Exact density-functional potentials for time-dependent quasiparticles

We calculate the exact Kohn-Sham potential that describes, within time-dependent density-functional theory, the propagation of an electron quasiparticle wave packet of nonzero crystal momentum added to a ground-state model semiconductor. The potential is observed to have a highly nonlocal functional dependence on the charge density, in both space and time, giving rise to features entirely lacking in local or adiabatic approximations. The dependence of the nonequilibrium part of the Kohn-Sham electric field on the local current and charge density is identified as a key element of the correct Kohn-Sham functional.     

Dynamic exchange-correlation potentials for the 2D electron gas

Recent progress in the formulation of a fully dynamical local approximation to time-dependent density functional theory (TD-DFT) appeals to the longitudinal and transverse components of the long-wavelength exchange and correlation kernel in the homogeneous electron gas, . We extend to the two-dimensional longitudinal and transverse case our work on the 3D [J. Phys.: Condens. Matter 9 (1997) 475], which accounts for two-pair excitations through an approximate decoupling of the equation of motion for the current–current response function. We present numerical results and compare with asymptotic behaviours and previous approximations.     

Exact short time dynamics for steeply repulsive potentials

The autocorrelation functions for the force on a particle, the velocity of a particle and the transverse momentum flux are studied for the power law potential v(r)=ε(σr)^ν (soft spheres). The latter two correlation functions characterize the Green–Kubo expressions for the self-diffusion coefficient and shear viscosity. The short-time dynamics is calculated exactly as a function of ν. The dynamics is characterized by a universal scaling function S(τ), where τ=t/τ_ν and τ_ν is the mean time to traverse the core of the potential divided by ν. In the limit of asymptotically large ν this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green–Kubo representation for hard-sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.     

Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials

We have obtained the exact expression of the diffusion propagator in the time-dependent anharmonic potential V(x,t)=1 / 2a(t)x(2)+b ln x. The underlying Euclidean metric of the problem allows us to obtain analytical solutions for a whole family of the elastic parameter a(t), exploiting the relation between the path integral representation of the short time propagator and the modified Bessel functions. We have also analyzed the conditions for the appearance of a nonzero flow of particles through the infinite barrier located at the origin (b<0).     

Bootstrap approximation for the exchange-correlation kernel of time-dependent density-functional theory

A new parameter-free approximation for the exchange-correlation kernel f(xc) of time-dependent density-functional theory is proposed. This kernel is expressed as an algorithm in which the exact Dyson equation for the response, as well as an approximate expression for f(xc) in terms of the dielectric function, are solved together self-consistently, leading to a simple parameter-free kernel. We apply this to the calculation of optical spectra for various small band gap (Ge, Si, GaAs, AlN, TiO(2), SiC), large band gap (C, LiF, Ar, Ne), and magnetic (NiO) insulators. The calculated spectra are in very good agreement with the experiment for this diverse set of materials, highlighting the universal applicability of the new kernel.     

Real-time electron dynamics with exact-exchange time-dependent density-functional theory

The exact exchange potential in time-dependent density-functional theory is defined as an orbital functional through the time-dependent optimized effective potential (TDOEP) method. We numerically solve the TDOEP integral equation for the real-time nonlinear intersubband electron dynamics in a semiconductor quantum well with two occupied subbands. It is found that memory effects become significant in the vicinity of intersubband resonances.     

基于多组态含时Hartree-Fock方法研究电子关联对于H_2分子强场电离的影响

发展了三维的处理双原子分子非微扰电子动力学的多组态含时Hartree-Fock方法,并利用该方法研究了电子关联对于H_2分子强场电离概率的影响.该方法采用能够精确处理双中心库仑势的椭球坐标系,以及减小双电子积分计算量的有限元-离散变量基函数方法.利用多组态含时Hartree-Fock方法计算了H_2分子随分子取向角度变化的XUV光电离结果,并通过与单组态结果的对比研究了电子关联对于单电离和双电离概率的不同影响.研究表明,电子关联对于单电离过程影响很小,而在双电离过程中则发挥了重要作用,导致了电离概率的减小.该方法为进一步研究强场物理过程中的电子关联效应奠定了基础.     

Bound electron dynamics: Exact solution for a one-dimensional oscillator-string model

The dynamical problem of a harmonically bound electron with standard dipole model coupling to the electromagnetic field in a finite one-dimensional space is solved exactly in a simple manner. It is easily shown that in this model the coupling between the electron and the field is “rigid”, in the sense of and in complete analogy with a recent treatment of a purely mechanical particle on a string. As a consequence the electron's quantum mechanical momentum fluctuations exhibit a logarithmic ultraviolet divergence. In the limit of infinite spatial extension of the field, and apart from quantal noise, the electron behaves exactly as a simple linearly damped harmonic oscillator.     

Exact propagator for the one-dimensional time-dependent quadratic Lagrangian

Extending Montroll's method [Montroll, E. W., Commun. Pure Appl. Math. 5, 415 (1952)] to the one-dimensional time-dependent quadratic Lagrangian, we first evaluate the propagator beyond caustics by including Maslov's correction factor. The propagator at caustics is then obtained by introducing the modified semigroup property. Finally, the wave functions are derived from the propagator obtained.     

强场非次序双电离中再碰撞动力学的强度依赖

利用三维经典系综模型系统地研究了不同强度线偏振激光脉冲驱动下He原子的非次序双电离.结果表明在非次序双电离中回碰电子的返回次数、两电子的碰撞距离和电子对的关联特性都强烈地依赖于激光强度.对于750 nm,随着激光强度的增加,单次返回诱导的非次序双电离事件逐渐减少,而多次返回事件的比例显著增加.对于1500 nm,随着激光强度的增加,前三次返回诱导的非次序双电离事件都会减少,返回次数大于3的轨道对非次序双电离的贡献逐渐增加.这是因为在高强度下每次返回过程中母核的库仑吸引对返回电子横向偏离的补偿较弱,所以需要更多次的返回来补偿电子的横向偏离以实现再碰撞.轨道分析表明非次序双电离中两电子的碰撞距离随激光波长和强度的增加而逐渐减小.最后讨论了非次序双电离中电子对的关联特性对返回次数的依赖.     

一般三生成元含时系统的精确解

在量子光学、凝聚态物理、原子分子物理中存在许多典型的具有三生成元李代数结构的量子系统或模型.用LewisRisenfeld不变量理论及与不变量有关的幺正变换方法精确求解了这些系统的含时薛定谔方程的精确解. 关键词： 不变量理论 精确解 生成元 几何相位     

Exact invariants for a class of three-dimensional time-dependent classical hamiltonians

An exact invariant is derived for three-dimensional Hamiltonian systems of N particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function f(2)(t), embodying a solution of a third-order differential equation whose coefficients depend on the explicitly known trajectories of the particle ensemble. Our result is applied to a one-dimensional time-dependent nonlinear oscillator and to a system of Coulomb interacting particles in a time-dependent quadratic external potential.     

Parametric instabilities in quantum plasmas with electron exchange-correlation effects

Parametric instabilities induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves in quantum plasmas with the electron exchange-correlation effects are presented.By using the quantum hydrodynamic equations with the electron exchange-correlation correction,we obtain an effective quantum Zaharov model,which is then used to derive the modified dispersion relations and the growth rates of the decay and four-wave instabilities.The influences of the electron exchange-correlation effects and the quantum effects on the existence of quantum Langmuir waves and the parametric instabilities are discussed in detail.It is shown that the electron exchange-correlation effects and quantum effects are strongly coupled.The quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange-correlation effects and the quantum effects satisfy a certain condition.The electron exchange-correlation effects tend to enhance the parametric instabilities,while quantum effects suppress the instabilities.     

Impact of electron exchange-correlation on drift acoustic solitary waves

The impact of electron exchange-correlation term on the linear and nonlinear quantum ion (QIA) acoustic drift waves in a highly degenerate plasma is investigated. An analytical approach is employed to derive the differential equation which is later on turned into Sagdeev energy integral equation that can be utilized to get drift solitons under existence conditions. It is noted that phase speed/frequency of the linear drift quantum ion acoustic (QIA) waves increases with electron exchange-correlation effect, but the amplitude of the corresponding solitons decreases with inclusion of these effects. Present study is carried out with reference to highly dense plasma environments like fast ignition inertial confinement fusion and white dwarfs etc.     

Exact quantization formula for affine linearly energy-dependent potentials

We construct an exact quantization formula for Schrödinger equations with potentials thatdepend affine linearly on the energy, that is, they contain a term linear in the energy plus an energy-independent term. If such an energy-dependent potential admits a discrete spectrum and its ground state solution is known, our formula predicts the complete energy spectrum in exact form.     

Exact solution for the diffusion in bistable potentials

We solve analytically the Fokker-Planck equation for a one-parameter family of symmetric, attractive, nonharmonic potentials which include double-well situations. The exact knowledge of the eigenfunctions and eigenvalues allows us to fully discuss the transient behavior of the probability density. In particular, for the bistable potentials, we can give analytical expressions for the probability current over the working barrier and for the onset time which characterizes the transition from uni- to bimodal probability densities.On leave from the Department of Theoretical Physics, Université de Genève, CH-1211, Genève 4, Switzerland.Supported by the Swiss National Fund for Scientific Research.On leave from the Institute of Theoretical Physics, Academia Sinica, Beijing, China.Supported in part by the Robert A. Welch Foundation.     

Exact solutions for a full time-dependent model describing four-photon parametric processes

It is shown that the full time-dependent problem of four-photon parametric interaction has a large set of exact wave solutions. This set includes normal and symbiotic periodic waves as well as solitary ones. Periodic solutions are given in terms of Jacobian elliptic functions.