The critical behavior of φ 1 4

The eigenvalues, eigenfunctions, and Schwinger functions of the ordinary differential operator $$H(\lambda ,m) = \tfrac{1}{2}\{ p^2 + \lambda q^4 + (m^2 - \lambda m^{ - 2} )q^2 \} $$ are studied as λ → ∞. It is shown that the scaling limit of the Schwinger functions equals the scaling limit of a one dimensional Ising model. Critical exponents ofH(λ,m) are shown to equal critical exponents of the Ising model, while critical exponents of the renormalized theory are shown to agree with those of a harmonic oscillator.     

Numerical simulations of strong-field processes in momentum space

The time-dependent Schrodinger equation(TDSE) is usually treated in the real space in the textbook.However,it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast oscillation of the electron wave packets under the interaction of intense laser fields.Here we demonstrate that the TDSE can be efficiently solved in the momentum space.The high-order harmonic generation and above-threshold ionization spectra obtained by numerical solutions of TDSE in momentum space agree well with previous studies in real space,but significantly reducing the computation cost.     

少周期激光脉冲附加太赫兹场对高次谐波发射的影响

本文通过数值求解非伯恩奥本海默近似下电子一维核一维的含时薛定谔方程,研究了少周期线偏振激光与氢分子离子相互作用下,太赫兹场的加入对高次谐波的发射影响.我们发现,在短周期线偏振激光脉冲的y方向上附加一个强度较弱的太赫兹场可以有效地扩展谐波的截止位置,并对量子轨道实现调控.通过时频分析、电子波包随时间变化以及半经典三步模型研究了高次谐波发射的物理机制,并对获得的物理现象给出合理的解释.     

数值研究二维含时薛定谔方程

采用二维渐近边界条件,将任意极化激光与原子相互作用的二维含时Schr(o)dinger方程无穷空间初值问题转化为有界空间的初边值问题,近而将截断后的初边值问题离散成线性正则方程组,而后利用辛算法求解正则方程得到含时波函数.最后利用含时波函数求得高次谐波谱,证明二维渐近边界条件和辛算法是合理而有效的.     

Wavelength scaling of high-harmonic yield: threshold phenomena and bound state symmetry dependence

Describing harmonic generation (HG) in terms of a system's complex quasienergy, the harmonic power P_{DeltaE}(lambda) (over a fixed interval, DeltaE, of harmonic energies) is shown to reproduce the wavelength scaling predicted recently by two groups of authors based on solutions of the time-dependent Schr?dinger equation: P_{DeltaE}(lambda) approximately lambda;{-x}, where x approximately 5-6. Oscillations of P_{DeltaE}(lambda) on a fine lambda scale are then shown to have a quantum origin, involving threshold phenomena within a system of interacting ionization and HG channels, and to be sensitive to the bound state wave function's symmetry.     

Laser phase effect on asymmetric harmonic distribution in H_2~+

The laser phase effect on the spatial distribution of the molecular high-order harmonic generation(MHHG) spectrum from H_2~+ is theoretically investigated through solving the Non-Bohn-Oppenheimer(NBO) time-dependent Schrodinger equation(TDSE).The results are shown as follows,(i) The generated harmonics from the two nuclei each present an asymmetric distribution.Particularly,when the laser phases are chosen from 0.0π to 0.6π and from 1.7π to 2.0π,the contribution from the negative-H plays a main role in harmonic generation.When the laser phases are chosen from 0.7πto 1.6k,the contribution from the positive-H to the harmonic generation is remarkably enhanced and becomes greater than that from the negative-H.The electron localization,the time-frequency analyses of the harmonic spectrum and the time-dependent wave function are shown to explain the asymmetric harmonic distribution in H_2~+,which provides us with a method to control the electron motion in molecules,(ⅱ) As the pulse duration increases,the asymmetric distributions of the MHHG in two H nuclei decrease,(ⅲ) Isotope investigation shows that the asymmetric harmonic distribution can be reduced by introducing the heavy nucleus(i.e.,D_2~+).     

Harmonic measure and winding of conformally invariant curves

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance r as H approximately r(alpha) while the curve logarithmically spirals with a rotation angle phi=lambdalnr. It obeys the scaling law f(alpha,lambda)=(1+lambda(2))f(alpha)-blambda(2) with alpha=alpha/(1+lambda(2)) and b=(25-c)/12, and where f(alpha) identical with f(alpha,0) is the pure harmonic measure spectrum, and c the conformal central charge. The results apply to O(N) and Potts models, as well as to stochastic L?wner evolution.     

Electron wavepacket phases in ionization and rescattering processes by intense laser pulses

Exact numerical solutions of the time-dependent Schrödinger equation, TDSE, are presented for the H atom and H^2/+ molecular ion ionized by short (10 optical cycles), intense I ₀ ≥ 10¹⁴ W/cm², 800 nm laser pulses. Calculations of the time dependent expectation values of the dipole moment d(t), velocity $ \dot d Exact numerical solutions of the time-dependent Schr?dinger equation, TDSE, are presented for the H atom and H^2/+ molecular ion ionized by short (10 optical cycles), intense I ₀ ≥ 10¹⁴ W/cm², 800 nm laser pulses. Calculations of the time dependent expectation values of the dipole moment d(t), velocity (t), and acceleration (t) are used to identify the phase of these physical parameters with respect to the laser field during the harmonic generation process. It is found in general that electron wavepackets in an inner region near the parent ion are out of phase with the response expected from the classical laser induced recollision model, whereas wavepackets in an outer region, far from the parent ion, are in phase with the field force. It is found furthermore that it is the inner electron wavepacket which contributes mainly to the high order harmonic generation, HHG, process, even though its acceleration is out of phase with the field force. This suggests strong Coulomb refocussing effects in the HHG process, especially in the case of H^2/+. Original Russian Text ? Astro, Ltd., 2009. In honor of Prof. N.B. Delone. The article is published in the original.     

Experimental verification of the mechanisms for nonlinear harmonic growth and suppression by harmonic injection in a traveling wave tube

Understanding the generation and growth of nonlinear harmonic (and intermodulation) distortion in microwave amplifiers such as traveling wave tubes (TWTs), free electron lasers (FELs), and klystrons is of current research interest. Similar to FELs, the nonlinear harmonic growth rate scales with the harmonic number in TWTs. In klystrons, the wave number scaling applies to the nonlinear harmonic bunching and associated nonlinear space-charge waves. Using a custom-modified TWT that has sensors along the helix, we provide the first experimental confirmation of the scaling of nonlinear harmonic growth rate and wave number in TWTs. These scalings of a nonlinearly generated harmonic mode versus an injected linear harmonic mode imply that suppression by harmonic injection occurs at a single axial position that can be located as desired by changing the injected amplitude and phase.     

Effect of pressure on the Ginzburg-Landau parameter kappa=lambda/xi in YB6

Measurements of the transition temperature Tc, the upper critical field Hc2, and the magnetic penetration depth lambda under hydrostatic pressure (up to approximately 9.2 kbar) in the YB6 superconductor were carried out. A pronounced and negative pressure effect (PE) on Tc and Hc2 with dTc/dp=-0.0547(4) K/kbar and micro0dHc2(0)/dp=-4.84(20) mT/kbar, and zero PE on lambda(0) were observed. The PE on the coherence length dxi(0)/dp=0.28(2) nm/kbar was calculated from the measured pressure dependence of Hc2(0). Together with the zero PE on the magnetic penetration depth lambda(0), our results imply that the Ginzburg-Landau parameter kappa(0)=xi(0)/lambda(0) depends on pressure and that pressure "softens" YB6, e.g., moves it to the type-I direction.     

Above-threshold ionization of hydrogen and hydrogen-like ions by X-ray pulses

This paper adresses the problem of above-threshold ionization (ATI) of hydrogen interacting with an intense X-ray electromagnetic field. Two approaches have been used. In the first approach, we calculate generalized differential and total cross sections based on second-order perturbation theory for the electron interaction with a monochromatic plane wave, with the A ² and A · P contributions from the nonrelativistic Hamiltonian (including retardation) treated exactly. In the second approach, we solve the time-dependent Schrödinger equation (TDSE) for a pulsed plane wave using a spectral approach with a basis of oneelectron orbitals, calculated with L ²-integrable B-spline functions for the radial coordinate and spherical harmonics Y _lm for the angular part. Retardation effects are included up to O(1/c), they induce extra terms forcing the resolution of the TDSE in a three dimensional space. Relativistic effects [of O (1/c ²)] are fully neglected. The isoelectronic series of hydrogen is explored in the range Z = 1 ? 5 in both TDSE and perturbative approaches. Photoelectron angular distributions are obtained for photon energies of 1 keV and 3 keV for hydrogen, and photon energy of 25 keV for the hydrogenic ion B⁴⁺. Perturbative and TDSE calculations are compared.     

Relaxation length of a polymer chain in a quenched disordered medium

Using Monte Carlo simulations, we study the relaxation and short-time diffusion of polymer chains in two-dimensional periodic arrays of obstacles with random point defects. The displacement of the center of mass follows the anomalous scaling law r(c.m.)(t)(2)=4D(*)t(beta), with beta<1, for times t相似文献   

Pseudospectral method with symplectic algorithm for the solution of time-dependent SchrSdinger equations

A pseudospectral method with symplectic algorithm for the solution of time-dependent Schrodinger equations （TDSE） is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral method and the time evolution is given in symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSE. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atom in strong laser field as compared with previously published work. The influence of the additional static electric field is also investigated.     

Submillimeter laser interferometer for high density plasma diagnostic

There are presented the results of investigation of the one-channel homodyne laser interferometer =119 µm made on the basis of the hollow dielectric beamguide and quasioptical functional devices. The interferometer is designed for determination of the plasma electron density of the TOKAMAK-7. The density response threshold is 0.7% from the expected plasma density and the phase difference measurement total error is 5°     

Diode-pumped Tm: YAG solid-state lasers with indirect and direct manifold pumping

We study the continuous-wave (cw) characteristics of both two-manifold and three-manifold Tm: YAG laser pumped at _p 1.8 µm or _p = 0.785 µm and lasing at ₁ = 2.02 µm. The three-manifold rate equations are adiabatically reduced to their two-manifold form. For each pumping scheme, the steady-state rate equations are combined with the cw differential equations for the forward- and reverse-lasing fields and the pump-depletion differential equation. These three coupled cw differential equations are solved analytically. This gives the linear flux-conservation law between the input pump and the laser output, the minimum crystal length, and optimal output couplings. We show that the major difference between these two pumping schemes is due to the different pump effective absorption cross sections and not the two-for-one cross relaxation. Our example shows that the minimum intensity threshold and optimal crystal length are smaller for pumping at _tp = 0.785 µm than pumping at _p 1.8 µm.     

Two-center interference in high-harmonic generation of H_2~+ in a combination of a mid-infrared laser field and a terahertz field

We theoretically investigate the two-center interference in high-order harmonics generated from the H_2~+ in a combination of a mid-infrared laser and a terahertz field by numerically solving the time-dependent Schr ¨odinger equation(TDSE).The interference minima in high-order harmonic generation(HHG) are effectively suppressed when a THz field is added.The contribution to HHG from the two separate nuclei is used to demonstrate the locating order of the harmonic minima.Furthermore, we also investigate the emission time of harmonics. The results show that the intensity of the short path around 60 thorder after adding a THz field is stronger than that in the mid-infrared laser field, which further illustrates the suppression of the interference minima in HHG.     

Carrier-envelope phase measurement using plasmonic-field-enhanced high-order harmonic generation of H atom in few-cycle laser pulses

We investigate the plasmonic-field-enhanced high-order harmonic generation (HHG) of H atom driven by few-cycle laser pulses, by solving the time-dependent Schrödinger equation (TDSE). Compared with the homogeneous field, HHG spectra generated by inhomogeneous field exhibit two-plateau structure. We analyze the origin of the two plateaus by using the semiclassical trajectory method. Our results from both classical and TDSE simulations show that the cutoffs of the two plateaus are dramatically affected by the carrier-envelope phase (CEP) of laser pulse in the inhomogeneous field, even for a little longer pulse. Thus, we can determine the CEP of driving laser based on the cutoff position of HHG generated in the inhomogeneous field.     

Gain of harmonic generation in high gain free electron laser

In a planar undulator employed free electron laser(FEL),each harmonic radiation starts from linear amplification and ends with nonlinear harmonic interactions of the lower nonlinear harmonics and the fundamental radiation.In this paper,we investigate the harmonic generation based on the dispersion relation driven from the coupled Maxwell-Vlasov equations,taking into account the effects due to energy spread,emittance,betatron oscillation of electron beam as well as diffraction guiding of the radiation field.A 3D universal scaling function for gain of the linear harmonic generation and a 1D universal scaling function for gain of the nonlinear harmonic generation are presented,which promise rapid computation in FEL design and optimization.The analytical approaches have been validated by 3D simulation results in large range.     

Gain of harmonic generation in high gain free electron laser

In a planar undulator employed free electron laser (FEL), each harmonic radiation starts from linear amplification and ends with nonlinear harmonic interactions of the lower nonlinear harmonics and the fundamental radiation. In this paper, we investigate the harmonic generation based on the dispersion relation driven from the coupled Maxwell-Vlasov equations, taking into account the effects due to energy spread, emittance, betatron oscillation of electron beam as well as diffraction guiding of the radiation field. A 3D universal scaling function for gain of the linear harmonic generation and a 1D universal scaling function for gain of the nonlinear harmonic generation are presented, which promise rapid computation in FEL design and optimization. The analytical approaches have been validated by 3D simulation results in large range.     

Multiphoton and tunneling ionization of atoms in an intense laser field

We study the ionization probabilities of atoms by a short laser pulse with three different theoretical methods,i.e.,the numerical solution of the time-dependent Schro¨dinger equation(TDSE),the Perelomov-Popov-Terent’ev(PPT) theory,and the Ammosov-Delone-Krainov(ADK) theory.Our results show that laser intensity dependent ionization probabilities of several atoms(i.e.,H,He,and Ne) obtained from the PPT theory accord quite well with the TDSE results both in the multiphoton and tunneling ionization regimes,while the ADK results fit well to the TDSE data only in the tunneling ionization regime.Our calculations also show that laser intensity dependent ionization probabilities of a H atom at three different laser wavelengths of 600 nm,800 nm,and 1200 nm obtained from the PPT theory are also in good agreement with those from the TDSE,while the ADK theory fails to give the wavelength dependence of ionization probability.Only when the laser wavelength is long enough,will the results of ADK be close to those of TDSE.