colloidal quasi-particles. For highly charged colloids with strong macroion-microion correlations, nonlinear effects can be incorporated into effective interactions by means of charge renormalization methods. Here, we compare and partially extend several practical mean-field methods of calculating renormalized colloidal interaction parameters, including effective charges and screening constants, as functions of concentration and ionic strength. Within the one-component description, we compute structural and thermodynamic properties from the effective interactions and assess the accuracy of the different methods by comparing predictions with elaborate primitive-model simulations [P. Linse, J. Chem. Phys. 113, 4359 (2000)]. We also compare various prescriptions for the osmotic pressure of suspensions in Donnan equilibrium with a salt ion reservoir and analyze instances where the macroion effective charge becomes larger than the bare one. The methods assessed include single-center cell, jellium, and multi-center mean-field theories. The strengths and weaknesses of the various methods are critically assessed, with the aim of guiding optimal and accurate implementations.

Strong-field vacuum polarisation with high energy lasers

When photons propagate in vacuum they may fluctuate into matter pairs thus allowing the vacuum to be polarised. This linear effect leads to charge screening and renormalisation. When exposed to an intense background field a nonlinear effect can arise when the vacuum is polarised by higher powers of the background. This nonlinearity breaks the superposition principle of classical electrodynamics, allowing for light-by-light scattering of probe and background photons mediated through virtual pairs dressed by the background. Vacuum polarisation is a strong-field effect when all orders of interaction between the virtual pair and the background must be taken into account. In this investigation we show that multiple scattering processes of this type may be observed by utilising high-energy laser pulses with long pulse duration, such as are available at facilities like ELI Beamlines. In combination with appropriate sources of high-energy probe photons, multiple probe-background light-by-light scattering allows for testing the genuine nonlinear regime of strong-field quantum electrodynamics. This provides access to the uncharted non-perturbative regime beyond the weak-field limit.

Generation of Electric Current by Magnetic Field at the Boundary: Quantum Scale Anomaly Versus Semiclassical Meissner Current Outside of the Conformal Limit

AbstractThe scale (conformal) anomaly can generate an electric current near the boundary of a system in the presence of a static magnetic field. The magnitude of this magnetization current, produced at zero temperature and in the absence of matter, is proportional to a beta function associated with the renormalization of the electric charge. Using first‐principle lattice simulations, this paper investigates how the breaking of the scale symmetry affects this “scale magnetic effect” near a Dirichlet boundary in scalar quantum electrodynamics (Abelian Higgs model). This study demonstrates the interplay of the generated current with vortex excitations both in symmetric (normal) and broken (superconducting) phases and compares the results with the anomalous current produced in the conformal, scale‐invariant regime. Possible experimental signatures of the effect in Dirac semimetals are discussed.

Consistency of potential energy in the dynamical vertex approximation

In the last decades, dynamical mean-field theory (DMFT) and its diagrammatic extensions have been successfully applied to describe local and nonlocal correlation effects in correlated electron systems. Unfortunately, except for the exact solution, it is impossible to fulfill both the Pauli principle and conservation laws at the same time. Consequently, fundamental observables such as the kinetic and potential energies are ambiguously defined. In this work, we propose an approach to overcome the ambiguity in the calculation of the potential energy within the ladder dynamical vertex approximation (D$\Gamma$A) by introducing an effective mass renormalization parameter in both the charge and the spin susceptibility of the system. We then apply our method to the half-filled single-band Hubbard model on a three-dimensional bipartite cubic lattice. We find that: (i) at weak-to-intermediate coupling, a reasonable modification of the transition temperature $\TN$ to the antiferromagnetically ordered state with respect to previous ladder D$\Gamma$A calculations without charge renormalization. This is in good agreement with dual fermion and Monte Carlo results; (ii) the renormalization of charge fluctuations in our new approach leads to a unique value for the potential energy which is substantially lower than corresponding ones from DMFT and non-self-consistent ladder D$\Gamma$A; and (iii) the hierarchy of the kinetic energies between the DMFT and the ladder D$\Gamma$A in the weak coupling regime is restored by the consideration of charge renormalization.

All-order renormalization of electric charge in the Standard Model and beyond

Electric charge, as defined in the Thomson limit of the electron–photon interaction vertex, is renormalized to all orders both in the Standard Model and in any spontaneously broken gauge theory with gauge group G\timesG×U(1) with a group factor U(1) that mixes with electromagnetic gauge symmetry. In the framework of the background-field method the charge renormalization constant Z_eZe is directly obtained from the photon wave-function renormalization constant, similar to the situation in QED, which proves charge universality as a byproduct. Exploiting charge universality in arbitrary R_\xiRξ gauge by formulating the charge renormalization condition for a ``fake fermion’’ that couples only via an infinitesimal electric charge, Z_eZe can be expressed in terms of renormalization constants that are obtained solely from gauge-boson self-energies.

Linear pair-creation damping of high-frequency plasma oscillation

We have studied the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac–Heisenberg–Wigner formalism. The vacuum contribution to the physical observables leads to ultraviolet divergences, which are removed by a charge renormalization. The remaining vacuum contribution is small and is in agreement with previously derived expressions for the time-dependent vacuum polarization. The main new feature of the theory is a damping mechanism similar to Landau damping, but where the plasmon energy gives rise to creation of electron–positron pairs. The dependence of the damping rate (pair-creation rate) on the wavenumber, temperature, and density is analyzed. Finally, the analytical results of linearized theory are compared with numerical solutions.

Optimizing Multisite λ-Dynamics Throughput with Charge Renormalization.

With the ability to sample combinations of alchemical perturbations at multiple sites off a small molecule core, multisite λ-dynamics (MSλD) has become an attractive alternative to conventional alchemical free energy methods for exploring large combinatorial chemical spaces. However, current software implementations dictate that combinatorial sampling with MSλD must be performed with a multiple topology model (MTM), which is nontrivial to create by hand, especially for a series of ligand analogues which may have diverse functional groups attached. This work introduces an automated workflow, referred to as msld_py_prep, to assist in the creation of a MTM for use with MSλD. One approach for partitioning partial atomic charges between ligands to create a MTM, called charge renormalization, is also presented and rigorously evaluated. We find that msld_py_prep greatly accelerates the preparation of MSλD ready-to-use files and that charge renormalization can provide a successful approach for MTM generation, as long as bookending calculations are applied to correct small differences introduced by charge renormalization. Charge renormalization also facilitates the use of many different force field parameters with MSλD, broadening the applicability of MSλD for computer-aided drug design.

A nonlocal electrostatics model for ions in concentrated primitive electrolyte solutions

In this paper, a nonlocal electrostatics model is developed for ions in primitive electrolyte solutions. When a charge renormalization process is applied to the Ornstein-Zernike(OZ) equation of an electrolyte mixture, an exact Debye-Hückel-like equation with the exclude volume effect is derived. Further assuming that linear response approximation applies to the solution, the electric potential ϕ(r) of an ion in the solution is further approximated by an extended Debye-Hückel equation ∇2ϕ(r)=κ2ϕ(r)+∫H(|r−r′|)∇2ϕ(r′)dr′, with H(r)=∑lMle−Λlr4πr the kernel function. The parameters, say κ, {Λl} and {Ml}, are determined in a self-consistent way to reproduce the bulk dielectric response function. The theory can reproduce the well known multi-Yukawa electric potentials in concentrated electrolyte solutions. Analytical expressions for induced charge densities, electric potentials and electrostatic energies are derived for spherical ions. The theory is applied to ions in concentrated electrolyte solutions, where the good agreement with hyper-netted-chain(HNC) theory demonstrates its validity.

Electric charge renormalization to all orders

The electric charge renormalization constant, as defined in the Thomson limit, is expressed in terms of self-energies of the photon--Z-boson system in an arbitrary ${R}_{\ensuremath{\xi}}$ gauge to all perturbative orders. The derivation as carried out in the Standard Model holds in all spontaneously broken gauge theories with the ${\mathrm{SU}(2)}_{\mathrm{w}}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(1)}_{Y}$ gauge group in the electroweak sector and is based on the application of charge universality to a fake fermion with infinitesimal weak hypercharge and vanishing weak isospin, which effectively decouples from all other particles. Charge universality, for instance, follows from the known universal form of the charge renormalization constant as derived within the background-field formalism. Finally, we have generalized the described procedure to gauge theories with gauge group ${\mathrm{U}(1)}_{Y}\ifmmode\times\else\texttimes\fi{}G$ with any Lie group $G$, only assuming that electromagnetic gauge symmetry is unbroken and mixes with ${\mathrm{U}(1)}_{Y}$ transformations in a nontrivial way.

Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-x action

The McLerran-Venugopalan (MV) model is a Gaussian effective theory of color charge fluctuations at small-x in the limit of large valence charge density, i.e., a large nucleus made of uncorrelated color charges. In this work, we explore the effects of the first non-trivial (even C-parity) non-Gaussian correction on the color charge density to the MV model (“quartic” term) in SU(2) and SU(3) color group in the non-perturbative regime. We compare our (numerical) non-perturbative results to (analytical) perturbative ones in the limit of small or large non-Gaussian fluctuations. The couplings in the non-Gaussian action, μ¯ for the quadratic and κ4 for the quartic term, need to be renormalized in order to match the two-point function in the Gaussian theory. We investigate three different choices for the renormalization of these couplings: i) κ4 is proportional to a power of μ¯; ii) κ4 is kept constant and iii) μ¯ is kept constant. We find that the first two choices lead to a scenario where the small-x action evolves towards a theory dominated by large non-Gaussian fluctuations, regardless of the system size, while the last one allows for controlling the deviations from the MV model.

Probing the protein corona around charged macromolecules: interpretation of isothermal titration calorimetry by binding models and computer simulations

Isothermal titration calorimetry (ITC) is a widely used tool to experimentally probe the heat signal of the formation of the protein corona around macromolecules or nanoparticles. If an appropriate binding model is applied to the ITC data, the heat of binding and the binding stoichiometry as well as the binding affinity per protein can be quantified and interpreted. However, the binding of the protein to the macromolecule is governed by complex microscopic interactions. In particular, due to the steric and electrostatic protein–protein interactions within the corona as well as cooperative, charge renormalization effects of the total complex, the application of standard (e.g., Langmuir) binding models is questionable and the development of more appropriate binding models is very challenging. Here, we discuss recent developments in the interpretation of the Langmuir model applied to ITC data of protein corona formation, exemplified for the well-defined case of lysozyme coating highly charged dendritic polyglycerol sulfate (dPGS), and demonstrate that meaningful data can be extracted from the fits if properly analyzed. As we show, this is particular useful for the interpretation of ITC data by molecular computer simulations where binding affinities can be calculated but it is often not clear how to consistently compare them with the ITC data. Moreover, we discuss the connection of Langmuir models to continuum binding models (where no discrete binding sites have to be assumed) and their possible extensions toward the inclusion of leading order cooperative electrostatic effects.Graphical Schematic plot of the ITC experiment and the binding cooperativity of protein corona formation revealed from computer simulations.

Realistic Ion Dynamics through Charge Renormalization in Nonaqueous Electrolytes.

While many practically important electrolytes contain lithium ions, interactions of these ions are particularly difficult to probe experimentally because of their small X-ray and neutron scattering cross sections and large neutron absorption cross sections. Molecular dynamics (MD) is a powerful tool for understanding the properties of nonaqueous electrolyte solutions from the atomic level, but the accuracy of this computational method crucially depends on the physics built into the classical force field. Here, we demonstrate that several force fields for lithium bistriflimide (LiTFSI) in acetonitrile yield a solution structure that is consistent with the neutron scattering experiments, yet these models produce dramatically different ion dynamics in solution. Such glaring discrepancies indicate that inadequate representation of long-range interactions leads to excessive ionic association and ion-pair clustering. We show that reasonable agreement with the experimental observations can be achieved by renormalization of the ion charges using a "titration" method suggested herewith. This simple modification produces realistic concentration dependencies for ionic diffusion and conductivity in <2 M solutions, without loss in quality for simulation of the structure.

Vacuum polarization of generalized quantum electrodynamics in the Heisenberg picture

In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Källén methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative aspects of vacuum polarization. In addition, the most general structure of induced current and polarization tensor that emerge naturally by a perturbative scheme “à la” Källén is also obtained. Afterward, we discuss the physical implication of charge renormalization in the perspective of unitary and stable Podolsky theory.

Modeling deswelling, thermodynamics, structure, and dynamics in ionic microgel suspensions.

Ionic microgel particles in a good solvent swell to an equilibrium size determined by a balance of electrostatic and elastic forces. When crowded, ionic microgels deswell owing to a redistribution of microions inside and outside the particles. The concentration-dependent deswelling affects the interactions between the microgels and, consequently, the suspension properties. We present a comprehensive theoretical study of crowding effects on thermodynamic, structural, and dynamic properties of weakly cross-linked ionic microgels in a good solvent. The microgels are modeled as microion- and solvent-permeable colloidal spheres with fixed charge uniformly distributed over the polymer gel backbone, whose elastic and solvent-interaction free energies are described using the Flory-Rehner theory. Two mean-field methods for calculating the crowding-dependent microgel radius are investigated and combined with calculations of the net microgel charge characterizing the electrostatic part of an effective microgel pair potential, with charge renormalization accounted for. Using this effective pair potential, thermodynamic and static suspension properties are calculated, including the osmotic pressure and microgel pair distribution function. The latter is used in our calculations of dynamic suspension properties, where we account for hydrodynamic interactions. Results for diffusion and rheological properties are presented over ranges of microgel concentration and charge. We show that deswelling mildly enhances self- diffusion and collective diffusion and the osmotic pressure, lowers the suspension viscosity, and significantly shifts the suspension crystallization point to higher concentrations. This paper presents a bottom-up approach to efficiently computing suspension properties of crowded ionic microgels using single-particle characteristics.

Direct measurement of a beta function and an indirect check of the Schwinger effect near the boundary in Dirac semimetals

The electric field inside typical conductors drops down exponentially with the screening length determined by an intrinsic length scale of the system such as the density of mobile carriers. We show that in a classically conformal system with boundaries, where the intrinsic length scale is absent, the screening of an external electric field is governed by the quantum conformal anomaly associated with the renormalization of the electric charge. The electric field decays algebraically with a fractional power determined by the beta function of the system. We argue that this `anomalous conformal screening effect' is an indirect manifestation of the Schwinger pair production in relativistic field theory. We discuss the experimental feasibility of the proposed phenomenon in Dirac and Weyl semimetals what would allow direct experimental access to the beta function.

Quantum Brownian motion of a magnetic skyrmion

Within a microscopic theory, we study the quantum Brownian motion of a skyrmion in a magnetic insulator coupled to a bath of magnon-like quantum excitations. The intrinsic skyrmion-bath coupling gives rise to damping terms for the skyrmion center-of-mass, which remain finite down to zero temperature due to the quantum nature of the magnon bath. We show that the quantum version of the fluctuation-dissipation theorem acquires a non-trivial temperature dependence. As a consequence, the skyrmion mean square displacement is finite at zero temperature and has a fast thermal activation that scales quadratically with temperature, contrary to the linear increase predicted by the classical phenomenological theory. The effects of an external oscillating drive which couples directly on the magnon bath are investigated. We generalize the standard quantum theory of dissipation and we show explicitly that additional time-dependent dissipation terms are generated by the external drive. From these we emphasize a friction and a topological charge renormalization term, which are absent in the static limit. The skyrmion response function inherits the time periodicity of the driving field and it is thus enhanced and lowered over a driving cycle. Finally, we provide a generalized version of the nonequilibrium fluctuation-dissipation theorem valid for weakly driven baths.

NLO corrections to h \u2192 b overline{b} decay in SMEFT

We calculate the full set of next-to-leading order (NLO) corrections to h → b overline{b} decay in the dimension-6 Standard Model Effective Field Theory (SMEFT). Our calculation forms the basis for precision studies of this decay mode in effective field theory, providing analytic and numerical results for contributions of the 45 dimension-6 operators appearing at NLO. On the technical side, we discuss several complications in NLO SMEFT computations which have not yet been addressed in the literature. These include subtleties in Higgs-Z mixing, electric charge renormalization, and especially the treatment of tadpoles in SMEFT. In particular, we highlight the role of decoupling relations in eliminating potentially large tadpole corrections to the decay rate in hybrid renormalization schemes which employ the overline{mathrm{MS}} scheme for some Standard Model parameters (such as the b-quark mass and electric charge) and the on-shell scheme for others.

Effect of charge renormalization on the electric and thermoelectric transport along the vortex lattice of a Weyl superconductor

Building on the discovery that a Weyl superconductor in a magnetic field supports chiral Landau level motion along the vortex lines, we investigate its transport properties out of equilibrium. We show that the vortex lattice carries an electric current $I=\tfrac{1}{2}(Q_{\rm eff}^2/h)(\Phi/\Phi_0) V$ between two normal metal contacts at voltage difference $V$, with $\Phi$ the magnetic flux through the system, $\Phi_0$ the superconducting flux quantum, and $Q_{\rm eff}<e$ the renormalized charge of the Weyl fermions in the superconducting Landau level. Because the charge renormalization is energy dependent, a nonzero thermo-electric coefficient appears even in the absence of energy-dependent scattering processes.