Discrete Charge Research Articles

Minimum energy principles in electrostatics

Abstract We employ the principle of minimum energy of the electrostatic field to derive Laplace's equation for electric potential in charge-free space. We also apply the principle of minimum electrical potential energy of a system of discrete charges to explain the possibility of the existence of their stable equilibrium configuration on the surface of a conductor.

Monolithically Integrated Quantum Dots in a 22‐nm Fully Depleted Silicon‐on‐Insulator Process Operating at 3 K

ABSTRACTQuantum computers comprising large‐scale arrays of qubits will enable complex algorithms to be executed to provide a quantum advantage for practical applications. A prerequisite for this milestone is a power‐efficient qubit control and detection system operating at cryogenic temperatures. Implementing such systems in complementary metal‐oxide‐semiconductor (CMOS) technology offers clear advantages in terms of scalability. Here, we present a fully integrated quantum dot array in which silicon quantum wells are co‐located with control and detection circuitry on the same die in a commercial 22‐nm fully depleted silicon‐on‐insulator (FDSOI) process. Our system comprises a two‐dimensional quantum dot array, integrated with 8 detectors and 32 injectors, operating at 3 K inside a cryo‐cooler. The power consumption of the control and detection circuitry is 2.5 mW per qubit without body biasing. The design utilizes 0.8‐V nominal devices. The setup allows us to verify discrete charge injection control and detection at the quantum dot array and demonstrate the feasibility of this architecture for scaling up the existing quantum core to hundreds and thousands of physical qubits.

Observation of Discrete Charge States of a Coherent Two-Level System in a Superconducting Qubit.

We report observations of discrete charge states of a coherent two-level system (TLS) that is strongly coupled to an offset-charge-sensitive superconducting transmon qubit. We measure an offset charge of 0.072e associated with the two TLS eigenstates, which have a transition frequency of 2.9GHz and a relaxation time exceeding 3ms. Combining measurements in the strong dispersive and resonant regime, we quantify both transverse and longitudinal coupling of the TLS-qubit interaction. We further perform joint tracking of TLS transitions and quasiparticle tunneling dynamics but find no intrinsic correlations. This Letter demonstrates microwave-frequency TLS as a source of low-frequency charge noise.

Charge regulation of nanoparticles in the presence of multivalent electrolytes.

We explore the charge regulation (CR) of spherical nanoparticles immersed in an asymmetric electrolyte of a specified pH. Using a recently developed reactive canonical Monte Carlo (MC) simulation method, titration isotherms are obtained for suspensions containing monovalent, divalent, and trivalent coions. A theory based on the modified Poisson-Boltzmann approximation, which incorporates the electrostatic ion solvation free energy and discrete surface charge effects, is used to compare with the simulation results. A remarkably good agreement is found without any fitting parameters, both for the ion distributions and titration curves, suggesting that ionic correlations between coions and hydronium ions at the nanoparticle surface play only a minor role in determining the association equilibrium between hydroniums and the functional sites on the nanoparticle surface. On the other hand, if suspension contains multivalent counterions, we observe a large deviation between theory and simulations, showing that the electrostatic correlations between counterions and hydronium ions at the nanoparticle surface are very significant and must be properly taken into account to correctly describe CR for such solutions.

A Variational Model of Charged Drops in Dielectrically Matched Binary Fluids: The Effect of Charge Discreteness

This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. Introducing the model that describes two immiscible fluids with the same dielectric constant, with a drop of one fluid containing a fixed number of elementary charges together with their solvation spheres, we interpret the equilibrium shape of the drop as a global minimizer of the sum of its surface energy and the electrostatic repulsive energy between the charges under fixed drop volume. For all model parameters, we establish the existence of generalized minimizers that consist of at most a finite number of components “at infinity”. We also give several existence and non-existence results for classical minimizers consisting of only a single component. In particular, we identify an asymptotically sharp threshold for the number of charges to yield existence of minimizers in a regime corresponding to macroscopically large drops containing a large number of charges. The obtained non-trivial threshold is significantly below the corresponding threshold for the Rayleigh model, consistently with the ill-posedness of the latter and demonstrating a particular regularizing effect of the charge discreteness. However, when a minimizer does exist in this regime, it approaches a ball with the charge uniformly distributed on the surface as the number of charges goes to infinity, just as in the Rayleigh model. Finally, we provide an explicit solution for the problem with two charges and a macroscopically large drop.

Aharonov-Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene.

In the fractional quantum Hall effect, quasiparticles are collective excitations that have a fractional charge and show fractional statistics as they interchange positions. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, fractional statistics is most notable through quantum interference. Here we study fractional statistics in a bilayer graphene Fabry-Pérot interferometer. We tune the interferometer from the Coulomb-dominated regime to the Aharonov-Bohm regime, both for integer and fractional quantum Hall states. Focusing on the fractional quantum Hall state with a filling factor ν = 1/3, we follow the evolution of the Aharonov-Bohm interference of quasiparticles while varying the magnetic flux through an interference loop and the charge density within the loop independently. When their combined variation is such that the Landau filling remains 1/3, the charge density in the loop varies continuously. We then observe pristine Aharonov-Bohm oscillations with a period of three flux quanta, as expected for quasiparticles of one-third of the electron charge. Yet, when the combined variation leads to discrete events of quasiparticle addition or removal, phase jumps emerge and alter the phase evolution. Notably, across all cases with discrete and continuous charge variation, the average phase consistently increases by 2π with each addition of one electron to the loop, as expected for quasiparticles, obeying fractional statistics.

Perturbing isoradial triangulations

We consider an infinite planar Delaunay graph \mathbf{G}_{\epsilon} which is obtained by locally deforming the coordinate embedding of a general isoradial graph \mathbf{G}_{\mathrm{cr}} , with respect to a real deformation parameter \epsilon . Using Kenyon’s exact and asymptotic results for the critical Green’s function on an isoradial graph, we calculate the leading asymptotics of the first- and second-order terms in the perturbative expansion of the log-determinant of the Laplace–Beltrami operator \Delta(\epsilon) , the David–Eynard Kähler operator \mathcal{D}(\epsilon) , and the conformal Laplacian {\underline{\boldsymbol{\Delta}}}(\epsilon) on the deformed Delaunay graph \mathbf{G}_{\epsilon} . We show that the scaling limits of the second-order bi-local term for both the Laplace–Beltrami and David–Eynard Kähler operators exist and coincide, with a shared value independent of the choice of the initial isoradial graph \mathbf{G}_{\mathrm{cr}} . Our results allow us to define a discrete analog of the stress-energy tensor for each of the three operators. Furthermore, we can identify a central charge ( c=-2 ) in the case of both the Laplace–Beltrami and David–Eynard Kähler operators. While the scaling limit is consistent with the stress-energy tensor and the value of the central charge for the Gaussian free field (GFF), the discrete central charge value of c=-2 for the David–Eynard Kähler operator is, however, at odds with the value of c=-26 expected by Polyakov’s theory of 2D quantum gravity; moreover, there are problems with convergence of the scaling limit of the discrete stress-energy tensor for the David–Eynard Kähler operator. The second-order bi-local term for the conformal Laplacian involves anomalous terms corresponding to the creation of discrete curvature dipoles in the deformed Delaunay graph \mathbf{G}_{\epsilon} ; we examine the difficulties in defining a convergent scaling limit in this case. Connections with some discrete statistical models at criticality are explored.

Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics

The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

Trap properties of novel UV-A persistent phosphor Sr3MgSi2O8:Ce3+

For the last few decades, there has been extensive research on the materials that persist to emit optical radiation long after any type of charging has stopped. Most of the established persistent luminescence (PersL) materials emit light in the visible part of the spectrum; however, in recent years, there has been a growing interest in UV-emitting persistent phosphors in recent years. These materials have been tested for various applications, such as photocatalysis, sterilization, and anti-counterfeiting, among others. Here, we report on the X-ray and UV-activated UV-A long PersL of Ce3+-doped Sr3MgSi2O8 material. We prepared samples with varied Ce3+ concentrations using solid–state reaction synthesis in an ambient atmosphere and conducted a thorough investigation using photoluminescence (PL), electron paramagnetic resonance (EPR), and thermally stimulated luminescence (TSL) spectroscopy methods. Our experiments show that the PersL signal of Ce3+ in the 300–450 nm range can be detected for at least 16 h when samples are irradiated with X-rays or UV. The TSL analysis reveals multiple discrete charge traps in the material with activation energies between 0.5 and 1.7 eV. Further EPR measurements confirm the presence of four paramagnetic centers. The thermal stability of these centers was analyzed, and it is established that one of these centers (g1 = 2.0056, g2 = 1.9981, and g3 = 1.9926) gradually decays at room temperature, which is correlated with the PersL processes.

The Effect of Charge Discretization on the Electrical Field Inside a Conductor

The Effect of Charge Discretization on the Electrical Field Inside a Conductor

Monte Carlo simulation of the planar discrete double layer for neutrally charged interfaces

A Monte Carlo simulation study on the charge distribution and structure of the electric double layer (EDL) that forms between two planar interfaces is presented, using a model electrolyte of monovalent hard-sphere ions and confining walls composed of two discrete and sign-alternating charge distributions. Symmetric and asymmetric plate-plate orientations, along with uncharged walls, are considered. Results are presented for effective wall-ion correlation functions and local integrated charge in the subvolumes defined by the charge domains on the plates. We report that, in the presence of multifaceted charged surfaces, the ions between the walls exhibit complex and rich behavior, with the formation of an EDL next to the charged domains of the interface, and having density profiles of counterions and coions that are established as function of the nature and configuration of the charged strips. These profiles present a structural frustration that renders the subvolumes with a net charge, in contrast to the null net charge from profiles next to a uniformly charged surface. Finally, with proper scaling, the integrated charge follows closely a master curve for each wall-wall configuration. Such phenomenology is visible in the regime of low and high surface charge.

Alaska's ban on sentence bargaining

AbstractPlea bargaining dominates the U.S. criminal justice system and has garnered calls to reduce its prevalence. In 2013 Alaska's Attorney General acted banning a practice known as sentencing bargaining where the prosecutor negotiates with the defense over the length of the incarceration. I provide the first causal identification of this policy's impact on the plea bargaining rate. I show that the policy, by leaving open the charging discretion (in effect allowing charge bargaining), was ineffective at changing plea bargaining's prevalence across the state. Policymakers should look elsewhere for tools if they want to mitigate its rate.

Symmetry-Breaking Charge Separation in a Chiral Bis(perylenediimide) Probed at Ensemble and Single-Molecule Levels.

Chiral molecular assemblies exhibiting symmetry-breaking charge separation (SB-CS) are potential candidates for the development of chiral organic semiconductors. Herein, we explore the excited-state dynamics of a helically chiral perylenediimide bichromophore (Cy-PDI2) exhibiting SB-CS at the ensemble and single-molecule levels. Solvent polarity-tunable interchromophoric excitonic coupling in chiral Cy-PDI2 facilitates the interplay of SB-CS and excimer formation in the ensemble domain. Analogous to the excited-state dynamics of Cy-PDI2 at the ensemble level, single-molecule fluorescence lifetime traces of Cy-PDI2 depicted long-lived off-states characteristic of the radical ion pair-mediated dark states. The discrete electron transfer and charge separation dynamics in Cy-PDI2 at the single-molecule level are governed by the distinct influence of the local environment. The present study aims at understanding the fundamental excited-state dynamics in chiral organic bichromophores for designing efficient chiral organic semiconductors and applications toward charge transport materials.

Квазиклассическое квантовое обобщение уравнений Лондонов и гипотеза монополей

The paper considers the London equation semi-classical generalization leading to a connection between the Cooper pairs magnetic flux quantization and the electric charge discreteness. Using the Bohr --- Sommerfeld quantization rule, a derivation of the magnetic flux quantization was made on the basis of the fluxoid uniqueness. The resulting quantization was applied to the magnetic monopoles hypothesis proposed by Dirac, which remains relevant due to the asymmetry present in the modern physics in describing electrical and magnetic properties of matter. On a fairly simple model of the possible experiment, an option of registering a monopole by a jump in the magnetic induction flux and the associated alteration in the circuit current were studied. The paper analyzed the problems of the monopole different measurement units and the results similar to those obtained on the basis of the Schwinger series of works, where he proceeded from considering introduction of a hypothetical particle with the electric and magnetic charges, i.e., the dyon. Possible explanation of the Abrikosov vortex is presented, it is based on vortex representation in the form of a magnetized thin thread through the magnetic tubes, at the ends of which monopoles of different charges (dipole) are positioned. Unlike most the works devoted to this problem, calculations were performed in the SI system. The monopole quantization conditions were derived

Some remarks on Swampland conjectures, fluxes and K-theory in IIB toroidal compactifications

In this note, we present a scenario in which the existence of dS vacua is jeopardized by topological transitions between non-BPS branes and fluxes in type IIB toroidal compactifications. We focus our study on a six-dimensional torus compactification modded out by an orientifold three-plane. In particular, we consider the presence of non-BPS five branes, which allows the construction of apparent stable dS vacua. Since moduli stabilization requires the presence of NS–NS fluxes, we also describe the minimal required conditions to avoid the appearance of Freed–Witten anomalies. Cancellation of these anomalies implies a topological transformation between non-BPS states and fluxes with the same discrete K-theory charge. After the transition, we observe that the scalar potential undergoes major changes, implying that the dS vacua are unstable. We discuss a scenario in which, even if the discrete K-theory charge is globally canceled, the above transitions could still be relevant, allowing the existence of short-lived dS minima. We briefly comment on how these implications seem to be in concordance with the Refined de Sitter and Trans-Planckian Censorship Conjectures.

Gauge dependence of the quark gap equation: An exploratory study

We study the gauge dependence of the quark propagator in quantum chromodynamics by solving the gap equation with a nonperturbative quark-gluon vertex which is constrained by longitudinal and transverse Slavnov-Taylor identities, the discrete charge conjugation and parity symmetries and which is free of kinematic singularities in the limit of equal incoming and outgoing quark momenta. We employ gluon propagators in renormalizable $R_\xi$ gauges obtained in lattice QCD studies. We report the dependence of the nonperturbative quark propagator on the gauge parameter, in particular we observe an increase, proportional to the gauge-fixing parameter, of the mass function in the infrared domain, whereas the wave renormalization decreases within the range $0 \leq \xi \leq 1$ considered here. The chiral quark condensate reveals a mild gauge dependence in the region of $\xi$ investigated. We comment on how to build and improve upon this exploratory study in future in conjunction with generalized gauge covariance relations for QCD.

Possible relation between the cosmological constant and standard model parameters

We propose possible properties of quantum gravity in de Sitter space, and find that they relate the value of the cosmological constant to parameters of the Standard Model. In de Sitter space we suggest (i) that the most sharply defined observables are obtained by scattering objects from the horizon and back to the horizon and (ii) that black holes of discrete charge are well defined states in the theory. For a black hole of minimal discrete electric charge, we therefore demand that a scattering process involving the black hole and a probe can take place within a Hubble time before evaporating away, so that the state of a discretely charged black hole is well defined. By imposing that the black hole's charge is in principle detectable, which involves appreciably altering the state of a scattered electron, we derive a relation between the Hubble scale, or cosmological constant, and the electron's mass and charge and order one coefficients that describe our ignorance of the full microscopic theory. This gives the prediction $\Lambda \sim 10^{-123 \pm 2} M_{Pl}^4$, which includes the observed value of dark energy. We suggest possible ways to test this proposal.

The discrete Green-Schwarz mechanism in 6D F-theory and elliptic genera of non-critical strings

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with G = ℤ3 gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a ’t Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau.

Electrical charge transport properties of caesium tin chloride perovskite microrods: An analysis of microstructure conductivity and charge trapping

This study presents the electrical charge transport properties of caesium tin chloride (CsSnCl3) perovskite microrods. The as-synthesized microstructure rods were characterized using XRD, FESEM, EDS, and elemental mapping. The current–voltage (I-V) characteristics of microstructures were recorded. The I-V analysis demonstrates that as the side length of a microrod varies from 356 µm to 136 µm, the conductivity, barrier height, and ideality factor changes from 3.08 × 10−4 to 1.32 × 10−4 S/m, 0.84 eV to 0.78 eV, and 2.09 to 2.86, respectively. The charge transport investigation revealed that the sample exhibited ohmic conduction at a lower voltage and trap charge-limited conduction (TCL) after a transition voltage. The discrete trap charge concentration was found to be in the order of 1014 /m3 in the TCL region. The excellent conductivity of microstructure rods and the low trap charge concentration suggest that microrods have the potential for use in optoelectronic device applications.

A split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger equations

In this paper, we propose a split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger (CNLS) equations. The space fractional CNLS equations can be split into two subproblems such that one of them is linear. The solution of the nonlinear subproblem is computed exactly. The Riesz space fractional derivative is approximated by a Fourier pseudo-spectral method. The unconditional stability, convergence, discrete charge and multi-symplectic preserving properties for the proposed method are investigated. Then, the proposed method is extended for solving the two-dimensional problem. Finally, some numerical experiments are performed to confirm our theoretical analysis and illustrate the efficiency of the proposed scheme.