Relativistic surface states of a semi-infinite chain acted on by an electric field

In this paper, we deal with the relativistic effect of surface states of a semi-infinite chain of the Kronig-Penney type potential acted on by an electric field. The crux of the problem is to solve Dirac equation with a linear potential. Combining the solution with other solutions in the various regions, known through the boundary conditions, we get a relativistic expression for energy of surface states. The form is similar to that obtained in the absence of an electric field, which the expression automatically approaches as the field vanishes.     

Non‐Volkov solutions for a charge in a plane wave

As it is known, a set of solutions of the Klein‐Gordon and Dirac equations with a plane‐wave field was found for the first time by Volkov. We construct new solutions of these equations different from the Volkov ones. In particular, the new solutions are characterized by quantum numbers different from Volkov solutions. In fact, our result is based on the demonstration that the transversal charge motion in a plane wave can be mapped by a special quantum transformation to transversal free particle motion. Similarly, we find new sets of solutions of the Klein‐Gordon and Dirac equations with the combined electromagnetic field.     

Massive Photons and the Volkov Solution

This article applies the theory of massive electrodynamics to the Dirac equation with the aim to find the generalized Volkov solution with massive photon field. The resulting equation is the Riccati equation which cannot be solved in general. We use the approximative Volkov function for massive photons and consider an electron in the periodic field and in the laser pulse of the -function form. We derive the modified Compton formulas for the interaction of the multiphoton object with an electron for both cases.     

强场下真空中粒子对产生的研究进展

随着激光技术的飞快发展,激光强度不断提高,超强外场下真空中正负电子对产生的过程,即能量向质量转化过程,已经成为一个研究热点。主要综述了近几年量子Vlasov方程方法和计算量子场论(数值求解Dirac方程)方法在研究强场下真空中正负电子对产生方面的进展,分别介绍了空间均匀场和空间不均匀场下的粒子对产生的情况。第一种情况主要介绍双脉冲结构振荡电场中电子-正电子对的产生、强双频振荡电场中非微扰电子-正电子对的产生、频率调制的激光场中电子-正电子对的产生和Dirac真空对啁啾外场的快速分辨。第二种情况主要介绍优化空间局域电场提高粒子对的产生率、多个势阱-垒结构的振荡场对粒子对产生的增强、振荡 Sauter 电势中正负电子对产生的问题、操纵Dirac真空以控制其在场诱导下的衰变、作为信息传输介质的Dirac真空还有正负电子对产生中的相干和非相干啁啾机制的转变。     

Noninertial Effects on a Dirac Neutral Particle Inducing an Analogue of the Landau Quantization in the Cosmic String Spacetime

We discuss the behavior of external fields interacting with a Dirac neutral particle with a permanent electric dipole moment in order to achieve relativistic bound state solutions in a noninertial frame and in the presence of a topological defect spacetime. We show that the noninertial effects of the Fermi?CWalker reference frame induce a radial magnetic field even in the absence of magnetic charges, which is influenced by the topology of the cosmic string spacetime. We then discuss the conditions that the induced fields must satisfy to yield the relativistic bound states corresponding to the Landau?CHe?CMcKellar?CWilkens quantization in the cosmic string spacetime. Finally, we obtain the Dirac spinors for positive-energy solutions and the Gordon decomposition of the Dirac probability current.     

Two-electron quantum ring in short pulses

The response of a two-electron quantum ring system to the short laser pulses of different shapes in the presence of external static electric field is studied.The variation of transition probabilities of the two-electron quantum ring from ground state to excited states with a number of parameters is shown and explained.The energy levels and wavefunctions of the system in the presence of static electric field are found by solving the time-independent Schrodinger equation numerically by the finite difference method.The shape of the pulse plays a dominant role on the dynamics.     

Particle resonance in the Dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential

We show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing weak electric field associated with a hyperbolic tangent potential. We solve the Dirac equation in terms of Gauss hyper-geometric functions and show explicitly how the resonant behavior depends on the strength of the electric field evaluated at the support of the point interaction. We derive an approximate expression for the value of the resonances and compare the results calculated for the hyperbolic potential with those obtained for a linear perturbative potential. Finally, we characterize the resonances with the help of the phase shift and the Wigner delay time.     

Phase dependence of enhanced ionization in asymmetric molecules

We study enhanced ionization (EI) in asymmetric molecules by solving the 3D time-dependent Schr?dinger equation for HeH2+ driven by a few-cycle laser pulse linearly polarized along the molecular axis. We find that EI is much stronger when the laser's carrier-envelope phase is such that the electric field at the peak of the pulse is antiparallel to the permanent dipole of the molecule (PDM). This phase dependence is explained by studying the molecule in the presence of a static electric field. When this field is antiparallel to the PDM, the energy of the dressed ground state moves up (with increasing internuclear distance R) to cross with excited states, leading to a stronger ionization via intermediate state resonances and via tunneling. We predict analytically the laser and molecular parameters at which these crossings are expected to occur in any asymmetric molecule.     

Fundamental Solutions of the Axial Symmetric Goursat Problem

Abstract

Fundamental solutions (FS) with a given boundary condition on the characteristics of relativistic problems with axial symmetry are considered. This is so-called the Goursat problem (GP) or zero plane formalism in Dirac’s terminology, or modification of the proper time method in the Fock-Nambu-Schwinger formalism (FNS).

Closed FS for the Volkov problem from the point of view of GP can be found. This means that integration over proper time in a FNS integral transformation can be performed. Using the special chosen dynamic symmetry of the initial state, FS for a particle in constant magnetic or constant electric field may also be calculated.     

On the quantum behavior of a neutral fermion in a pseudoscalar potential barrier

In this Letter we have studied the quantum behavior of a spin half neutral fermion interacting with a pseudoscalar potential barrier in (1+1$1+1$)-dimensional spacetime. Exact solutions for the corresponding Dirac equation are obtained both for bound and scattering states. The exact energy levels are obtained from the solutions of Dirac equation. The validity of the quasi-classical quantization rule is examined. For the scattering process the transmission and reflection coefficients are exactly calculated. The absence of the Klein?s paradox is also discussed.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Resonances in the one-dimensional Dirac equation in the presence of a point interaction and a constant electric field

We show that the energy spectrum of the one-dimensional Dirac equation in the presence of a spatial confining point interaction exhibits a resonant behavior when one includes a weak electric field. After solving the Dirac equation in terms of parabolic cylinder functions and showing explicitly how the resonant behavior depends on the sign and strength of the electric field, we derive an approximate expression for the value of the resonance energy in terms of the electric field and delta interaction strength.     

High intensity Compton scattering in a strong plane-wave field of general form

Photon emission by an electron embedded in a strong external field of general form is studied theoretically. The external field considered is a plane-wave electromagnetic field of any number of components, period and polarisation. Exact, Volkov solutions of the Dirac equation with the 4-potential of the general external field are obtained. The photon emission is considered in the usual perturbation theory using the Volkov solutions to represent the electron. An expression for the transition probability of this process is obtained after the usual spin and polarisation sums, trace calculation and phase space integration. The final transition probability in the general case contains a single sum over contributions from external field photons, an integration over one of the phase space components and the Fourier transforms of the Volkov phases. The validity of the general expression is established by considering specific external fields. Known specific analytic forms of the transition probability are obtained after substitution of the 4-potential for a circularly polarised and constant crossed external field. As an example usage of the general result for the transition probability, the case of two circularly polarised external fields separated by a phase difference is studied both analytically and numerically.     

Relativistic stellar models

We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric field intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to specific neutron star models. We find two charged solutions in terms of elementary functions for particular parameter values. The first charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.     

Electric field controlled, pulsed autoionization in two electron wave packets

In this paper, control of the evolution of a two electron wave packet through the application of a static electric field is demonstrated. Specifically, application of a small electric field is used to produce pulsed autoionization events, the timing of which can be controlled on a picosecond time scale. The technique is demonstrated by exciting calcium atoms using a short-pulsed laser to the 4p(3/2)19d doubly excited state, which is energy degenerate with the 4p(1/2)nk stark states. Evolution of the resultant wave packet is monitored through the application of a second short laser pulse, which stimulates the atoms to emit a photon producing singly excited Rydberg states which are detected using field ionization.     

Electron in an Ultrashort Laser Pulse

After the classical approach to acceleration of a charged particle by -form impulsive force, we consider the corresponding quantum theory based on the Volkov solution of the Dirac equation. We determine the modified Compton formula for frequency of photons generated by the scattering of the -form laser pulse on the electron in a rest frame.     

Radiation from electrons in graphene in strong electric field

We study the interaction of electrons in graphene with the quantized electromagnetic field in the presence of an applied uniform electric field using the Dirac model of graphene. Electronic states are represented by exact solutions of the Dirac equation in the electric background, and amplitudes of first-order Feynman diagrams describing the interaction with the photon field are calculated for massive Dirac particles in both valleys. Photon emission probabilities from a single electron and from a many-electron system at the charge neutrality point are derived, including the angular and frequency dependence, and several limiting cases are analyzed. The pattern of photon emission at the Dirac point in a strong field is determined by an interplay between the nonperturbative creation of electron–hole pairs and spontaneous emission, allowing for the possibility of observing the Schwinger effect in measurements of the radiation emitted by pristine graphene under DC voltage.     

Laser-manipulated the multiphoton transitions of a harmonically trapped particle

A single particle magneto-confined in a one-dimensional (1D) quantum wire experiences a harmonic potential, and imposing a sharply focused laser beam on an appropriate site shapes a $\delta$ potential. The theoretical investigation has demonstrated that for a sufficiently strong $\delta$ pulse the quantum motional stationary state of the particle is one of the eigenstates of the free harmonic oscillator, and it is determined by the site of the laser beam uniquely, namely a quantum state is admissible if and only if the laser site is one of its nodes. The numerical computation shows that all the nodes of the lower energy states with quantum numbers $n \le 20$, except the coordinate origin, are mutually different. So we can manipulate the multiphoton transitions between the quantum states by adjusting the position of the laser $\delta$ pulse and realize the transition from an unknown higher excitation state to a required lower energy state.     

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.     

Classical electrodynamics of a nonlinear Dirac field free solutions

In previous papers it has been shown that adding a positive scalar self-interaction ($\text{ψ}$ψ)² to the Dirac field Lagrangian provides a reasonably satisfactory model to describe the barions. In this work, we analyze other solutions of the same nonlinear Dirac equation, making progress in the direction of a systematic analysis. These solutions could provide the ground states for more elaborate interacting schemes of the real particles. Unfortunately the new solutions appear to have energies consistently higher than the ones analyzed in previous papers. Also, the more complicated solutions, whose energy seems to be much higher than the simplest one, leave us little hope for a low minimum energy state.