Two-photon absorption and third-order nonlinear optical characterization of pyrrolo-tetrathiafulvalene derivatives

To provide an insight into the third-order nonlinear optical (NLO) behaviour of a series of tetrathiafulvalene (TTF)-based molecules, the third-order NLO properties and two-photon absorption characterizations have been theoretically investigated by means of the time-dependent Hartree–Fock method. According to ab-initio calculation results, the examined molecules exhibit second hyperpolarizabilities $(\gamma )$ with non-zero values, implying microscopic third-order optical nonlinearity. Our computed results are also in good agreement with the previous experimental observations on the title compounds.     

QCD nuclear factor and moments of multiplicity distributions in higher orders of perturbation theory

Perturbative solutions to the gluodynamics equations withmodified integral kernel in the second and third orders of the perturbation theory (2NLO, i.e., next-to-next-to-leading order, and 3NLO, i.e., next-to-next-to-next-to-leading order approximations) were found. The effect of the nuclear factor N _S on the behavior of the ratio H _q of cumulant and factorial moments of multiplicity distributions was analyzed. Theoretical conclusions were compared to the results of simulation of p-Pb and Pb-Pb collisions of nuclei with energies of 200 and 546 GeV/nucleon.     

Change in the lattice properties and melting temperature of a face-centered cubic iron under compression

All four parameters of the Mie–Lennard-Jones pair interatomic potential have been determined, and the state equation (P) and baric dependences of the lattice properties of an fcc iron are calculated using a previously proposed method. The dependences have been studied for the following properties: Debye temperature; the first, second, and third Gruneisen parameters; isothermal bulk modulus B _T and B′(P); isochoric specific heat C _v and C _v ′(P); isobaric specific heat C _p ; coefficient of thermal expansion α _p and α _p ′(P); specific surface energy σ and σ′(P). Calculations performed along two isotherms (1500 and 3000 K) have shown good agreement with the experimental data. Analytical approximations of the baric dependences for B′(P), α _p (P), C _p (P), and σ′(P) have been obtained, and it is shown that at P → ∞ the functions B _T (P) and σ(P) change linearly, while the functions α _p′(P) and C _p ′(P) tend to zero. The calculated baric dependence of the melting temperature shows good agreement with the experimental data.     

The nonsinglet spin-dependent structure function evolution by Laplace and characteristics methods

We evaluate the non-singlet spin-dependent structure function g₁^NS at leading order (LO) and next-to-leading order (NLO) by using the Laplace-transform technique and method of characteristics and also obtain its first moment at NLO. The polarized non-singlet structure function results are compared with the data from HERMES (A. Airapetian et al., Phys. Rev. D 75, 012007 (2007)) and E143 (K. Abe et al. (E143 Collab.), Phys. Rev. D 58, 112003 (1998)) at LO and NLO analyses and the first-moment the result at NLO is compared with the result of the NLO GRSV2000 fit. Considering the solution, this method is valid at low- and large-x regions.     

O(N) Random Tensor Models

We define in this paper a class of three-index tensor models, endowed with \({O(N)^{\otimes 3}}\) invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U(N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.     

Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

Hyperpolarizabilities of alkaline-earth metal ions Be+, Mg+, and Ca+

The knowledge of the hyperpolarizabilities of atoms and ions is helpful for the analysis of the high order effects of the frequency shifts in precision spectroscopy experiments. Liu et al. [Phys. Rev. Lett. 114, 223001(2015)] proposed to establish all-optical trapped ion clocks using laser at the magic wavelength for clock transition. To evaluate the high-order frequency shifts in this new scheme of optical clocks, hyperpolarizabilities are needed, but absent. Using the finite field method based on the B-spline basis set and model potentials, we calculated the electric-field-dependent energy shifts of the ground and low-lying excited states in Be+, Mg+, and Ca+ in the field strength range of 0.0-6×10.5 a.u.. The scalar and tensor polarizabilities(α0, α2) and hyperpolarizabilities(γ0, γ2, γ4) were deduced. The results of the hyperpolarizabilities for Be+ showed good agreement with the values in literature, implying that the present method can be applied for the effective estimation of the atomic hyperpolarizabilities,which are rarely reported but needed in experiments. The feasibility of optical trapping of Ca+ is discussed, and the contributions of hyperpolarizabilities to the transition frequency shift for Ca+ in the optical dipole trap are estimated using quasi-electrostatic approximation.     

On rational functions of first-class complexity

It is proved that, for every rational function of two variables P(x, y) of analytic complexity one, there is either a representation of the form f(a(x) + b(y)) or a representation of the form f(a(x)b(y)), where f(x), a(x), b(x) are nonconstant rational functions of a single variable. Here, if P(x, y) is a polynomial, then f(x), a(x), and b(x) are nonconstant polynomials of a single variable.     

The effects of the composition,temperature and geometry on the hysteretic properties of the Ising-type barcode nanowire

In the present study, a theoretical approach to investigate the magnetic hysteresisproperties in barcode nanowire are used and applied to study Ising system on hexagonalstructure. The hysteresis behaviors of Ising-type barcode nanowire (IBN) are studiedwithin the effective-field theory with correlations. The effects of the composition(p),temperature (T) and geometry (interlayer length (d), shell length(s), andwire length (r)) on the hysteresis behaviors are examined indetail. The phase diagrams are presented in the five different planes, namely(p,T),(d,r),(d, T), (r, T) and (s, T) as function of coercive field (H _C ) and remanence(M _r ), and investigatedsoft/hard the magnetic characteristics of the system. We find that the hysteresis loopsareas decrease case as the temperature, wire and lengths increase. Moreover, whenp increasesthe hysteresis loop areas increase. Moreover, H _C exhibits an increasein around d =1 value, then H _C does not change withthe increasing d values. Theoretical results have qualitativelycompatible with some experimental works of multilayer nanowire.     

Low-Temperature Transport Properties of Lanthanum Hexaboride La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript> Single Crystals

Resistivity (ρ), thermal conductivity (k) and Seebeck coefficient (S) of La_1–xCe_xB₆ single crystals with various concentrations of cerium Ce ions was measured in a wide temperature range 3?300 K. The obtained data were analyzed in the framework of the Coqblin–Shrieffer model. The contributions of scattering of carriers on magnetic ions Ce for all transport parameters ρ(T), k(T), S(T) are revealed. Strong dependence of the magnetic scattering on concentration of the cerium ions are identified. The anomalous behavior of the transport parameters ρ(T), k(T), S(T) in the region near 30 K is attributed to the Δ ~ 30 K splitting of Г₈ level.     

Experimental Research to Confirm the Excitation of Gamov–Teller Resonance in Compound Nucleus <Superscript>118</Superscript>Sb

At proton energies of 4–9 MeV, trial experimental investigations were performed to confirm the excitation of Gamov–Teller resonance (GTR) 1⁺ in the compound nucleus ¹¹⁸Sb discovered by B.Ya. Guzhovskiy’s research group in the ¹¹⁷Sn(p,xn) reaction at proton energies of 7.2 MeV (the first component is GTR1) and 9.9MeV (the second component is GTR2). The ¹¹⁷Sn(p,xn) reaction was used, whose neutrons and background neutrons were registered by an all-wave long counter arranged at an angle of 140° to the direction of the proton beam propagation. Simultaneously, along with the registration of neutrons, elastically and inelastically scattered protons at angles of 20° and 160° were registered. At the proton energy equal to ~7.2 MeV, in the excitation functions for ¹¹⁷Sn(p,xn), ¹¹⁷Sn(p,p₀), and ¹¹⁷Sn(p,p₄)¹¹⁷Sn* (1004.5 keV, 3/2⁺), a resonance with a width of ≈1.2 MeV having an energy structure was discovered. Its possible quantum numbers are 1⁺.     

A Theoretical Study on <Emphasis Type="Italic">N</Emphasis>′-[(<Emphasis Type="Italic">Z</Emphasis>)-(4-Methylphenyl)Methylidene]-4-Nitrobenzohydrazide (NMPMN)

Quantum mechanical calculations of ground state energy, vibration wavenumbers, and electronic absorption wavelengths of N′-[(Z)-(4-methylphenyl)methylidene]-4-nitrobenzohydrazide with C15H13N3O3 empirical formula was performed by using Gaussian 09 program. Becke’s three-parameter exchange functional in conjunction with the Lee-Yang-Parr correlation functional and Heyd-Scuseria-Ernzerhof functional levels of density functional theory (DFT) with the 6-311++G(d,p) basis set were used in the performing of above mentioned calculations. The highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO) energies have been also calculated at the same levels. Stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analyzed using natural bond orbital (NBO) analysis. Nonlinear optical (NLO) behavior of the title molecule has been examined by the determining of electric dipole moment (μ), polarizability (α), and static first-order hyperpolarizability (β). Finally, molecular electrostatic potential (MEP) surface as well as Mulliken and NBO atomic charges were calculated by using Gaussian 09 program.     

RETRACTED ARTICLE: Density,viscosity and speed of sound of benzaldehyde with benzene at 303.15, 308.15, and 313.15 K

The values of density, viscosity and speed of sound for the binary liquid mixture of Benzaldehyde with Benzene were measured over the entire range of composition at 303.15, 308.15, and 313.15 K. These values are used to calculate the excess molar volume (V ^E), deviation in viscosity (Δη), deviation in speed of sound (ΔU), deviation in isentropic compressibility (Δβ _s ), excess internal pressure (Δπ), excess intermolecular free length (ΔL _f ), excess free volume (V _E ^f ) and excess acoustic impedance (ΔZ). McAllister’s three-body interaction model is used for correlating Kinematic Viscosity of binary mixtures. The excess values were correlated using the Redlich–Kister polynomial equation to obtain their coefficients and standard deviations. The thermophysical properties (density, viscosity, and speed of sound) under the study were fit to the Jouyban–Acree model.     

Variations in thermal properties of diamond under isothermal compression

State equation P(V/V ₀, T) and baric dependences of thermal properties of diamond have been obtained without any fitting parameters from the interatomic pair Mie–Lennard-Jones potential and the Einstein model of a crystal. Calculations have been performed along two isotherms (at T = 300 and 3000 K) up to P = 10000 kbar = 1000 GPa, i.e., to a relative volume of V/V ₀ = 0.5. The baric dependences have been obtained for the following characteristics: isothermal elastic modulus B _T and B'(P), isochoric heat capacity C _v and C _v ' (P), isobaric heat capacity C _p ; thermal expansion coefficient α _p and α _p ' (P); and specific surface energy σ, as well as its derivatives σ'(P) and σ'(T). It is shown that for P → ∞, functions B _T (P) and σ(P) vary linearly, functions B'(P), α _p (P), C _v (P), C _p (P) and σ'(P) tend to constants, while functions α _p '(P), C _v '(P), and difference C _p (P)–C _v (P) tend to zero. Good agreement with experimental data has been demonstrated.     

Analysis of the angular distribution of Auger electrons in a Xe atom

The angular distribution of Auger electrons, and the numerically calculated anisotropy parameters of the angular distribution α for (M₃ → N₂N₃), (M₃ → N₃N₃), (M₄ → N₁N₃), (M₄ → N₄N₅), (M₄ → N₅N₅), and (M_4,5 → O_{2, 3}O_{2, 3}) transitions in a Xe atom are given. The matrix elements are calculated by using the nonrelativistic Hartree-Fock method in LS coupling and the relativistic Hartree-Fock-Dirac method in both jj coupling (the single-configuration approximation) and intermediate coupling (the multiconfiguration approximation).     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Magnetoresistance of a highly correlated electron liquid

The behavior in a magnetic field of a highly correlated electron liquid approaching the fermion condensation quantum phase transition from the disordered phase is considered. We show that, at sufficiently high temperatures T≥T*(x), the effective mass starts to depend on T, M* ∝T^?1/2. This T^?1/2 dependence of the effective mass at elevated temperatures leads to the non-Fermi liquid behavior of the resistivity, σ(T) ∝ T and at higher temperatures σ(T) ∝ T^3/2. The application of a magnetic field B restores the common T² behavior of the resistivity. The effective mass depends on the magnetic field, M*(B) ∝ B^?2/3, being approximately independent of the temperature at T≤T*(B) ∝ B^4/3. At T≥T*(B), the T^?1/2 dependence of the effective mass is reestablished. We demonstrate that this B-T phase diagram has a strong impact on the magnetoresistance (MR) of the highly correlated electron liquid. The MR as a function of the temperature exhibits a transition from negative values of MR at T→0 to positive values at T ∝ B^4/3. Thus, at T≥T*(B), MR as a function of the temperature possesses a node at T ∝ B^4/3.     

Galvanomagnetic properties of atomically disordered Sr<Subscript>2</Subscript>RuO<Subscript>4</Subscript> single crystals

The effect of neutron-bombardment-induced atomic disorder on the galvanomagnetic properties of Sr₂RuO₄ single crystals has been experimentally studied in a broad range of temperatures (1.7–380 K) and magnetic fields (up to 13.6 T). The disorder leads to the appearance of negative temperature coefficients for both the in-plane electric resistivity (ρ_a) and that along the c axis (ρ_c), as well as the negative magnetoresistance Δρ, which is strongly anisotropic to the magnetic field orientation (H ∥ a and H ∥ c), with the easy magnetization direction along the c axis and a weak dependence on the probing current direction in the low-temperature region. The experimental ρ_a(T) and ρ_c(T) curves obtained for the initial and radiation-disordered samples can be described within the framework of a theoretical model with two conductivity channels. The first channel corresponds to the charge carriers with increased effective masses (～10m _e , where m _e is the electron mass) and predominantly electron-electron scattering, which leads to the quadratic temperature dependences of ρ_a and ρ_c. The second channel corresponds to the charge carriers with lower effective masses exhibiting magnetic scattering at low temperatures, which leads to the temperature dependence of the ρ_{a, c}(T) ∝ 1/T type.