Peculiarities of the SEHRS spectrum of 4,4′-bipyridine molecule

The SEHRS spectrum of 4,4′-bipyridine is analyzed on the base of the Dipole-Quadrupole theory. It is demonstrated that there appear strong lines caused by vibrations transforming after the unit irreducible representation of the D₂ symmetry group, which is most probably describes the symmetry properties of the molecule. These lines are nearly forbidden for the molecule, adsorbed on rough metal surfaces. Appearance of these lines is associated with a strong quadrupole light–molecule interaction, which exists in this system. In addition, there are lines caused by contributions from both the vibrations transforming after the unit irreducible representation A and the representation B₁, which describes transformational properties of the d_z component of the dipole moment, which is perpendicular to the surface. This result is associated with the specific geometry of the molecule, when the indicated vibrations can be nearly degenerate and cannot be resolved by the SEHRS spectra analysis. Analysis of the SEHRS spectra for the possible geometry of the molecule with the D_2h symmetry group leads to similar results. This issue is in a full coincidence with the results of the SEHRS Dipole-Quadrupole theory.     

Behavior of intense acoustic noise at large distances

Propagation of intense acoustic noise waves is investigated in the case of a nonplanar geometry. It is shown that, at large distances from the source, where the nonlinear effects become negligible, the spectrum of such waves has a universal self-similar shape. The amplitude of the spectrum is determined by a single constant D _∞ = D _∞(?, R ₀) (the spectrum steepness at zero-valued argument) whose value depends on two dimensionless parameters: the inverse acoustic Reynolds number ? and the dimensionless radius R ₀. It is shown that the plane of dimensionless parameters (?, R ₀) can be divided into four regions, so that, within each of them, the quantity D _∞ is described by a universal function of these parameters. The numerical factors of these parameters are found from numerical simulations.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

The simplest non-minimal matter–geometry coupling in the <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) cosmology

f(R, T) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar R and the trace of the energy-momentum tensor T. In this way, f(R, T) models are capable of describing a non-minimal coupling between geometry (through terms in R) and matter (through terms in T). In this article we construct a cosmological model from the simplest non-minimal matter–geometry coupling within the f(R, T) gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter–geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the f(R, T) formalism in order to check its reliability in other fields, rather than cosmology.     

Black-hole solutions in <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity with conformal anomaly

In this paper, we consider F(R)=R+f(R) theory instead of Einstein gravity with conformal anomaly and look for its analytical solutions. Depending on the free parameters, one may obtain both uncharged and charged solutions for some classes of F(R) models. Calculation of Kretschmann scalar shows that there is a singularity located at r=0. The geometry of uncharged (charged) solution corresponds to the Schwarzschild (Reissner–Nordström) singularity. Further, we discuss the viability of our models in detail. We show that these models can be stable, depending on their parameters and in different epochs of the universe.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

Manifestation of a strong quadrupole interaction and peculiarities in the SERS and SEHRS spectra of 4,4'-bipyridine

The paper analyzes Surface Enhanced Raman Scattering (SERS) and Surface Enhanced Hyper Raman Scattering (SEHRS) spectra of 4,4'-bypiridine molecule for two possible geometries, which are described by D ₂ and D _2h symmetry groups. It is pointed out on appearance of sufficiently strong lines, caused by vibrations with the unit irreducible representation for both possible configurations. Appearance of these lines in the SEHRS spectrum points out the existence of a strong quadrupole light-molecule interaction. In addition one observes the lines, caused by vibrations both with the unit irreducible representations A or A _g and the irreducible representation B ₁ or B _1u . The last ones describe transformational properties of the d _z component of the dipole moment, which is perpendicular to the surface. This property of the spectrum is caused by peculiarity of the geometry of the molecule, which consists of two benzene rings, which are weakly connected with each other. The linear combinations of the vibrations of the rings create two nearly degenerated symmetric and anti symmetrical states, which cannot be identified in the experimental spectra. The result is in a full agreement with the dipole-quadrupole theory of SERS and SEHRS.     

Molecular structure and spectral (FT-IR,Raman) investigations of 3-aminocoumarin

The molecular structure of 3-Aminocoumarin was determined by conformational analysis. Conformational space was scanned by conformer distribution option of Spartan 08 program package using Merck Molecular Force Field (MMFF) method. Then obtained conformers were optimized by B3LYP/6-311++G(d, p) and B3LYP/6-311G(d, p) levels of Density Functional Theory. As a result of these calculations, only one conformer was determined. Vibrational frequencies of this conformer were calculated by Gaussian 03 program package using the same levels of geometry optimizations. The FT-IR and Raman spectra of 3-Aminocoumarin were recorded and compared with the calculated values. Consequently, a good agreement between experimental and the calculated values were founded. Molecular electrostatic potentials (MEPs), HOMO-LUMO energies, thermodynamic properties and Mulliken atomic charges were also covered in this study.     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.     

Low energy frontier: Physics with polarized cold neutrons

Recent developments in investigations of beta decay of the free neutron are discussed. Measurements of the neutron lifetime τ _n and the electron emission asymmetry A _n are a classic source of determination of the Standard Model parameters G _v , G _A and λ _n . Combined with the results of the muon decay experiments, the nuclear superallowed 0→0 transitions and decays of particles containing heavy quarks, they provide tests of the SM assumptions: the unitarity of the CKM matrix, the number of the neutrino families, or the CVC hypothesis. In contrast, more complex correlations between the spins and the momenta of the emitted particles, (e.g. B _n , D _n , R _n or G _n ), are uniquely sensitive to the so called “Physics beyond the Standard Model”. Thus the question of the right handed bosons, the admixture of the scalar or tensor interaction, with or without time reversal violating terms, may be addressed separately in a dedicated, single experiment. Further development of powerful beams of polarized cold neutrons and sources of ultracold neutrons is imperative for progress in these studies.     

Molecular dynamics study of the growth of a metal nanoparticle array by solid dewetting

We investigated the effect of the substrate and the ambient temperature on the growth of a metal nanoparticle array (nanoarray) on a solid-patterned substrate by dewetting a Au liquid film using an atomic simulation technique. The patterned substrate was constructed by introducing different interaction potentials for two atom groups (C₁ and C₂) in the graphene-like substrate. The C₁ group had a stronger interaction between the Au film and the substrate and was composed of regularly distributed circular disks with radius R and distance D between the centers of neighboring disks. Our simulation results demonstrate that R and D have a strikingly different influence on the growth of the nanoparticle arrays. The degree of order of the nanoarray increases first before it reaches a peak and then decreases for increasing R at fixed D. However, the degree of order increases monotonously when D is increased and reaches a saturated value beyond a critical value of D for a fixed R. Interestingly, a labyrinth-like structure appeared during the dewetting process of the metal film. The simulation results also indicated that the temperature was an important factor in controlling the properties of the nanoarray. An appropriate temperature leads to an optimized nanoarray with a uniform grain size and well-ordered particle distribution. These results are important for understanding the dewetting behaviors of metal films on solid substrates and understanding the growth of highly ordered metal nanoarrays using a solid-patterned substrate method.     

On double polarization asymmetries in the elastic electron-proton scattering

Double polarization asymmetry D_p^(M) for the process of elastic electroweak scattering of the longitudinally polarized electrons by polarized proton target is considered with account of anapole G_1p and electric dipole moment (EDM) G_2p proton form factors. This asymmetry is only due to T-parity violating form factor G_2p, but does not directly depend on it, and having a significant value, allows to confirm the existence of the EDM of the proton.     

Collisional Broadening of CO<Subscript>2</Subscript> Transition Lines 10<Superscript>0</Superscript>0–00<Superscript>0</Superscript>1 by Inert Gas Atoms at 300–700 K

The spectrum of excitation of Rydberg states of thallium atoms has been investigated using a collimated atomic beam in a two-step isotope selective laser scheme 6²P_1/2 → 6²D_3/2 → Tl** in the presence of an electric field with a strength of up to 1.5 kV/cm near the level 16F_5/2. The optical transitions 6D_3/2 → 18D_3/2 and 6D_3/2 → 16G_7/2, which were induced by an external electric field and dipole-forbidden, have been studied experimentally. The values for the scalar polarizabilities (in units сm^–1/(kV/сm)²) α₀(16F_5/2) = 3.71 ± 0.3, α₀(18D_3/2) = 11.70 ± 0.25, and α₀(16G_7/2) = 44.1 ± 0.9, which are compared with the calculated one, have been obtained. The new values of energy parameters for the states 18D_3/2 and 16G_7/2 have been determined.     

Early stages of generation of two-dimensional structures by the Hastings-Levitov method of conformal mapping dynamics

Two-dimensional structures obtained by the Hastings-Levitov conformal mapping were studied for a relatively small number of mappings n. The fractal dimension D of these structures is computed by the recent Davidovitch-Procaccia technique [6] as a function of n. For small n < n₀ (where n₀ is the number of particles at the first layer), D exponentially decreases, which should have supported the conclusion made in [6] about the possibility of determining the fractal dimension with an arbitrary accuracy using a relatively small number of mappings n≈ n₀. On the other hand, it turned out that D irregularly deviates from a certain quantity D₀ depending on the initial size of the bump \(\sqrt {\lambda _0 } \), which contradicts the main assertion of     

Optimal Synthesis of the Joint Unitary Evolutions

Joint unitary operations play a central role in quantum communication and computation. We give a quantum circuit for implementing a type of unconstructed useful joint unitary evolutions in terms of controlled-NOT (CNOT) gates and single-qubit rotations. Our synthesis is optimal and possible in experiment. Two CNOT gates and seven R _x , R _y or R _z rotations are required for our synthesis, and the arbitrary parameter contained in the evolutions can be controlled by local Hamiltonian or external fields.     

Homogeneous interaction of ion-pair states of ClF

The energies, rotational constants, and isotope shifts of vibrational levels of the homogeneously perturbed ion-pair states E, f, β, and Gof the ClF molecule are calculated by the methods of diabatic and adiabatic potentials. The spectroscopic constants of initial diabatic potentials and the parameters of interaction for which the best agreement between theory and experiment is achieved are presented.     

Optimization of sub-Doppler absorption contour in gas-dynamic beams

The formation of the Doppler contour P _D(?) of absorption lines upon the excitation of particles in the volume of a gas-dynamic beam by light propagating in a direction orthogonal (reduced) to the beam axis is analyzed. Integral representations of P _D(?) are obtained for arbitrary relations between the nozzle outlet diameter D and the collimating aperture diameter B in the excitation region are obtained. An optimal configuration at which the reduced Doppler contour is the narrowest at a high density of beam particles is revealed to be B/D = 2.     

Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics

The Rényi entropies R_p [ ρ], p> 0,≠ 1 of the highly-excited quantum states of the D-dimensional isotropicharmonic oscillator are analytically determined by use of the strong asymptotics of theorthogonal polynomials which control the wavefunctions of these states, the Laguerrepolynomials. This Rydberg energetic region is where the transition from classical toquantum correspondence takes place. We first realize that these entropies are closelyconnected to the entropic moments of the quantum-mechanical probability ρ_n(r)density of the Rydberg wavefunctions Ψ_{n,l, { μ}}(r); so, to the?_p-norms of the associated Laguerrepolynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques ofapproximation theory based on the strong Laguerre asymptotics. Finally, we determine thedominant term of the Rényi entropies of the Rydberg states explicitly in terms of thehyperquantum numbers (n,l), the parameter order p and the universedimensionality D for all possible cases D ≥ 1. We find that (a) theRényi entropy power decreases monotonically as the order p is increasing and (b) thedisequilibrium (closely related to the second order Rényi entropy), which quantifies theseparation of the electron distribution from equiprobability, has a quasi-Gaussianbehavior in terms of D.     

The Hilbert series of the one instanton moduli space

The moduli space of k G-instantons on \( {\mathbb{R}^4} \) for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have \( \mathcal{N} = 2 \) supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.     

Finite-size scaling from the self-consistent theory of localization

Accepting the validity of Vollhardt and Wölfle’s self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case and based on the consideration of auxiliary quasi-1D systems. The obtained scaling functions for d = 2 and d = 3 are in good agreement with numerical results: it signifies the absence of substantial contradictions with the Vollhardt and Wölfle theory on the level of raw data. The results ν = 1.3–1.6, usually obtained at d = 3 for the critical exponentν of the correlation length, are explained by the fact that dependence L + L ₀ with L ₀ > 0 (L is the transversal size of the system) is interpreted as L ^1/ν with ν > 1. The modified scaling relations are derived for dimensions d ≥ 4; this demonstrates the incorrectness of the conventional treatment of data for d = 4 and d = 5, but establishes the constructive procedure for such a treatment. The consequences for other finite-size scaling variants are discussed.