Electric Field Of Arbitrary Strength Research Articles

The Maximum Entropy Principle: General Extended Hydrodynamic Approach for Dynamic High-Field Transport in Monolayer Graphene

Within the maximum entropy principle, we present a general theory able to describe in a dynamical context the transport properties of hot carriers in monolayer graphene under electric fields of arbitrary strength. Therefore, we obtain a closed extended hyperbolic system of hydrodynamic (HD) equations in which all the unknown constitutive functions are completely determined. In particular, we consider the different scattering mechanisms used in the literature in the kinetic approaches. The closed extended HD system is applied to monolayer graphene at 300 K and is validated by comparing numerical calculations with ensemble Monte Carlo simulations.

Numerical calculation of the runaway electron distribution function and associated synchrotron emission

Synchrotron emission from runaway electrons may be used to diagnose plasma conditions during a tokamak disruption, but solving this inverse problem requires rapid simulation of the electron distribution function and associated synchrotron emission as a function of plasma parameters. Here we detail a framework for this forward calculation, beginning with an efficient numerical method for solving the Fokker–Planck equation in the presence of an electric field of arbitrary strength. The approach is continuum (Eulerian), and we employ a relativistic collision operator, valid for arbitrary energies. Both primary and secondary runaway electron generation are included. For cases in which primary generation dominates, a time-independent formulation of the problem is described, requiring only the solution of a single sparse linear system. In the limit of dominant secondary generation, we present the first numerical verification of an analytic model for the distribution function. The numerical electron distribution function in the presence of both primary and secondary generation is then used for calculating the synchrotron emission spectrum of the runaways. It is found that the average synchrotron spectra emitted from realistic distribution functions are not well approximated by the emission of a single electron at the maximum energy.

Density of states and extent of wave function: two crucial factors for small polaron hopping conductivity in 1D

We introduce a theoretical model to scrutinize the conductivity of small polarons in 1D disordered systems, focusing on two crucial – as will be demonstrated – factors: the density of states and the spatial extent of the electronic wave function. The investigation is performed for any temperature up to 300 K and under electric field of arbitrary strength up to the polaron dissociation limit. To accomplish this task, we combine analytical work with numerical calculations.

Influence of hydrodynamic coupling on the electric linear dichroism of DNA fragments

In the present work, we study the effect of translational-rotational hydrodynamic coupling on the stationary electric linear dichroism of DNA fragments. The theoretical resolution of the problem has, so far, been dealt with analytic methods valid only in the limit of low electric fields. In this work, we apply numerical methods that allow us to study the problem and also consider electric fields of arbitrary strength. We use the bent rod molecules model to describe DNA fragments with physical properties characterized by their electric charge, electric polarizability tensor, rotational diffusion tensor, and translation-rotation coupling diffusion tensor. The necessary orientational distribution function to calculate electric dichroism is obtained by solving the Fokker-Planck equation through the finite difference method. We analyze the different contributions due to electric polarizability and translational-rotational coupling to the electric dichroism.

Plasma Currents and Electron Distribution Functions under a dc Electric Field of Arbitrary Strength

The currents induced by arbitrarily strong dc electric fields in plasma and the evolution of electron distributions have been studied by Fokker-Planck simulations. We find that the electron distributions evolve distinctly under different fields; especially, the electron distribution is well represented by the sum of a stationary and drifting Maxwellian at the moderate field. A set of hydrodynamiclike equations, similar to Spitzer's but without the weak-field limit, is given for calculating the current. It is more suitable for application in hybrid particle-in-cell simulations and may extend plasma transport theory in models that do not employ a kinetic description of the electrons.

Maximum-entropy principle for static and dynamic high-field transport in semiconductors

Within the maximum entropy principle we present a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport under electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. The theoretical approach is applied to $n\text{\ensuremath{-}}\mathrm{Si}$ at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with experimental data.

Transient electric birefringence of wormlike macromolecules in electric fields of arbitrary strength: A computer simulation study

We have studied the birefringence decay of linear models of macromolecules for two different types of flexibility, the broken-rod chain and the wormlike chain, using a computer simulation of a transient electric birefringence experiment. We have paid particular attention to the influence of the intensity of the orienting field, including two orienting mechanisms, the induced dipole, and the permanent dipole. We have compared wormlike and broken-rod models of the same radius of gyration, finding that they present a different decay curve under the influence of the same intensity of the field. We have seen that these differences are due to the faster relaxation times (smaller in the wormlike chain model) and amplitudes, because, regardless of the type of flexibility, the overall size of a molecule (measured by the radius of gyration) essentially determines the longest relaxation time. We have also analyzed how the relaxation process is affected by the degree of flexibility, the orientation mechanisms, and the intensity of the field. Studying a different aspect, we have paid attention to the deformation of a molecule in a transient electric birefringence experiment as a source of information. In this work we have developed equations to characterize this deformation in terms of one of the components of the gyration tensor, if a dynamic light scattering experiment under the influence of an electric field could be performed. To develop this work we have simulated the Brownian dynamics of the different models, relaxing after the removal of an orienting external electric field of arbitrary strength. A comparison with other methods such a the rigid body treatment or the correlation analysis of Brownian trajectories has also been included. We have seen that differences between the two Brownian dynamics methods are small and that the rigid-body treatment is only an acceptable approximation to obtain the longest relaxation time.

Calculation of the Dynamic Stark Effect in the Many-Level Approximation

A new method for calculating the dynamic Stark effect in a circular polarized electric field of arbitrary strength and frequency is proposed. The basic equations of the method are given. By way of illustration the results of calculation of the shift and splitting of energy levels of a He atom in a circular polarized electric field are considered.

Quantum electron transport beyond linear response

After a brief historical survey and summary of previous work involving the linear response theory (LRT) Hamiltonian, H= H( system)− AF( t), where the latter part refers to the effect of an applied field F( t) as in Kubo's theory, we deal with the nonlinear problem in which the applied electric field of arbitrary strength, as well as a possible magnetic field, are included in the system Hamiltonian, H= H[ system( E, B)]. In Part A of this study we deal with the general formalism on the many-body level. Projection operators are applied to the Von Neumann equation in the interaction picture, H( system)= H 0+ λV, which after the Van Hove limit, λ→0, t→∞, λ 2t finite, leads to the master equation for ∂ρ/ ∂t, containing both the Pauli–Van Hove diagonal part involving the transitions W γγ′ , and a nondiagonal quantum-interference part, as obtained by us previously. Likewise, the full many-body current operator J A is obtained by manipulation of the Heisenberg equation of motion for d A/d t in the interaction picture. The second division, Part B, concerns the quantum Boltzmann theory. Employing the formalism of second quantization ( c †,c fermion operators, a †,a boson operators) we obtain a general quantum Boltzmann equation for an electron gas in interaction with phonons or impurities in the adiabatic approximation (no phonon drag). On the ‘one-body’-level the current operator leads to a generalized Calecki form for arbitrary electric and magnetic fields. For extended states this transport equation yields the Boltzmann transport equation (BTE) for the Wigner occupancy function f( k, r, t) of a Fermi gas, thus furnishing a definitive proof, fully rooted in the quantum description, for Boltzmann's much criticized irreversible BTE of 1871. For localized states Titeica's foreseen ‘collisional current’ (1935) is established in terms of the matrix elements of the state-centers and the hopping probabilities w ζ ζ′ . Also, for the limiting case of small fields, |qE ΔR ζ ζ′ |⪡kT , our previous LRT results as well as the well-known results for the magneto-conductivity by Adams and Holstein and by Argyres and Roth, are recovered.

Transient Electric Birefringence of Segmentally Flexible Macromolecules in Electric Fields of Arbitrary Strength

We study in this work the decay of the electric birefringence from the steady-state value to zero when an orienting electric field applied on a macromolecule is switched off. We consider specifically the case of segmentally flexible macromolecule with only two subunits and one hinge. Using Brownian dynamics as the predicting tool for the dynamics of the molecule, we have paid special attention to important aspects such as hydrodynamic interaction, field strength, and orienting mechanism. Improving statistics to obtain data with very good signal-to-noise ratio, we have found a different behavior of the induced and permanent dipoles in the relaxation process: the first one can be described independently of the intensity of the field while the second shows a dependence of the field strength. Moreover, the time spectrum shows no dependence on the type of dipole or the field intensity, and amplitudes appear to be essential in characterizing the relaxation of the molecule. According to our results, hydrodynami...

Slater Sum in Cylindrically Symmetric Inhomogeneous Electron Liquids: Towards A Differential Equation for the Stark Effect in Hydrogen Atom

Attention is focussed here on a variety of cylindrically symmetric inhomogeneous electron liquids. These include separable potentials in which a general variation along the (z) axis of cylindrical symmetry is combined with isotropic harmonic confinement in the (x, y) plane. in this case, an explicit differential equation is derived for the Slater sum along the z axis by projecting out of the (off-diagonal) canonical density matrix the states with zero angular momentum about the axis of symmetry. Some attention is then given to the calculation of the Slater sum for a hydrogen-like atom in a uniform electric field of arbitrary strength. the model of a separable potential with harmonic confinement, though no longer exact, is shown to lead directly to a (now approximate) equation for the Slater sum along the z axis for the Stark effect in hydrogen. Finally some further progress is shown to be possible in the extreme high field limit.

Balance-equation approach to hot-electron transport in semiconductors irradiated by an intense terahertz field

We investigate the effect of a uniform intense terahertz radiation on hot-electron transport in semiconductors driven by a dc or slowly varying electric field of arbitrary strength. Using a vector potential for the high-frequency field and a scalar potential for the dc or slowly varying field, we are able to separate the center-of-mass motion from relative motion of electrons and to distinguish the slowly varying part from the rapidly oscillating part of the center-of-mass velocity. Considering the fact that relevant transport quantities are measured over a time interval much longer than the period of the terahertz radiation field, we obtain a set of momentum and energy balance equations, without invoking a perturbational treatment of the electron-photon interaction. These equations, which include all the multiphoton processes, are applied to the examination of hot-carrier transport in a GaAs-based quantum well subjected to a weak or a strong dc bias and irradiated by a terahertz radiation of various frequency and strength in both the parallel and vertical configurations. Up to as many as |n|=50 absorption and emission multiphoton channels are included in the numerical calculation. The present approach turns out to be a very convenient and efficient tool to study the effect of an intense high-frequency radiation on dc or slowly varying carrier transport in semiconductors. Its applicable frequency range and its connection with previously developed balance-equation treatment are discussed.

Multiwell potentials of endohedral complexes of icosahedral symmetry

We examine multiwell potentials that correspond to the displacements of off-center ions in complexes with icosahedral symmetry (dodecahedrons, icosahedrons, fullerenes, etc.) along symmetry directions (toward vertices, midpoints of edges, and centers of faces). An expression is derived for an effective Hamiltonian, which describes the behavior of endohedral complexes with off-center ions placed in external electric fields of arbitrary strength and orientation. We find the eigenvalues of this Hamiltonian and calculate the intensities of the lines of all possible transitions between tunneling levels. We also predict and analyze the spectra of paraelectric resonances in the absence of an external static electric field (zero-field resonances) and in the presence of such a field. Finally, we provide recommendations for detecting these effects and discuss the specific features of the effects and the possibility of studying them.

Enhancement of acoustic- and optic-phonon generation by terahertz radiations in a two-dimensional electron system

We present a theoretical study on the angular and frequency distributions of the acoustic and optic-phonon generation by hot electrons during the terahertz-driven transport in a GaAs-based quantum well. Based on the detailed solution of the nonlinear balance equations in the presence of an oscillating electric field of arbitrary strength, we find that, when the system is exposed to an intense terahertz radiation, emissions of acoustic and optic phonons are significantly enhanced, especially along the polarized direction of the electric field.

BLOCH ELECTRON DYNAMICS IN SPATIALLY HOMOGENEOUS ELECTRIC FIELDS

The theory of Bloch electron dynamics in spatially homogeneous electric fields of arbitrary strength and time dependence is presented. In the formalism, the electric field is described through the use of the vector potential, and the instantaneous eigenstates of the Hamiltonian are used as basis stated to depict the Bloch dynamics and quantum properties. This approach leads to a natural indication of high- and low-filed limits, and allows for the inclusion of general band-structure effects and multiband coupling in the quantum dynamics. A variety of dc electric field effects, such as Bloch oscillations, Zener tunneling, and localization, and ac electric field effects, such as interband absorption, and phonon-assisted transport, will be discussed.

Monte Carlo analysis of electronic noise in semiconductor materials and devices

We review recent results concerning the microscopic analysis of electronic noise in semiconductor unipolar structures in the frequency range where 1/f noise can be neglected. Calculations are based on a Monte Carlo simulator of the carrier motion self-consistently coupled with a Poisson solver. Both current- and voltage-noise operation modes are considered and their respective advantages illustrated. The analysis is applied to structures with increasing degree of complexity, that is: homogeneous materials, resistors, n + nn + diodes., Schottky-barrier diodes and GaAs MESFETs. The main sources of noise like diffusion, generation-recombination, coupling between velocity and local electric field fluctuations, etc. are treated in the presence of electric fields of arbitrary strength. Results should constitute the basis for a physical interpretation of electronic noise in most semiconductor materials and devices thus providing inputs for improving quality and reliability figures of merit.

Modified Lanczos procedure for Wannier-Stark resonances in solids.

We present a real-space analysis of Wannier-Stark resonances based on an extension of the Lanczos iterative procedure. Our method is well suited for multiband structures also in the presence of Zener tunneling. It can be applied to systems of very large dimensions with superimposed uniform electric fields of arbitrary strength and provides a valuable tool for the study of the degree of localization of the wave functions at the Wannier-Stark energies. As an example, the method is applied to one-dimensional single- and two-band tight-binding Hamiltonians. \textcopyright{} 1996 The American Physical Society.

Transient Orientation and Electrooptical Properties of Axially Symmetric Macromolecules in an Electric Field of Arbitrary Strength

The transient orientation, birefringence, and dichroism of macromolecules or particles in solution or suspension, resulting when an electric field is applied or reversed, have been studied by Brownian dynamics simulation. We consider the particular case of axisymmetric particles, for which the dynamics depends on a single rotational diffusion coefficients. In our simulations, we employ arbitrarily strong field−molecule interactions, so that our results are useful to characterize the deviation of the behavior at moderate and high fields from that predicted by existing theories for low fields. We propose the use of relaxation times that characterize the initial and the mean rate of the electrooptic transients. The variation of these relaxation times with field strength is very informative for the electrical properties of the particles.

Stark energy levels of symmetric-top molecules: an elementary algebraic treatment

We derive simple semi-analytical expressions for the Stark energy levels of a general symmetric-top molecule placed in a uniform electric field of arbitrary strength. These are obtained by means of third-order perturbation theory following a suitable canonical transformation of the system Hamiltonian, which is conveniently written in terms of the generators of either of the Lie algebras SO(3) or SO(2,1).

Multiband theory of Bloch-electron dynamics in a homogeneous electric field.

A multiband theory of Bloch electron dynamics in a uniform electric field of arbitrary strength is presented. In this formalism, the electric field is described through the use of the vector potential. Multiband coupling is treated through the use of the Wigner-Weisskopf approximation, thus allowing for a Bloch-electron transition out of the initial band due to the power absorbed by the electric field; also, the approximation insures conservation of total transition probability over the complete set of excited bands. The choice of the vector-potential gauge leads to a natural set of extended time-dependent basis functions for describing Bloch-electron dynamics in a homogeneous electric field; an associated basis set of localized, electric-field-dependent Wannier and related envelope functions are utilized in the analysis to demonstrate the inherent localization manifest in Bloch dynamics in the presence of relatively strong electric fields. From the theory, a generalized Zener tunneling time is derived in terms of the applied uniform electric field and the relevant band parameters; specific results are derived from the general theory using a nearest-neighbor tight-binding, multiband model, and are shown to have identical parametric dependence on electric field, but different, more realistic dependence on the appropriate band-structure parameters than those of the well-known Kane and effective-mass two-band model. Further, the analysis shows an electric-field-enhanced broadening of the excited-state probability amplitudes, thus resulting in spatial lattice delocalization and the onset of smearing of discrete, Stark-ladder, and band-to-band transitions due to the presence of the electric field.