Electron-Positron Pair Production in a Strong Laser Field Enhanced by an Assisted High Frequency Weak Field

Electron-positron pair production in a strong laser field enhanced by an assisted high frequency weak field is investigated by solving the quantum Vlasov equation.The average and residual pair number densities are obtained for sinusoid electric field and it is found that the high frequency assisted weak field will enhance pair production significantly.There exists an optimal frequency of assisted field that makes the pair production number density get a maximum one,which is a few orders of higher than that without assisted field.We also discuss the other possible assisted fields.     

VLASOV EQUATION,GENERALIZED POISSON EQUATION AND DISPERSION RELATION

A quantum mechanical analog of the Vlasov equation is derived. If the residual nuclear field is taken as generalized Poisson equation, the dispersion relation is consistent with the classical dispersion relation in Ref.[1].     

Solution of the Vlasov equation for collective modes in nuclei

A semiclassical theory of giant resonances based on the Vlasov equation is developed. The linearized Vlasov equation is solved for the bound motion of particles in a central potential with an external time-dependent multipole field. The solution obeys an RPA-type integral equation. If the time-dependent part of the self-consistent field is neglected, the solution of the Vlasov equation has a simple analytical form. The strength function for each multipole can be expressed in terms of the natural frequencies of classical orbits and of radial integrals over the classical motion. The method is illustrated by studying the isoscalar monopole, quadrupole and octupole response in medium-heavy nuclei without residual interaction. There are remarkable similarities between the solutions of the semiclassical problem and the corresponding quantum problem. For a central potential with Saxon-Woods shape there is an interesting shift and concentration of strength in the quadrupole and octupole response functions.     

Semiclassical kinetic equation and the WKB approximation

We study the connection between the classical response function of a nucleus described by the Vlasov equation and the corresponding quantum response function. In the limit of large quantum numbers, the Fourier coefficients which appear in the Vlasov theory correspond to the quantum matrix elements evaluated in the WKB approximation. The classical frequencies of motion give the quantum excitation energies according to the correspondence principle.For a central potential, we identify the normal modes of the classical systems with the corresponding shell-model transitions. Thus we can improve the Vlasov theory by excluding excitation modes which correspond to forbidden quantum transitions. Also, we study the effect of a spin-orbit force in the context of the Vlasov theory.Finally, always by exploiting the close analogy between the classical and the quantum response functions, we introduce exchange (Fock) term in the semiclassical RPA equation given by the Vlasov theory.     

Quantum generalized Vlasov equation

An electronic system is considered as a quantum plasma characterized by a plasma parameter γ₀ 1, over short times. Using the Dynamics of Correlations (a many-body theory based on the Liouville-von Neumann equation in the Fourier transform of the Wigner-Weyl representation), in first and second order, a generalized Vlasov equation (GVE) has been derived. GVE describes as a particular situation the STLS (Singwi, Tosi, Land and Sjölander) ansatz. Discarding correlation terms in GVE, a non-linear Vlasov equation with exchange terms is derived. The classical limit and the linearization of GVE are also studied.     

Enhanced electron positron pair creation by the frequency chirped laser pulse

Based on the quantum Vlasov equation, the effect of frequency chirp on electron-positron pair production is investigated. The cycle parameter, which characterizes the laser field cycle degree within the pulse, is also considered. In both supercycle and subcycle laser pulses the frequency chirp can greatly enhance the momentum distribution function of created pairs and the pair number density. The pair number density created by a supercycle laser pulse is larger than that by a subcycle pulse under the same laser frequency and chirping. There exists an optimal cycle parameter corresponding to the maximum value of the created pair number density for different chirp rates. It is found that the pair number density is sensitive/insensitive to chirping rate when the cycle parameter lies below/above the optimal one.     

Enhanced electron–positron pair production by frequency chirping in one-and two-color laser pulse fields

Enhanced electron–positron pair production by frequency chirping in one- and two-color laser pulse fields is investigated by solving the quantum Vlasov equation. A small frequency chirp shifts the momentum spectrum along the momentum axis. The positive and negative frequency chirp parameters play the same role in increasing the pair number density. The sign change of the frequency chirp parameter at the moment t = 0 leads the pulse shape and momentum spectrum to be symmetric, and the number density to be increased. The number density of produced pairs in the two-color pulse field is much higher than that in the one-color pulse field and the larger frequency chirp pulse field dominates more strongly. In the two-color pulse fields, the relation between the frequency ratio of two colors and the number density is not sensitive to the parameters of small frequency chirp added in either a low frequency strong field or a high frequency weak field but sensitive to the parameters of large frequency chirp added in a high frequency weak field.     

Fokker-Planck方程与Vlasov方程在模耦合理论研究中的比较

模耦合理论比较成功地解释了微波不稳定性的发生,其理论基础是Vlasov方程.Fokker-Planck方程包含了束团的辐射阻尼效应和量子激发效应,是比较完备地描述粒子运动状态的束团分布方程.比较了Fokker-Planck方程和Vlasov方程在来源、意义和解法方面的关联和不同,同时介绍了一种多项式展开束团耦合模式来求解Fokker-Planck方程的方法,并在静态分布中包含了势阱畸变的效应.     

球坐标动量空间下相对论Vlasov方程的数值算法

针对相对论Vlasov方程动量区间跨度大、难以计算的困难,将相对论Vlasov方程在球坐标动量空间中进行数值求解.对相对论Vlasov方程球坐标动量空间构造4阶非分裂守恒型数值格式.数值模拟相对论Landau阻尼问题并与解析理论进行比较,验证数值模型和算法的有效性.对激光等离子体相互作用进行初步模拟分析,表明通过采用球坐标下的动量空间,可在相对较少动量网格情形下,获得与粒子模拟可相互验证的结果.     

Description of isovector giant dipole resonances in relativistic Vlasov equation at small amplitude limit

A more general relativistic Vlasov equation has been derived in the framework of relativistic quantum hadron dynamical theory. In the small amplitude limit we use this Vlasov equation to study the isovector giant dipole resonances built on groundstate in spherical nuclei¹⁶O,⁴⁰Ca,⁹⁰Zn and²⁰⁸Pb. The results show that the spin-orbit coupling and the non-linear terms of scalar meson can influence the resonance energies to a certain extent comparing with those obtained from the non-relativistic Vlasov equation approach and are in good agreement with the experimental ones, especially for the case which vacuum fluctuation is included.     

Dynamically assisted pair production for scalar QED by two fields

By solving the quantum Vlasov equation, the dynamically assisted pair production for scalar quantum electrodynamics (QED) is investigated. It is verified that this mechanism still holds true for boson pair production. Two combinations of two electric fields having different time scales under various time delays are considered; it is found that the oscillations of the momentum spectrum and the number density of created bosons decrease with increasing time delay, and the latter has a maximum value when the time delay equals zero. Furthermore, the differences in vacuum pair production between bosons and fermions are also studied, and they are helpful for distinguishing the created bosons from fermions.     

A Numerical Investigation of the Pinning Phenomenon in Quasi-Periodic Frenkel Kontrova Model Under an External Force

We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in Benedikter et al. (Arch Rat Mech Anal 221(1): 273–334, 2016). The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.     

巨共振激发的相对论效应

在相对论量子场论（ＱＨＤ）的框架下,得到了相对论线性Ｖｌａｓｏｖ方程．依此计算了球形核１６Ｏ、４０Ｃａ、９０Ｚｒ及２０８Ｐｂ的巨偶极共振的强度函数分布．结果表明,相对论效应是不可忽视的．计算得到的巨共振中心能量稍高于非相对论线性Ｖｌａｓｏｖ方程给出的对应值,与实验结果比较都有较好的符合．对计算结果作了简要的讨论,发现核子有效质量和平均场自旅轨道耦合力对巨共振能量有重要影想． In the framework of relativistic quantum hadron dynamical (QHD) theory,under semiclassical approximation and taking into vacuum fluctuation, a relativistic Vlasov equation (RVE) has been derived. Using RVE and considering other relativistic effects, we have studied the isovector dipole giant resonances built on ground state in spherical nuclei.The main results show that the resonance energies for each multipole are larger than those obtained from the non-relativistic classical Vlasov approach...     

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。     

Zur Reversibilität der Vlasov-Gleichung

The difference between Landaus decaying solutions of the linearized Vlasov equation and the damped solutions of a loaded electrical circuit is shown. An integral equation for the field acting in the plasma is investigated and the Laplace transforms of its solutions are considered. Some simple initial value problems for the Cauchy distribution for a perturbation by external fields too, are solved. It is demonstrated that the time arrow in the behaviour of measurable quantities of the Vlasov plasma stems from the accentuation of a non-probable initial state.     

Verallgemeinerung der Methode der singulären Normallösungen für isotherme irreversible Vlasov-Systeme

Irreversible Vlasov systems, i.e. systems governed by a Vlasov-type kinetic equation including entropy-producing collision terms, are treated by the techniques of singular normal modes and singular integral equations using a new indirect method which renders possible a straightforward generalization of the Case formalism as developed originally for collision-free Vlasov plasmas. This method is in contrast to a more complex method given by the present authors for the first application of the singular normal mode expansion to irreversible Vlasov systems (1970). The linearized Vlasov operator supplemented by complete Bhatnagar-Gross-Krook collision integrals as the most important model collision terms is analyzed in detail for a nonrelativistic, nondegenerate, stationary electron gas with neutralizing positive ions and neutral particles without a magnetic field at constant temperature, generalizations for more complex irreversible Vlasov systems being possible. The key of the indirect method given is the introduction of a transformed electron distribution function containing as an additive term an integral over the usual distribution function.     

Wave propagation and Landau-type damping in liquids

Intermolecular forces are modeled by means of a modified Lennard-Jones potential, introducing a distance of minimum approach, and the effect of intermolecular interactions is accounted for with a self consistent field of the Vlasov type. A Vlasov equation is then written and used to investigate the propagation of perturbations in a liquid. A dispersion relation is obtained and an effect of damping, analogous to what is known in plasmas as “Landau damping”, is found to take place.     

Short-time correlations of many-body systems described by nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations

Analytical expressions for short-time correlation functions, diffusion coefficients, mean square displacement, and second order statistics of many-body systems are derived using a mean field approach in terms of nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations. The results are illustrated for the Desai–Zwanzig model, the nonlinear diffusion equation related to the Tsallis statistics, and a Vlasov–Fokker–Planck equation describing bunch particles in particle accelerator storage rings.     

Internal geometric current,and the Maxwell equation as a Hamiltonian system on configuration surfaces

Internal tension tensors on Riemannian manifolds with magnetic field are defined by means of a quantization mapping and quantum statistical averaging. The internal geometric density, current, and stress are derived from asymptotic expansions of the corresponding quantum tensors in the quantization parameter. On Riemannian surfaces with magnetic field, the Maxwell-Lorentz equation is interpreted as a Hamiltonian system. The effect of geometric superconductivity is discussed. The research was supported by the Russian Foundation for Basic Research under grant no. 05-01-00918.