Equations Of Motion For Electrons Research Articles

Phonon Drag Contribution to Thermopower for a Heated Metal Nanoisland on a Semiconductor Substrate.

The possible contribution of phonon drag effect to the thermoelectrically sustained potential of a heated nanoisland on a semiconductor surface was estimated in a first principal consideration. We regarded electrons and phonons as interacting particles, and the interaction cross-section was derived from the basic theory of semiconductors. The solution of the equation of motion for average electrons under the simultaneous action of phonon drag and electric field gave the distributions of phonon flux, density of charge carriers and electric potential. Dimensional suppression of thermal conductance and electron-phonon interaction were accounted for but found to be less effective than expected. The developed model predicts the formation of a layer with a high density of charge carriers that is practically independent of the concentration of dopant ions. This layer can effectively intercept the phonon flow propagating from the heated nanoisland. The resulting thermoEMF can have sufficient magnitudes to explain the low-voltage electron emission capability of nanoisland films of metals and sp2-bonded carbon, previously studied by our group. The phenomenon predicted by the model can be used in thermoelectric converters with untypical parameters or in systems for local cooling.

Chaotic dynamics in X-ray free-electron lasers with an optical undulator.

In this work, the chaotic motions of relativistic electrons in X-ray free-electron lasers are investigated using an optical undulator in the presence of a magnetized ion-channel background. To miniaturize X-ray light sources, the optical undulator is a promising concept. The optical undulator provides higher optical gain than conventional magnetostatic undulators due to its micrometer wavelength. In addition, it reduces the required electron beam energy from several GeV to the multi-MeV range to produce X-ray pulses. The interaction of an optical undulator with an intense relativistic electron beam is a highly non-linear phenomenon that can lead to chaotic dynamics. At synchrotron radiation sources, the possibility of chaos control for X-ray FELs can be critical for certain classes of experimental studies. The equations of motion for a relativistic electron propagating through the optical undulator in the presence of a magnetized ion-channel can be derived from the Hamiltonian of the interaction region. Simulation results revealed that the intensity of the perturbation route from orderly behavior to chaos depends on the beam density, axial magnetic field strength, ion-channel density parameter, and pump laser undulator. Specific values of parameters were obtained for the transition from regular to chaotic paths. Bifurcation diagrams of the system were plotted to demonstrate the origin of chaos at a critical point, and Poincaré maps were created to distinguish between chaotic and orderly motions of electrons. The proposed new scheme can help to improve X-ray FELs, which have potential usages in basic sciences, medicine, and industry.

Molecular Simulation Study of Surface-Enhanced Raman Scattering of Liquid Water.

We developed in our previous study [J. Chem. Phys., 2021, 155, 174118, J. Phys. Chem. A, 2022, 126, 4762] a classical electronic and molecular dynamics simulation method to describe the optical response of metal material in solution based on an atomistic model by incorporating the classical equation of motion for free electrons under an applied electric field. To show further usefulness of the method, in the present study, we apply it to surface-enhanced Raman scattering of liquid water to examine the signal enhancement of the solution system caused by plasmon resonance effects of a silver nanoparticle.

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation.

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

Electron drift velocity in acetylene and carbon dioxide determined from rf breakdown curves

In this work, we measured the breakdown curves of radio-frequency (13.56 MHz) capacitive discharge in acetylene and in carbon dioxide. The electron drift velocity values were determined in the reduced electric field range 319 Td ≤ E/N ≤ 3409 Td (1 Townsend = 10−17 Vcm2) in acetylene and 272 Td ≤ E/N ≤ 6240 Td in carbon dioxide from turning points on the measured breakdown curves. Treating the electron motion equations and the gas breakdown criterion in the rf electric field we have demonstrated that the method of electron drift velocity determination we employed is universal for arbitrary gasses, and a possible dependence of the electron mobility and diffusion on the reduced electric field strength E/N does not affect the drift velocity values obtained with it. We have demonstrated that in the range of E/N values we have studied the ionization rate exceeds the attachment rate considerably therefore one may neglect the effect the attachment of free electrons to gas molecules plays on electron drift velocity. We have explained the reason why the values of the electron drift velocity we have obtained differ from those obtained by other authors.

Regulation of Continuum Harmonic Generation by Using Near-infrared Chirped Pulses

It has been known that the broadband of continuum harmonics, a regular periodicity or a wide smooth range, is essential for generating attosecond pulses. However, the high-order rescatterings of electrons (HOR) can significantly affect this important part of high-order harmonic spectra. In the present work, we apply the method suggested in our previous studies to limit the HOR effect on the continuum harmonics by using up-chirped pulses with frequency increasing in time to regulate the high-order harmonic generation of an asymmetric molecule such as CO subjected to a near-infrared laser. To do so, we numerically calculate the high-order harmonic spectra using the time-dependent wave functions obtained within the framework of the single-active electron approximation. To analyze and regulate the HOR effect, we use the time-frequency analysis together with the kinetic energy maps obtained from the equation of electron motion in the laser electric field. These techniques reveal the high-order harmonic dynamics, especially the effect of chirped pulse on the manifestation of continuum harmonics. Based on this, we release the notice on choosing appropriate parameters to obtain the optimal continuum range of harmonics. Although the detailed analysis is given for the CO molecule, the method suggested is applicable for other polar molecules.

Computational Analyses of Plasmonics of a Silver Nanoparticle in a Vacuum and in a Water Solution by Classical Electronic and Molecular Dynamics Simulations.

We present basic optical responses of a silver nanoparticle (Ag309) in a vacuum and a water solution obtained by classical electronic and molecular dynamics (CEMD) calculations, where the CEMD is our previously developed force-field based molecular dynamics simulation method that incorporates the classical equation of motion for free electrons in metal and an interaction with the applied oscillating electric field (Yamada, A. J. Chem. Phys. 2021, 155, 174118)). The present work is the follow-up of the previous study. Calculated absorption spectra in the visible region with various conditions are reported together with parameter determination for realistic analyses as well as the verification of the method. Time-domain optical responses of Ag309 in water solvent are as well analyzed in terms of the plasmon resonance excitation under a subpicosecond light pulse and its thermal relaxation.

Electronic Chips Acting as Capacitors or Inductors when Laser Act as Information Transmitter

To increase the speed of information flow and storage capacity in electronic devices laser can be used to carry information instead of electric current. Since the photon is faster than electrons, one expects information to be transmitted very fast through the internet when photons replace electrons. This requires searching for chips that act as capacitors, inductors or resistors. To do this Maxwell's equation for the electric field intensity beside the electron equation of motion were used. The electron is assumed to vibrate naturally inside a frictional medium in the presence of a local electric and magnetic fields. These equations have been used to find a useful expression for the absorption coefficient. The absorption coefficient was found to be dependent on the laser and natural frequencies beside the coefficient of friction in addition to the internal electric and magnetic fields. These parameters can be fine-tuned to make the chip act as a capacitor, inductor or resistor. The laser intensity decreases when the absorption coefficient inecreases. Thus, the absorption coefficient acts as an electic resistor. Therefore, if the absorption coefficient inecreases upon decreasing the frequency the chip acts as a capacitor. But when the absorption coefficient inecreases when the laser frequency inreases the chip acts as an inductor. In the case that the absorption coefficient inecreases with the concentration of the carriers it acts in this situation as a resistor. For magnetic materials with magnetic flux density that cancels the frictional force, when the laser frequency is equal nearly to the atom’s natural frequency the material acts as an inductor. But when the frictional force is low with the internal and external electric fields in phase, the material acts as a capacitor. However, it acts as a resistor for negligible natural frequency, when no electric dipoles exist and when the internal magnetic field force balance the frictional force.

Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions

Starting with general semiclassical equations of motion for electrons in the presence of electric and magnetic fields, we extend the Chambers formula to include in addition to a magnetic field, time-dependent electric fields and bands with Berry curvature. We thereby compute the conductivity tensor ${\sigma}_{{\alpha}{\beta}}(B,{\omega})$ in the presence of magnetic field for bands in two (2D) and three (3D) dimensions with Berry curvature. We focus then on several applications to magnetotransport for metals with Fermi surface topological transitions in 2D. In particular, we consider a rectangular lattice and a model related to overdoped graphene, to investigate the signatures of different types of Fermi surface topological transitions in metals in the Hall coefficient, Hall conductivity ${\sigma}_{xy}$ and longitudinal conductivity ${\sigma}_{xx}$. The behavior of those quantities as a function of frequency, when the electric field is time dependent, is also investigated. As an example of non-zero Berry curvature, we study the magnetotransport of the Haldane model within this context. In addition, we provide the linear and nonlinear electric current formula to order $E^2$.

Investigation of TE and TM modes fields and injected electron dynamic in the plasma waveguide with Piet Hein cross section

In this paper, we consider a metallic waveguide with Piet Hein cross section filled by cold unmagnetized plasma. First by introducing a Piet Hein waveguide and considering a suitable approximation, wave equation as two differential equations are presented. Then electromagnetic fields for TM and TE modes in the Piet Hein waveguide filled plasma are analytically obtained and plotted. Using the boundary conditions in the Piet Hein plasma waveguide the dispersion relations for TM and TE modes are analytically derived and plotted. Electron dynamics in the fields associated with a transverse magnetic and electric wave propagating inside the considered Piet Hein plasma waveguide is investigated. The equations of electron motion in the considered Piet Hein plasma waveguide by fourth-order Runge Kutta method for TM and TE modes are solved. The motion path and kinetic energy of electron injected into the purposed configuration for two modes are graphically investigated.

Reduction of Electron Dephasing Rate by Bessel Function Laser Pulse Propagation in Underdense Plasma (April 2021)

In laser acceleration dynamics of the electron, the approximate value of the longitudinal component of the electric field has been considered in all analytical and numerical calculations. In this article, an exact analytical expression for the longitudinal component of the electric field in a spindle-shaped laser-produced plasma channel formed by Bessel laser pulse propagation is derived. To this end, first, the dimensions of the channel are obtained by balancing the ponderomotive and electrostatic forces acting on the plasma channel, and then an analytical expression for the longitudinal electric field of the channel is calculated. Finally, substituting the exact fields in the electron equation of motion, the dynamics of the electron inside the channel and also the electron energy gain are studied. The result of the numerical analysis shows that the real longitudinal component of the electric field of the channel changes the electron energy gain significantly. We also found that the longitudinal electric field of laser does not always counteract the transverse component of the field so that the electron can gain or lose energy from both of them simultaneously.

Material properties for absorption, lasing, micro capacitors and inductors using Maxwell’s equations

We were able to obtain useful expressions for absorption coefficient, lasing condition, and acceptable materials for integrated circuit capacitors and inductors. Ordinary Maxwell’s equations were combined with the electron equation of motion in the presence of external, internal electric, and internal magnetic fields, as well as friction, to achieve this. According to the findings, the absorption coefficient is related to the friction coefficient. In the presence of a static magnetic field, lasing occurs in a non-frictional fictional medium. The amplification factor is proportional to the magnetic field strength in the free-electron lasing situation. When the internal magnetic force balances the frictional force with no internal electric field for capacitors, the material can serve as a micro capacitor or a micro inductor. These conditions can be applied easily for human cells which act as nano electronic systems.

Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems

Non-Hermitian materials can exhibit not only exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is unclear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functions can only affect the Hall conductivity. However, we are surprised to find a non-Hermitian anomalous Berry connection induced anomalous linear longitudinal conductivity independent of the scattering time. We also show the emergence of a second-order nonlinear longitudinal conductivity induced by non-Hermitian anomalous Berry connection, violating a well-known fact of its absence in a Hermitian system with symmetric energy spectra. These anomalous phenomena are illustrated in a pseudo-Hermitian system with large non-Hermitian anomalous Berry connection. Finally, we propose a practical scheme to realize the anomalous oscillations in an optical system.

Mechanism of Proton Pumping in Complex I of the Mitochondrial Respiratory Chain

We propose a physical mechanism of conformation-induced proton pumping in mitochondrial Complex I. The structural conformations of this protein are modeled as the motion of a piston having positive charges on both sides. A negatively charged electron attracts the piston, moving the other end away from the proton site, thereby reducing its energy and allowing a proton to populate the site. When the electron escapes, elastic forces assist the return of the piston, increasing proton site energy and facilitating proton transfer. We derive the Heisenberg equations of motion for electron and proton operators and rewrite them in the form of rate equations coupled to the phenomenological Langevin equation describing piston dynamics. This set of coupled equations is solved numerically. We show that proton pumping can be achieved within this model for a reasonable set of parameters. The dependencies of proton current on geometry, temperature, and other parameters are examined.

Interband tunneling effects on materials transport properties using the first principles Wigner distribution

Electronic transport in narrow gap semiconductors is characterized by spontaneous vertical transitions between carriers in the valence and conduction bands, a phenomenon also known as Zener tunneling. However, this effect is not captured by existing models based on the Boltzmann transport equation. In this work, we propose a new fully first principles model for electronic transport using the Wigner distribution function and implement it to solve the equations of motion for electrons. The formalism generalizes the Boltzmann equation to materials with strong interband coupling and include transport contributions from off-diagonal components of the charge current operator. We illustrate the method with a study of Bi2Se3, showing that interband tunneling dominates the electron transport dynamics at experimentally relevant small doping concentrations, a behavior that is likely shared with other semiconductors, including topological insulators. Surprisingly, Zener tunneling occurs also between band subvalleys separated by energy much larger than the band gap.

Theory of electron motion in combined magnetic trap under conditions of gyromagnetic autoresonance

Using the Bogolyubov method, the solution of equations of electron motion in a combined mirror-type magnetic trap is obtained in cases when the electron approaches the cyclotron resonance region and when it passes through it. It is assumed that the synchronism between particle and the resonator standing wave is maintained by means of slow time variation of the guiding magnetic field. The problem is solved within the framework of the simplified model using the weakly relativistic approximation.

Steady state densities in a plasma confined by a dipole magnet: Diffusion induced transport explored through direct measurements and modeling

Steady state densities in a plasma confined by a permanent dipole magnet are determined through detailed experiments and modeling. Two diffusion models are developed, and the resulting equations are solved numerically to yield the radial and angular plasma density profiles, which are compared with those obtained experimentally. The models consider the fluid and continuity equations along with Fick’s law and take into account the experimentally determined electron temperature (Te) and the static dipole magnetic fields (B) in space, as a common input. In model I, the equation of motion for both charges (ions and electrons) is used to self-consistently generate the ambipolar electric field (E), while model II considers the electron equation of motion and takes into account the experimentally determined plasma potential (Vs) as another input, whose gradient provides the ambipolar electric field. Results indicate that the plasma density peaks around r ∼ (2–12) cm depending on the polar angle and the discharge pressure and decreases for large r, while its angular variation shows a maximum in the equatorial plane (θ = 90°) and decreases toward the polar regions. Te and Vs are higher in the polar cusp regions and decrease toward the equatorial plane, with the profiles becoming more spherically symmetric away from the magnet. The numerically obtained density profiles from the models agree well with those obtained experimentally. The phenomenon of inward diffusion resulting in peaked density profiles as reported by earlier authors is found to be a natural outcome of the solution of the diffusion equation.

Extended Lagrangian Born-Oppenheimer molecular dynamics using a Krylov subspace approximation.

It is shown how the electronic equations of motion in extended Lagrangian Born-Oppenheimer molecular dynamics simulations [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008); J. Chem. Phys. 147, 054103 (2017)] can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born-Oppenheimer molecular dynamics. The low-rank approximation of the Jacobian is directly related to Broyden's class of quasi-Newton algorithms and Jacobian-free Newton-Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

Theory Analysis of Nonlinear Excitation of Second Harmonic THz Gyrotron for DNP-NMR

As an important parameter, start current reveals the excitation condition of cavity modes. Normally, the method of successive iterations with one mode associated in the calculation is used to get the start current, which just reflects the self-excitation conditions in the presence of single mode. Nevertheless, in many cases, the prior-excited mode may affect the start current of the subsequent ones. In this article, we re-derived electron motion equations with two modes involved in the calculation and calculated the start current numerically based on those equations. We analyzed start currents of operation mode TE26+ and parasitic modes of a 394-GHz gyrotron with the two methods. In the calculation using the conventional method, TE26+ satisfies self-excitation condition while TE26− does not. In the calculation using the latter method, the start current of TE26− decreases under the influence of TE26+. This nonlinear oscillation of TE26− is further observed in time domain multimode simulation. In practical application, the beam velocity spread, ohmic loss, and high-frequency loss are inevitable. We studied their effects on mode interaction and then optimized the operation parameters. When the equivalent conductivity is $1.7e^{7}~\text {s/m}$ and beam velocity spread is 0.03, the optimized output power is 149.2 W.

Analysis of discharge channel characteristics based on plasma flow and heat transfer in USV-MF complex assisted WEDM-LS

In this paper, the analysis of discharge channel characteristics from the view of plasma flow and heat transfer in ultrasonic vibration (USV) and magnetic field (MF) assisted low speed wire electrical discharging machine (WEDM-LS) process is proposed. According to the particle orbit theory, the motion equations of multi electrons are modified by Monte Carlo collision model. The study of discharge channel parameters reveals that the spatial shape of channel is changed and the length of channel path is increased when additional magnetic field is applied to the discharge machining, thus causing the channel current fluctuation. The simulation results of electrons motion process in magnetic field indicates that the time from cathode to anode increase by 15.38% and the diffusion of electrons reduce by 5%. The electron distribution on anode surface is relatively homogeneous after the completion of the discharge. The experimental results indicate that under the influence of magnetic field, the peak current in discharge channel increases obviously, the material removal rate (MRR) increases by 48.8% on average, and the number of micro cracks on machined surface decreases significantly.