Arrested swelling of highly entangled polymer globules

Upon aging, a collapsed long chain evolves from a crumpled state to a self-entangled globule which can be thought of as a large knot. Swelling of an equilibrium globule in good solvent is a two-step process: (i) fast swelling into an arrested stretched structure with conserved entanglement topology followed by (ii) slow disentanglement. Using computer simulation, we found both mass-mass (m-m) and entanglement-entanglement (e-e) power law correlations inside the swollen globule. The m-m correlations are characterized by a set of two exponents in agreement with a Flory-type argument. The e-e correlations are also characterized by two exponents, both of them larger (by approximately 0.3) than the related m-m exponents. We interpret this difference as evidence of distance-dependent repulsion E=-0.3ln((rho)k(B)T between entanglements sliding along the polymer chain.     

Scaling of cross-sections for asymmetric (e, 3e) process on helium-like ions by fast electrons

An approximate simple scaling law is obtained for asymmetric (e, 3e) process on helium-like ions for double ionization by fast electrons. It is based on the equation (Z ^′3π) exp[-Z(r₁ + r₂)],Z′ = Z – (5/16) for ground state wave function of helium-like ions and Z^′2 scaling of energies. The scaling law is found to work very well if the lower energy electron is ejected along the momentum transfer direction and the other one is ejected in the opposite direction. It also works quite well if this electron is ejected within about 90° of the momentum transfer direction with the other electron going in the opposite direction. The scaling law becomes increasingly accurate as the target nuclear charge and the energy increase.     

Quasi-binary incident electron—centre of mass collision in (e, 3e) process on He and He-like ions

We present in this communication the results of our first Born calculation in the three-Coulomb (3C) wave approach for the (e, 3e) process on He and He-like ions at an incident electron energy 5599 eV in the coplanar constant θ12 as well as out-of-plane constant φ12 modes. These two geometrical modes are such that the quasi-binary collision between the incident electron and centre of mass of the ejected electrons is in the scattering plane. The theoretical formalism has been developed using plane waves, Le Sech wave function and approximated BBK-type wave function respectively for the incident and scattered, bound and ejected electrons to calculate five-fold differential crosssection (FDCS) of the (e, 3e) process. We emphasize on the similarities and dissimilarities (asymmetries) in the angular profile of the FDCS in two modes as well as the effects of post-collision interaction (between the ejected electrons) and nuclear chargeZ on the angular profile of the FDCS. We observe that with the increment of nuclear charge the two quasi-binary collisions approach towards identical behaviour at larger mutual angles and thus bringing less asymmetry in FDCS for higherZ target.     

Quasi-free (e,e'N) reactions on polarized targets

The quasi-free nucleon knockout by the electron is studied in the general case of both polarized beams and polarized targets. The coincidence cross section involves nine structure functions which give detailed information on the nuclear current operator. However, their measurement requires out-of-plane experiments. Results on ⁷Li and ³⁹K obtained within the nonrelativistic DWIA framework indicate that some structure functions, very sensitive to final state interactions, are probably too small to be separated. On the other side, cross sections, asymmetries and electron polarization ratios in coplanar kinematics have measurable size. They add complementary information to the unpolarized quasi-free nucleon knockout because of their sensitivity to spin degrees of freedom which are averaged out without target polarization. In the particular case of a nucleon ejected along the direction of the momentum transfer from a target with spin oriented in the same direction (superparallel kinematics) only three structure functions survive and can be simply separated.     

Electron dichroism effects in the relativistic (e, 2e) process for K-shell ionization of atoms

In this communication we present theoretical demonstration of electron dichroism in the relativistic (e, 2e) process for K-shell ionization of atoms in non-coplanar asymmetric geometry. The theoretical formalism has been developed in plane wave Born approximation and in this approximation the triple differential cross-section (TDCS) has been expressed as a product of kinematical factors and atomic structure functions. The longitudinal spin asymmetry in the relativistic (e, 2e) process on K-shell of atoms has been shown to depend on the interference between the transition charge and component of the transition current in the direction perpendicular to the scattering plane. Further, the longitudinal spin asymmetry has been shown to depend on incident electron energy, atomic number of the target, azimuthal angle of the ejected electron and scattered electron angle.     

理论计算电子碰撞氢分子(e,2e)反应的三重微分截面

通过发展的分子畸变波玻恩近似（MDWBA）方法,把坐标空间的分子多中心问题转化为动量空间的单中心问题,入射电子、散射电子以及被电离电子的波函数都使用了畸变波表象,经过求解动量空间Lippmann-Schwinger方程获得电子的畸变波函数。应用MDWBA方法计算了共面非对称动力学条件下入射能量为100eV 的电子碰撞氢分子（e,2e）反应的三重散射微分截面,并与其它理论和实验结果进行了比较。MDWBA方法的计算结果与实验结果符合的很好。     

理论计算电子碰撞氢分子(e,2e)反应的三重微分截面

通过发展的分子畸变波玻恩近似（MDWBA）方法,把坐标空间的分子多中心问题转化为动量空间的单中心问题,入射电子、散射电子以及被电离电子的波函数都使用了畸变波表象,经过求解动量空间Lippmann-Schwinger方程获得电子的畸变波函数。应用MDWBA方法计算了共面非对称动力学条件下入射能量为100eV 的电子碰撞氢分子（e,2e）反应的三重散射微分截面,并与其它理论和实验结果进行了比较。MDWBA方法的计算结果与实验结果符合的很好。     

Xe(4d~(10))(e,2e)反应三重微分截面的理论研究

采用修正后的扭曲波玻恩近似理论,计算了共面不对称几何条件下Xe(4d~(10))(e,2e)反应的三重微分截面.散射电子能量为1000 eV,敲出电子能量为20 eV,散射电子角度分别固定在2°,4°和7.5°.理论计算与Avaldi等人的实验结果和扭曲波玻恩近似理论计算进行了比较,发现出射电子之间的后碰撞相互作用较弱,极化效应在反应过程中起着重要作用.     

Mutual rectification of cnoidal and sinusoidal electromagnetic waves with orthogonal polarization planes in a graphene-based superlattice

The effect of mutual rectification of two electromagnetic waves in a graphene superlattice is studied for a cnoidal wave polarized along the superlattice axis and a sinusoidal wave polarized along the orthogonal direction. An expression for the density of the direct current generated by mixing of these waves is obtained. The direct current is studied as a function of the cnoidal wave amplitude. The possibility of varying both the value and the direction of the direct current with varying the cnoidal wave amplitude is shown.     

Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.     

Delay of Spatial Quantum Correlations in Magnetic Nanostructures

Simultaneous quantum correlations between two spins in magnetic nanostructures are considered in the model of a linear chain of a finite number of atoms with exchange interaction between electron spins of neighboring atoms in the framework of the Heisenberg ferromagnetism theory. We assume that in the initial state, the spins of all chain atoms except the first two are oriented along the same direction. The spins of the first two atoms are flipped. Due to the exchange interaction, this initial state generates a spin flip wave along the chain. The expressions obtained for nonstationary quantum amplitudes of the flip probability waves for an even number of spins can be used for calculating quantum correlations between two spins separated by a large distance in a chain. Numerical calculations of the spin correlator reveal that the correlation between two spins in the chain occurs with a delay on the order of the time of propagation of the exchange interaction along the spin chain. After the delay, the spin correlation amplitude abruptly increases followed by subsequent oscillatory temporal behavior.     

Calculation by plane wave Born approximations of electron-impact ionization of silver and copper

The plane wave Born approximation is used to calculate total electron impact ionization cross section of silver and copper. Wavefunctions of the target and residual ions were modeled by non orthogonal Hartree-Fock and Dirac-Fock orbitals. The wave functions of the atom and residual ion are calculated with allowance for relaxation effects. The one-electron wavefunction of the continuous spectrum for the ejected electron is obtained using single-configuration Hartree-Fock and Dirac-Fock method. The orthogonalization of the ejected electron wave functions to all occupied orbitals of the target atom is performed. Results of calculations are compared to available experimental measurements and theoretical calculations performed by non relativistic one-electron PWBA, where the ejected electrons is modeled by the hydrogenic Coulomb wave function.     

A GROUP OF EXACT (3+1) DIMENSIONAL CYLINDRICALLY SYMMETRIC WAVE SOLUTIONS TO THE EINSTEIN GRAVITATIONAL FIELD EQUATION

Starting with the diagonal spacetime metric tensor, the Einstein gravitational field equation is solved, and a set of exact (3+1) dimensional cylindrically symmetric wave solutions with two arbitrary functions are found. In these solutions all nonvanishing components of spacetime metric tensor are varying with the same propagating factor (ct-z) while the waves are travelling along z axis. The physical picture and the condition of positive energy density of the wave solutions are discussed.     

Young-type interference in (e, 2e) ionization of H(2)

We have investigated the electron impact single ionization of the hydrogen molecule, with fully determined kinematics. The experimental and theoretical results are compared with He ionization under the same conditions. The results indicate that the ejected electron angular distribution for H(2) is modified due to Young-type interference between ionization amplitudes for scattering from the two centers in the hydrogen molecule. The observable result is a suppression of the backward scattering (recoil) peak compared with the binary peak.     

Phase-modulus relations in cyclic wave functions

We derive reciprocal integral relations between phases and amplitude moduli for a class of wave functions that are cyclically varying in time. The relations imply that changes of a certain kind (e.g. not arising from the dynamic phase) obligate changes in the other. Numerical results indicate the approximate validity of the relationships for arbitrarily (non-cyclically) varying states in the adiabatic (slowly changing) limit.     

渐变折射率介质中标准矢量波函数的构成

研究了在渐变折射率介质中构成标准矢量波函数的必要条件。研究结果表明在渐变折射率介质中构成标准矢量波函数除了仍需遵循Morse-Feshbach判据外，领示矢量仅能选取与折射率变化方向一致的那根坐标轴的单位矢量。     

(e, 2e) spectroscopy

We present a detailed treatment of the theoretical and experimental aspects of the symmetric (e, 2e) reaction in atoms, molecules and solids. Two experimental arrangements are described for measuring angular correlations and separation energy spectra. the one arrangement employing coplanar and the other noncoplanar symmetric kinematics. The latter arrangement is shown to be particularly suitable for extracting structure information. The basic approximation, the factorized distorted-wave off-shell impulse approximation with fully distorted waves, is shown to correctly describe the reaction in some test cases, as does the phase distortion approximation. At energies of the order of 1200 eV the simple eikonal and plane wave approximations adequately describe the valence shell cross sections for light atoms and molecules containing first row elements. Energy independent structure information is obtained on: (a) shapes and magnitudes of the square of the momentum space wave functions for individual electron orbitals; (b) separation energies for individual ion eigenstates; (c) the characteristic orbital of each state; and (d) spectroscopic factors describing the probability that an eigenstate contains the principal configuration of a hole in the characteristic orbital for each eigenstate. Comparison is made with photoelectron spectroscopy and Compton scattering, since they separately yield some of the information obtained by the (e, 2e) method. A brief summary is given of other electron-electron coincidence experiments.     

Measurement of long-range wave-function correlations in an open microwave billiard

We investigate the statistical properties of wave functions in an open chaotic cavity. When the number of channels in the openings of the billiard is increased by varying the frequency, wave functions cross over from real to complex. The distribution of the phase rigidity, which characterizes the degree to which a wave function is complex, and long-range correlations of intensity and current density are studied as a function of the number of channels in the openings. All measured quantities are in perfect agreement with theoretical predictions.     

Li+低能(e,2e)反应角分布

利用修正的BBK理论，考虑入射道的库仑相互作用及出射电子的交换对称性，在共面-等能分享-垂直角度碰撞几何中，分别计算了能量为79.6，105.6，227.6和375.6eV的入射电子碰撞Li⁺(1s²)(e，2ｅ)反应三重微分截面(TDCS).结果表明：在接近阈能的碰撞中，两出射电子连线平行于入射电子方向时，TDCS最大；两出射电子连线垂直于入射电子方向时，TDCS最小；入射电子能量达5倍的电离阈能时，主要为单次双体碰撞，而且入射道库仑场对决定低能碰撞的TDCS起着重要作用. 关键词：     

Linear polarization of radiation from ZnCdSe/ZnSe quantum wells induced by the anisotropic profile of interfaces

The low-temperature spectra of the exciton luminescence of the ZnCdSe/ZnSe quantum well grown in the [100] direction have been analyzed. It has been found that the observed radiation is linearly polarized in the well plane along either the [011] axis or the orthogonal $[0\bar 11]$ axis depending on the energy of exciting light. Polarization along the [011] axis is associated with the anisotropy of the geometric profiles of interfaces and corresponds to the polarization of excitons localized in the terraces elongated along the [011] axis, which are regions corresponding to an increase in the well thickness by a depth of one or several monolayers. The terraces appear due to the existence of growth steps on the interfaces. Anisotropy in the distribution of growth steps, i.e., a longer length of the steps along the [011] axis, is also responsible for the appearance of polarization along the $[0\bar 11]$ axis. Such a polarization appears due to the found specific channel of anisotropic exciton absorption. As a result of such absorption, free excitons with large wave vectors are excited. The excitation of excitons by light is indirect, because it involves additional processes of the elastic scattering of excitons on the interface growth steps. Prevailing scattering on an ensemble of longer growth steps (along the [011] axis) leads to the alignment of the wave vectors of excited excitons. A difference between the absorption probabilities for the polarizations of excitation along the [011] and $[0\bar 11]$ axes is caused by a difference between the probabilities of scattering on steps for excitons whose dipole moments and, correspondingly, the axes of the P-type wave functions for the holes involved in the process are oriented along and across the direction of the alignment of wave vectors of excitons.