Structure of multicorrelation sequences with integer part polynomial iterates along primes

Let $T$ be a measure preserving $\mathbb{Z}^\ell$-action on the probability space $(X,{\mathcal B},\mu),$ $q_1,\dots,q_m:{\mathbb R}\to{\mathbb R}^\ell$ vector polynomials, and $f_0,\dots,f_m\in L^\infty(X)$. For any $\epsilon > 0$ and multicorrelation sequences of the form $\displaystyle\alpha(n)=\int_Xf_0\cdot T^{ \lfloor q_1(n) \rfloor }f_1\cdots T^{ \lfloor q_m(n) \rfloor }f_m\;d\mu$ we show that there exists a nilsequence $\psi$ for which $\displaystyle\lim_{N - M \to \infty} \frac{1}{N-M} \sum_{n=M}^{N-1} |\alpha(n) - \psi(n)| \leq \epsilon$ and $\displaystyle\lim_{N \to \infty} \frac{1}{\pi(N)} \sum_{p \in {\mathbb P}\cap[1,N]} |\alpha(p) - \psi(p)| \leq \epsilon.$ This result simultaneously generalizes previous results of Frantzikinakis [2] and the authors [11,13].Comment: 7 page

Theoretical analysis of dynamic chemical imaging with lasers using high-order harmonic generation

We report theoretical investigations of the tomographic procedure suggested by Itatani {\it et al.} [Nature, {\bf 432} 867 (2004)] for reconstructing highest occupied molecular orbitals (HOMO) using high-order harmonic generation (HHG). Using the limited range of harmonics from the plateau region, we found that under the most favorable assumptions, it is still very difficult to obtain accurate HOMO wavefunction, but the symmetry of the HOMO and the internuclear separation between the atoms can be accurately extracted, especially when lasers of longer wavelengths are used to generate the HHG. We also considered the possible removal or relaxation of the approximations used in the tomographic method in actual applications. We suggest that for chemical imaging, in the future it is better to use an iterative method to locate the positions of atoms in the molecule such that the resulting HHG best fits the macroscopic HHG data, rather than by the tomographic method.Comment: 13 pages, 14 figure

Simple Model of Nonlinear Spin Waves in Graphene Structures

A series of theoretical and experimental works are known which investigated the magnetic properties of graphene structures. This is due, among other things, to the prospects of using graphene as a material for the needs of the future nanoelectronics and spintronics. In particular, it is known about the presence of ferromagnetic properties at temperatures up to 200 C and above in single-layer graphene films that are free from impurities. Previously there was proposed a quantum field theoretical model describing the possible mechanism of ferromagnetism in graphene as a result of the spontaneous breaking of spin symmetry of the surface density of valence electrons. The possible spatial configurations of the localized spin density were described. In this paper, we investigate such spatially localized nonlinear spin configurations of the valence electron density on the graphene surface such as kinks, and their interactions, as well as quasibound metastable states of the interacting kinks and antikinks, that are breathers. The spectrum of such breathers is investigated. It is shown that under certain conditions, this spectrum has a discrete sector, which, in turn, allows us to speak about the possibility of coherent quantum generation of spin waves in graphene structures, which is important in terms of practical applications in nanoelectronics and spintronics. &nbsp

Theory of high-order harmonic generation from molecules by intense laser pulses

We show that high-order harmonics generated from molecules by intense laser pulses can be expressed as the product of a returning electron wave packet and the photo-recombination cross section (PRCS) where the electron wave packet can be obtained from simple strong-field approximation (SFA) or from a companion atomic target. Using these wave packets but replacing the PRCS obtained from SFA or from the atomic target by the accurate PRCS from molecules, the resulting HHG spectra are shown to agree well with the benchmark results from direct numerical solution of the time-dependent Schr\"odinger equation, for the case of H$_2^+$ in laser fields. The result illustrates that these powerful theoretical tools can be used for obtaining high-order harmonic spectra from molecules. More importantly, the results imply that the PRCS extracted from laser-induced HHG spectra can be used for time-resolved dynamic chemical imaging of transient molecules with temporal resolutions down to a few femtoseconds.Comment: 10 pages, 5 figure

Extracting conformational structure information of benzene molecules via laser-induced electron diffraction

Citation: Ito, Y., Wang, C., Le, A. T., Okunishi, M., Ding, D., Lin, C. D., & Ueda, K. (2016). Extracting conformational structure information of benzene molecules via laser-induced electron diffraction. Structural Dynamics, 3(3). doi:10.1063/1.4952602We have measured the angular distributions of high energy photoelectrons of benzene molecules generated by intense infrared femtosecond laser pulses. These electrons arise from the elastic collisions between the benzene ions with the previously tunnel-ionized electrons that have been driven back by the laser field. Theory shows that laser-free elastic differential cross sections (DCSs) can be extracted from these photoelectrons, and the DCS can be used to retrieve the bond lengths of gas-phase molecules similar to the conventional electron diffraction method. From our experimental results, we have obtained the C-C and C-H bond lengths of benzene with a spatial resolution of about 10 pm. Our results demonstrate that laser induced electron diffraction (LIED) experiments can be carried out with the present-day ultrafast intense lasers already. Looking ahead, with aligned or oriented molecules, more complete spatial information of the molecule can be obtained from LIED, and applying LIED to probe photo-excited molecules, a "molecular movie" of the dynamic system may be created with sub-Ångström spatial and few-ten femtosecond temporal resolutions. © 2016 Author(s)

Operator method in solving non-linear equations of the Hartree-Fock type

The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron ground-state energy. Energies for 2s- and 3s-states are also calculated. The other excited states are briefly discussed.Comment: 7 page

Imaging an Isolated Water Molecule with an Attosecond Electron Wave Packet

We use laser-induced electron diffraction (LIED) to self-image the molecular structure of an isolated water molecular ion using its own retuning attosecond electron wave packet (EWP). Using LIED\u27s subfemtosecond and picometre spatio-temporal resolution imaging capabilities, we observe the symmetric stretching of the O-H and H-H internuclear distances with increasing laser field strength

Synthesis and Photocatalytic Activity for Toluene Removal of CDs/TiO2 - Zeolite Y

Hydrothermally synthesized carbon nanodots (CDs) were impregnated on TiO2. The product (CDs/TiO2) was mechanically mixed with zeolite Y for application in toluene photocatalytic oxidation reaction under UV radiation. Material properties of the samples were investigated by different methods. Toluene vapor was chosen as a typical volatile organic compound to investigate the performance of CDs/TiO2 – zeolite Y photocatalyst when these technological parameters were changed: toluene concentration, gas flow rate, humidity and UV light intensity. In each reaction, only one parameter was changed and the remaining conditions were fixed. The toluene concentrations at the beginning and the end of each reaction were analyzed with the use of gas chromatography (GC). The results of different reaction conditions show the trends for toluene treatment of the CDs/TiO2 – zeolite Y catalyst, thereby providing specific explanations for these trends. The experiments also show that toluene removal is highest when the toluene concentration in the inlet gas is 314 ppmv, the flow rate is 3 L/h, the humidity is 60%, and the catalyst (CDs/TiO2 – zeolite Y composite with 70% zeolite in weight) is illuminated by 4 UV lamps. Copyright © 2022 by Authors, Published by BCREC Group. This is an open access article under the CC BY-SA License (https://creativecommons.org/licenses/by-sa/4.0).