Time-dependent Electric Field Research Articles

Two-dimensional open quantum system in dissipative bosonic heat bath, external magnetic field, and two time-dependent electric fields.

Non-Markovian dynamics of a charged particle in a two-dimensional harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field and two perpendicular time-dependent electric fields. The analytical expressions for the time-dependent and asymptotic angular momentum are derived for the Markovian and non-Markovian dynamics. The dependence of the angular momentum on the frequency of the electric field, cyclotron frequency, collective frequency, and anisotropy of the heat bath is studied. The angular momentum (or magnetization) of a charged particle can be ruled by varying the frequency of the electric field.

Cavity-modified molecular dipole switching dynamics.

Polaritonic states, which are formed by resonances between a molecular excitation and the photonic mode of a cavity, have a number of useful properties that offer new routes to control molecular photochemistry using electric fields. To provide a theoretical description of how polaritonic states affect the real-time electron dynamics in molecules, a new method is described where the effects of strong light-molecule coupling are implemented using real-time electronic structure theory. The coupling between the molecular electronic states and the cavity is described by the Pauli-Fierz Hamiltonian, and transitions between polaritonic states are induced via an external time-dependent electric field using time-dependent configuration interaction (TDCI) theory, producing quantum electrodynamics TDCI (QED-TDCI). This method is used to study laser-induced ultrafast charge transfer and dipole-switching dynamics of the LiCN molecule inside a cavity. The increase in cavity coupling strength is found to have a significant impact on the energies and transition dipole moments of the molecule-cavity system. The convergence of the polaritonic state energies as a function of the number of included electronic and photonic basis states is discussed.

An efficient solution of the multi-term multi-harmonic electron Boltzmann equation for use in global models

Solving the electron Boltzmann equation is an essential but costly step in simulating low-temperature plasma kinetics. This work addresses the problem by introducing a solution of the general multi-term multi-harmonic Boltzmann equation (MTMH-BE) optimized for electrons in time-dependent non-equilibrium gases and electric fields. This is accomplished by configuring the numerical Jacobian as the product of a time-independent sparse matrix and an array of time-dependent coefficients. As this approach requires a fixed energy grid, the MTMH-BE is discretized using a finite volume scheme with support for non-uniform cell size, enabling robust solutions across a wide range of reduced field strengths. The new MTMH-BE solver is tested against a range of benchmarks, demonstrating excellent agreement with existing methods. Performance with time-dependent electron energy is evaluated using LoKI-B's pulsed electric field model, with the new solver demonstrating improved wall time scaling and an improvement in grid convergence of over three orders of magnitude. Alternatively, performance with quasi-stationary electrons in an evolving non-equilibrium gas is tested using a nitrogen cross-section set with up to 58 vibrational states and 3,570 processes. Here, the MTMH-BE solver achieves a wall time reduction of up to 99.6% over MultiBolt for error-controlled simulations in the two-term limit, reducing the average solution time from 1-2 seconds to less than 10 ms. These results indicate that the new MTMH-BE solver can improve accuracy and performance in state-to-state global models without the use of grid refinement, cross-section pruning, and other time-saving procedures.

Optimal control of a semiclassical Boltzmann equation for charge transport in graphene

An ensemble optimal control problem governed by a semiclassical space-homogeneous Boltzmann equation for charge transport in graphene is formulated and analyzed.The control mechanism is an external time-dependent electric field having the purpose of driving the material density of electrons in graphene to follow a desired trajectory. For this purpose, an ensemble cost functional with quadratic H1 costs is considered.Well-posedness of the control problem is proved, and the characterization of optimal controls by an optimality system is discussed. This system is approximated by a discontinuous Galerkin scheme and solved using a nonlinear conjugate gradient method. Results of numerical experiments are presented that demonstrate the ability of the proposed control framework to design control fields.

Polarization effects in higher-order guiding-centre Lagrangian dynamics

The extended guiding-centre Lagrangian equations of motion are derived by the Lie-transform perturbation method under the assumption of time-dependent and inhomogeneous electric and magnetic fields that satisfy the standard guiding-centre space–time orderings. Polarization effects are introduced into the Lagrangian dynamics by the inclusion of the polarization drift velocity in the guiding-centre velocity and the appearance of finite-Larmor-radius corrections in the guiding-centre Hamiltonian and guiding-centre Poisson bracket.

Dielectric Response and Linear Absorption Spectroscopy of Ionic Systems.

Time-dependent electric fields applied to ionic systems can induce both a dielectric and a conductive response, leading to the generation of macroscopic polarization and current, respectively. It has long been recognized that it is not possible to determine the two types of responses separately. However, this aspect is often not adequately accounted for in dielectric and absorption spectroscopies of ionic systems. To clarify this, we theoretically investigate the dielectric and conductive responses of ionic systems containing polyatomic ions based on linear response theory. We derive general expressions for the frequency-dependent dielectric functions, conductivity, and absorption coefficient, including those measured experimentally. Furthermore, we show that the dielectric and conductive responses cannot be uniquely distinguished even at the theoretical level and, therefore, cannot represent experimentally measured quantities. Instead, dielectric and absorption spectra of ionic systems should be expressed in terms of the generalized dielectric function that encompasses both dielectric and conductive responses. We propose a computational method to calculate this generalized dielectric function reliably. Model calculations on concentrated aqueous solutions of NaCl, a monatomic salt, and LiTFSI, a polyatomic salt, show that the dielectric and linear absorption spectra of the two systems based on the generalized dielectric function are significantly different from purely dielectric counterparts in the far-IR, terahertz, and lower-frequency regions. Moreover, the spectra are mainly determined by the autocorrelations of total dipole and total current, but dipole-current cross-correlation can also significantly contribute to the spectra of the LiTFSI solution. The present theoretical approach could be extended to nonlinear spectroscopy of ionic liquids and electrolyte solutions.

Theoretical study of double oscillating fields induced electron-positron pairs creation process

<sec>We investigate an important aspect of electron-positron pair creation from vacuum in the presence of a strong background field, where the combined field plays a key role in the pair creation process. By utilizing computational quantum field theory, we explore electron-positron pair creation induced by double-located oscillating electric fields by numerically solving the Dirac equation in full spacetime dimensions. We demonstrate theoretically that computational quantum field theory is equivalent to the first-order time-dependent perturbation theory for single-photon transition pair creation in a spatially inhomogeneous and time-dependent electric field, and verify their equivalence through numerical simulations of pair creation in double-located oscillating fields. We show some interesting results about the periodic oscillation of the momentum spectrum structure of the created particle and the asymmetric multi-photon pair creation process due to the interference between two fields. By using first-order time-dependent perturbation theory, we find that the periodic oscillation in the momentum distribution of the created particle is affected by the field width, the field frequency and the distance between two fields. The period of the oscillation of momentum spectrum structure is changed by the distance between two fields, while the field width has an influence on both the difference between the peak and valley of the momentum spectra and the width of the momentum space available to the created particle. Increasing the frequency of the electric field results in larger momentum for the created particle pairs, while correspondingly reducing the coupling matrix element <inline-formula><tex-math id="M1">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.png"/></alternatives></inline-formula> and diminishing the probability of electron-positron pair creation.</sec><sec>The interference between two fields significantly enhances the yield of pair numbers for small distances between two fields. When the distance is too large, the number of pairs created by double oscillating fields is twice that created by a single field, and the enhancement is vanished. When the distance between two fields increases, the period of oscillation decreases. In turn, the creation of electron-positron pairs can become more monochromatic in momentum (energy), while the number of pairs created remains almost constant. As the electric field broadens, the yield of the created pairs decreases for constant potential height. Increasing the field width will reduce the number of particles for each momentum and narrow the momentum space of the created particle. Increasing the field frequency leads to the reduction of the coupling matrix element <inline-formula><tex-math id="M2">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.png"/></alternatives></inline-formula> and subsequently reduces the total number of electron-positron pairs created. The field profile parameters such as frequency, width, and distance between two fields can be utilized to select a specific momentum (energy) of particles in future electron-positron pair creation experiments.</sec>

The Fingerprints of Periodic Electric Fields on Line Shapes Emitted in Plasmas

Periodic electric fields are found in many kinds of plasmas and result from the presence of collective fields amplified by plasma instabilities, or they are created by external sources such as microwave generators or lasers. The spectral lines emitted by atoms or ions in a plasma exhibit a frequency profile characteristic of plasma conditions, such as the temperature and density of charged particles. The fingerprints of periodic electric fields appear clearly on the line shape for a large range of frequencies and magnitudes of the oscillating electric field. Satellite structures appear near to multiples of the oscillation frequency and redistribute the intensity of the line far from the line center. The modeling of the simultaneous effects of the plasma microfield and of a periodic electric field has been active since the seventies, but it remains difficult to be conducted accurately since the quantum emitter is submitted to several time-dependent electric fields, each with their own characteristic time. We describe here a numerical approach which couples a simulation of the motion of charged plasma particles with an integration of the emitter Schrödinger equation. Resulting hydrogen line shapes are presented for different plasmas and periodic fields encountered in laboratory and astrophysical plasmas.

Multistate Dynamic Pathways for Anisotropic Colloidal Assembly and Reconfiguration.

We report the controlled interfacial assembly and reconfiguration of rectangular prism colloidal particles between microstructures of varying positional and orientational order including stable, metastable, and transient states. Structurally diverse states are realized by programming time dependent electric fields that mediate dipolar interactions determining particle position, orientation, compression, and chaining. We identify an order parameter set that defines each state as a combination of the positional and orientational order. These metrics are employed as reaction coordinates to capture the microstructure evolution between initial and final states upon field changes. Assembly trajectory manifolds between states in the low-dimensional reaction coordinate space reveal a dynamic pathway map including information about pathway accessibility, reversibility, and kinetics. By navigating the dynamic pathway map, we demonstrate reconfiguration between states on minute time scales, which is practically useful for particle-based materials processing and device responses. Our findings demonstrate a conceptually general approach to discover dynamic pathways as a basis to control assembly and reconfiguration of self-organizing building blocks that respond to global external stimuli.

Variational formulation of higher-order guiding-center Vlasov–Maxwell theory

Extended guiding-center Vlasov–Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-timescale orderings. The guiding-center Vlasov–Maxwell equations are derived up to second order, which contains dipole and quadrupole contributions to the guiding-center polarization and magnetization that include finite-Larmor-radius corrections. Exact energy-momentum conservation laws are derived from the variational formulation of these higher-order guiding-center Vlasov–Maxwell equations.

Tailoring role of Al and Ti particles in the microstructure and property of electrodeposited Ni matrix nanocomposite coatings

Ni–Al–Ti nanocomposite coatings were synthesized by electrodeposition. The tailoring role of Al and Ti particles in the co-deposition behaviors of nanocomposite coatings was comprehensively investigated by analyzing the time-dependent current density and electric field near the co-deposited particles. The results showed that the Al and Ti particles caused different co-deposition behaviors of Ni deposits, consequently bringing in the gradual increase in the surface dendritic structure, the refinement of grain sizes, and the decrease in the [200] fiber texture of the nanocomposite coatings with the decrease in the Al/Ti weight ratio. COMSOL simulations verified the different co-deposition mechanisms of Ni grains near the two kinds of particles, which was vitally determined by the different conditions of current density and electric field near the particles. The micro-hardness results revealed that the decreased Al/Ti weight ratio led to enhanced micro-hardness of the nanocomposite coating; in addition, the maximum hardness of the nanocomposite coating was 604.3 HV0.2 for an Al/Ti weight ratio of 1:4. Thus, the time-dependent current density and electric field near co-deposited Al and Ti particles determined the microstructure and property of the Ni–Al–Ti nanocomposite coatings.

Lattice Boltzmann Modeling of Cholesteric Liquid Crystal Droplets Under an Oscillatory Electric Field

We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates coherently triggering a concurrent orbital motion of both droplets around each other, an effect due to the momentum transfer to the surrounding fluid. In addition the topological defects, resulting from the conflict orientation of the liquid crystal within the drops, exhibit a chaotic-like motion in cholesterics with a high pitch, in contrast with a regular one occurring along circular trajectories observed in nematics drops. Such behavior is found to depend on magnitude and frequency of the applied field as well as on the anchoring of the liquid crystal at the droplet interface. These findings are quantitatively evaluated by measuring the angular velocity of fluid and drops for various frequencies of the applied field.

Vortex Structures and Momentum Sharing in Dynamic Sauter-Schwinger Process

Vortex pattern formation in electron-positron pair creation from vacuum by a time-dependent electric field of linear polarization is analyzed. It is demonstrated that in such scenario the momentum distributions of created particles exhibit vortex-antivortex pairs. Their sensitivity to the laser field parameters such as the field frequency and intensity is also studied. Specifically, it is shown that with increasing field frequency accross the one-photon threshold additional vortex-antivortex pairs appear. Their location in the momentum space is consistent with a general threshold behavior of probability distributions of created electrons (positrons). Namely, while for small field frequencies the particles tend to be created along the field polarization direction, for large enough frequencies they are predominantly generated in the perpendicular direction. Such change in longitudinal and transverse momentum sharing of created particles occurs accross the one-photon threshold.

Quantum Coulomb problem in a Gaussian time-dependent electric field within the path integral formalism

Quantum Coulomb problem in a Gaussian time-dependent electric field within the path integral formalism

Lagrangian descriptor and escape time as tools to investigate the dynamics of laser-driven polar molecules.

We consider the nonlinear dynamics of a diatomic polar molecule under a linearly polarized laser field. We assume a model in which the molecule dipole is coupled with a time-dependent electric field. This system presents a bound energy region where the atoms are bound, and a free-energy region where the atoms are dissociated. Due to the nonalignment between the dipole axis and the laser direction, and the time dependence of the external field, this system presents two and a half degrees of freedom, namely the vibrational degree, the rotation degree, and the time. To investigate the system dynamics, instead of using the Poincaré surface-of-section technique, we propose the use of the Lagrangian descriptor associated with the escape times. The Lagrangian descriptor is a quantity that reveals complex structures in the phase space, whereas the escape times are the time span in which a trajectory is initially in the bound region before escaping to the unbound region. The combination of these two quantities allows us to distinguish between real stability regions from other complex structures, including stickiness regions, and a different formation, which we call escape islands. With the help of these tools, we find that for high-field amplitudes the inclusion of rotation leads to an increase of the stability regions, which implies a decrease of the dissociation in comparison with the one-dimensional case.

Modeling of the Transient Electric Field in Multilayer Dielectric Composites Under Impulsive HV Energization

This article presents the theoretical analysis of composite electrical insulation, formed from layered dielectric materials and subjected to impulsive energization. The 1-D planar and cylindrical geometries were considered, consisting of an arbitrary number of layers with arbitrary relative permittivity and electrical conductivity. Analytical solutions have been successfully derived for the time-dependent electric field inside the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${i}$ </tex-math></inline-formula> th layer. To demonstrate the usage of the model under complex multilayer topologies where analytical solutions are nontrivial, the characteristics of a 20-layer-graded composite under microsecond and sub-microsecond impulses were analyzed and validated against a finite-element (FE) solver. Results indicate that the transient electric field response under impulsive energization is strongly dependent on the interplay between the composite relaxation time constants and the characteristic timescales associated with the applied impulse. The model is a further development for the design and coordination of functionally graded materials (FGMs) and composite insulation for high-voltage (HV) system design. This is particularly relevant under fast-rising impulsive conditions as often encountered in many pulsed power applications.

Anomalous dielectric relaxation with multispecies linear reaction dynamics

Anomalous dielectric relaxation in complex reactions is difficult to specify, since there is no classic model for the reacting species with anomalous subdiffusion in the presence of an external electric field. In this paper, the anomalous dielectric relaxation of a multispecies system with linear reaction dynamics is studied based on the biased continuous time random walks. Different reaction–subdiffusion equations are derived via the mathematical random subordination time and the deterministic physical time. The mathematical random subordination time is based on the assumption that the jumping probabilities are determined at the end of the waiting times, while the deterministic physical time is based on the assumption that the jumping probabilities are independent of time and evaluated at the start of the waiting times. The force fields are operated by the Riemann–Liouville fractional derivative in the reaction–subdiffusion equations with the deterministic physical time, while the opposite results are found in the reaction–subdiffusion equations with the mathematical random subordination time. The explicit expressions for the anomalous dielectric relaxation of a reversible reaction are further derived according to the two reaction–subdiffusion equations in the presence of space- and time-dependent electric fields. The numerical calculations are carried to validate the reliability of the different expressions for the anomalous dielectric relaxation, and the reaction–subdiffusion equation with the deterministic physical time is proved to be suitable for describing the anomalous dielectric relaxation.

Supercurrent-induced resonant optical response

The optical conductivity encodes the current response to a time dependent electric field. We develop a theory of the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the presence of a dc supercurrent. Current induced optical response is prohibited when current is conserved, an illustrative example of which is Galilean invariant systems. However, we show that lattice effects give rise to a pronounced current dependent peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ at the gap edge $\ensuremath{\omega}=2\mathrm{\ensuremath{\Delta}}$, which diverges in the clean limit. We demonstrate this in a model of a multiband superconductor. Our theory predicts the current induced peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ to scale quadratically with the super-current density, as was recently reported in experiments on NbN by Nakamura et al. [Phys. Rev. Lett. 122, 257001 (2019)]. This provides the potential for a new mechanism for direct activation of the Higgs mode with light.

Effect of Electric Field Modulation on The Onset of Electroconvection in a Couple Stress Fluid

The problem of a convectional instability in a horizontal dielectric fluid layer with electric field modulation under couple stress fluid is examined. The horizontal dielectric upper boundary fluid layer is cooled, and the lower boundary is subjected to an isothermal boundary condition. The regular perturbation method based on the small magnitude of modulation is used to compute the critical Rayleigh number and the corresponding wavenumber. The solidity of the system is the characterised by a correction Rayleigh number, which is computed as a function of thermal, electric, and couple stress parameters and the frequency of electric field modulation. Some of the known findings are retrieved as specific cases in this study. It is demonstrated that the onset of the convection may be advanced or delayed by the proper regulation of different regulation parameters. The outcomes of this study have potential implications for the control of electroconvection with a time-dependent electric field.

Sauter-Schwinger Effect for Colliding Laser Pulses.

Via a combination of analytical and numerical methods, we study electron-positron pair creation by the electromagnetic field A(t,r)=[f(ct-x)+f(ct+x)]e_{y} of two colliding laser pulses. Employing a generalized Wentzel-Kramers-Brillouin approach, we find that the pair creation rate along the symmetry plane x=0 (where one would expect the maximum contribution) displays the same exponential dependence as for a purely time-dependent electric field A(t)=2f(ct)e_{y}. The prefactor in front of this exponential does also contain corrections due to focusing or defocusing effects induced by the spatially inhomogeneous magnetic field. We compare our analytical results to numerical simulations using the Dirac-Heisenberg-Wigner method and find good agreement.