The introduction, within a π-conjugated donor−acceptor molecule, of an intermediate barrier to electron tunneling and its size scaling and influence on electronic polarization properties have remained so far elusive issues of great potential interest toward the fine-tuning of the linear and nonlinear optical properties of molecular materials. Paracyclophane (pCP) provides a most relevant cornerstone for more elaborate compounds where donor and acceptor substituents are made to interact through a sterically constrained π−π stack. A first attempt in this direction is reported here with the synthesis of a model dipolar 4-(4-dihexylaminostyryl)-16-(4-nitrostyryl)[2.2]paracyclophane and the subsequent experimental and theoretical study of its quadratic nonlinear optical properties. A major outcome of this investigation is the evidence of a significant “through-space” charge transfer as unambiguously designated by the strong departure of the β quadratic hyperpolarizability tensor of the full doubly substituted molecule (60 × 10-30 esu) from the additive β value (18 × 10-30 esu) expected for strictly noninteracting singly substituted pCP moieties. This desired increase of nonlinear efficiency upon substitution is not offset by the usual red-shift of the absorption spectrum which generally curtails application perspectives in more common uninterrupted conjugated chains. The collective nonlinear polarization behavior involving the full end-to-end molecular structure is confirmed by theoretical calculations using the Collective Electron Oscillator (CEO) approach which furthermore indicates a significantly enhanced role of electron−hole pair delocalization in the higher order nonlinear response, compared to the linear polarizability or the static dipole moment.

A new subtraction procedure for removal both ultraviolet and infrared divergences in Feynman integrals is proposed. This method is developed for computation of QED corrections to the electron anomalous magnetic moment. The procedure is formulated in the form of a forest formula with linear operators that are applied to Feynman amplitudes of UV-divergent subgraphs. The contribution of each Feynman graph that contains propagators of electrons and photons is represented as a finite Feynman-parametric integral. Application of the developed method to the calculation of 2-loop and 3-loop contributions is described.

The relation between the orientation of particles in ice-crystal clouds and backscattering phase matrices (BSPMs) is considered. Parameters characterizing the predominant orientation of particles in the azimuthal direction and in the horizontal position are presented. The parameters are expressed through BSPM elements. A technique for measuring BSPM elements with lidar is described. Examples of some measurements are presented along with a statistical generalization of the results from more than 400 BSPM measurements. It is found that the orientation of coarse particles with large diameters in an azimuthal direction and in a horizontal position is more probable than in a random direction. However, the orientation of large particles is often masked by small particles that are not subject to the effect of orienting factors. Thus the mean parameters characterizing the state of orientation of particles in clouds as a whole correspond to weak orientation. It is supposed that the orientation of particles in the azimuthal direction is caused by wind-velocity pulsations.

We predict nanoscale field and dipole patterns due to the broken uniformity of a laser-driven local field in 1D and 2D lattices. They may result in size-related resonances and large field enhancement, which in turn can give rise to low-intensity nonlinear optical effects, e.g., optical bistability, even in the ultimate case of a pair of coupled atoms. At certain, "magic" numbers and configurations of atoms in a lattice, the system may exhibit the self-induced cancellation of the suppression of a local field.

This paper presents a new method of numerical computation of the massindependent QED contributions to the electron anomalous magnetic moment which arise from Feynman graphs without closed electron loops. The method is based on a forest-like subtraction formula that removes all ultraviolet and infrared divergences in each Feynman graph before integration in Feynman-parametric space. The integration is performed by an importance sampling Monte-Carlo algorithm with the probability density function that is constructed for each Feynman graph individually. The method is fully automated at any order of the perturbation series. The results of applying the method to 2-loop, 3-loop, 4-loop Feynman graphs, and to some individual 5-loop graphs are presented, as well as the comparison of this method with other ones with respect to Monte Carlo convergence speed.

The major assumption of the Lorentz-Lorenz theory about uniformity of local fields and atomic polarization in dense material does not hold in finite groups of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett. 101, 133902 (2008)]. The uniformity is broken at sub-wavelength scale, where the system may exhibit strong stratification of local field and dipole polarization, with the strata period being much shorter than the incident wavelength. In this paper, we further develop and advance that theory for the most fundamental case of one-dimensional arrays, and study nanoscale excitation of so called "locsitons" and their standing waves (strata) that result in size-related resonances and related large field enhancement in finite arrays of atoms.The locsitons may have a whole spectrum of spatial frequencies, ranging from long waves, to an extent reminiscent of ferromagnetic domains, -to super-short waves, with neighboring atoms alternating their polarizations, which are reminiscent of antiferromagnetic spin patterns. Of great interest is the new kind of "hybrid" modes of excitation, greatly departing from any magnetic analogies. We also study differences between Ising-like near-neighbor approximation and the case where each atom interacts with all other atoms in the array. We find an infinite number of "exponential eigenmodes" in the lossless system in the latter case. At certain "magic" numbers of atoms in the array, the system may exhibit self-induced (but linear in the field) cancellation of resonant local-field suppression. We also studied nonlinear modes of locsitons and found optical bistability and hysteresis in an infinite array for the simplest modes. This paper is now published, with very minor changes, in Phys. Rev. A 79, 053834 (2009).

This paper describes a computation of a part of the QED contribution to the electron anomalous magnetic moment that was performed by the author with the help of a supercomputer. The computed part includes all 5-loop QED Feynman graphs without lepton loops. The calculation has led to the result A (10) 1 [no lepton loops] = 6.793(90) that is slightly different than the value 7.668(159) presented by T. Aoyama, T. Kinoshita, and M. Nio in 2018. The discrepancy is about 4.8σ . The computation gives the first independent check for that value. A shift in the fine-structure constant prediction is revealed in the paper. The developed calculation method is based on (a) a subtraction procedure for removing all ultraviolet and infrared divergences in Feynman parametric space before integration; (b) a nonadaptive Monte Carlo integration that uses the probability density functions that are constructed for each Feynman graph individually using its combinatorial structure. The method is described briefly in the paper (with the corresponding references to the previous papers). The values for the contributions of nine gauge-invariant classes splitting the whole set are presented in the paper. Moreover, the whole set of all 5-loop graphs without lepton loops is split into 807 subsets for comparison (in the future) of the calculated values with the values obtained by another methods. These detailed results are presented in the supplemental materials. Also, the supplemental materials contain the contribution values for each of 3213 individual Feynman graphs. An "oscillating" nature of these values is discussed. A realization of the numerical integration on the graphics accelerator NVidia Tesla V100 (as a part of the supercomputer "Govorun" from JINR, Dubna) is described with technical details such as pseudorandom generators, calculation speed, code sizes and structure, prevention of round-off errors and overflows, etc.

Virtual reality techniques provide a unique new way to interact with three-dimensional digital objects. Virtual prototyping refers to the use of virtual reality to obtain evaluations of designs while they are still in digital form before physical prototypes are built. While the state-of-the-art in virtual reality relies mainly on the use of stereo viewing and auditory feedback, commercial haptic devices have recently become available that can be integrated into the virtual environment to provide force feedback to the user. This paper outlines a study that was performed to determine whether the addition of force feedback to the virtual prototyping task improved the ability of the participants to make design decisions. Seventy-six people participated in the study. The specific task involved comparing the location and movement of two virtual parking brakes located in the virtual cockpit of an automobile. The results indicate that the addition of force feedback to the virtual environment did not increase the accuracy of the participants' answers, but it did allow them to complete the task in a shorter time. This paper describes the purpose, methods, and results of the study.