Theory of spatial dispersion of dielectric and magnetic constants in magnetic uniaxial gyrotropic crystals

The theory of spatial dispersion of dielectric and magnetic constants of magnetic uniaxial crystals based on generalized Maxwell’s equations D = ε?E = (ε + inγ E = ?ns ^× H and B = μ?H = (μ + inδ)H = ns ^× E with spatial dispersion parameters γ and δ is considered. Generalized Fresnel’s and polarization equations for the obtained vectors E, D, H, and B are analyzed for the wave normal direction s ⊥ C (where C is the optic axis of a crystal). The possibility of the existence of a third natural wave in a crystal is proved.     

Specific features of the thermal electromotive force in Bi quantum wires in transverse magnetic and electric fields

The thermal electromotive force (emf) in Bi quantum wires has been calculated in the model of potential in the form of a paraboloid of revolution in a uniform magnetic field H, which is normal to the axis of the studied nanostructure, and in a direct-current (dc) electric field E ‖ H. It has been shown that, with an increase in E, the thermal emf α _xx is described by a nonmonotonic function at different values of H. A physical interpretation of this behavior of α _xx as a function of E is proposed with account for the interaction between carriers and the rough surface of the nanowire.     

Magnetic-field and temperature effects on the optical properties of dicyano-2,2′-bipyridyl-platinum(II) single crystals

Studies of the polarized emission of [Pt(CN)₂(bipy)] single crystals as function of temperature (1.9 K ⩽ T ⩽ 295 K) and homogeneous magnetic fields (0 ⩽ H ⩽ 6 T), and the temperature dependence of the polarized absorption spectrum are reported. Raising the temperature from 1.9 to 7 K or increasing the magnetic field from 0 to 1 T results in a blue shift of ≈175 cm^-1 in the E ⊥ a polarized emission (E: electric field vector, a: crystallographic a axis). Between 1.9 and 295 K at H = 0) and between 0 and 6 T (at T = 1.9 K), the emission lifetime decreases by factors of ≈10³ and ≈10², respectively. The results are explained within the C'_2v symmetry of the single complex assuming a coupling between neighboring central ions.     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Optical absorption band edge in single-crystal GeS

The absorption band edge of single-crystal orthorhombic GeS has been measured in all three polarizations at 4.2, 77 and 300°K. Strong excitonic absorption is observed for E ∥ a, and the transitions in this direction are identified as direct-allowed. Transitions in the E ∥ b and E ∥ c polarizations are tentatively identified as direct forbidden and direct allowed, respectively, with values for E_g similar to those found for E ∥ a. Evidence for the partially two-dimen?ional character of GeS is discussed.     

Nature of electric and magnetic dipoles gleaned from the Poynting theorem and the Lorentz force law of classical electrodynamics

Starting with the most general form of Maxwell's macroscopic equations in which the free charge and free current densities, ρ_free and J_free, as well as the densities of polarization and magnetization, P and M, are arbitrary functions of space and time, we compare and contrast two versions of the Poynting vector, namely, S = μ_o^− 1E × B and S = E × H. Here E is the electric field, H is the magnetic field, B is the magnetic induction, and μ_o is the permeability of free space. We argue that the identification of one or the other of these Poynting vectors with the rate of flow of electromagnetic energy is intimately tied to the nature of magnetic dipoles and the way in which these dipoles exchange energy with the electromagnetic field. In addition, the manifest nature of both electric and magnetic dipoles in their interactions with the electromagnetic field has consequences for the Lorentz law of force. If the conventional identification of magnetic dipoles with Amperian current loops is extended beyond Maxwell's macroscopic equations to the domain where energy, force, torque, momentum, and angular momentum are active participants, it will be shown that “hidden energy” and “hidden momentum” become inescapable consequences of such identification with Amperian current loops. Hidden energy and hidden momentum can be avoided, however, if we adopt S = E × H as the true Poynting vector, and also accept a generalized version of the Lorentz force law. We conclude that the identification of magnetic dipoles with Amperian current loops, while certainly acceptable within the confines of Maxwell's macroscopic equations, is inadequate and leads to complications when considering energy, force, torque, momentum, and angular momentum in electromagnetic systems that involve the interaction of fields and matter.     

High pressure tuning of optical transitions in Mg[Pt(CN)4]·7H2O

Mg[Pt(CN)₄]·7H₂O belongs to the class of tetracyanoplatinates(II) which crystallize in columnar structures. In different M_x[Pt(CN)₄]·yH₂O (MCP) single crystals the in-chain Pt-Pt-distance R varies between 3.67 Å (NaCP) and 3.15 Å (MgCP). Two optical transitions can be observed in polarized emission with the electric field vector E either parallel or perpendicular to the columnar (c)-axis. Polarized emission spectra of MgCP are recorded under hydrostatic pressure up to p ≈ 18 kbar (at 295 K). The transition energy v?₆ can be tuned from 17,600 cm^-1 to about 12,000 cm^-1 (2.18-1.48 eV). The pressure induced red shift for the two transitions is: E 6 c: dv?₆/dp = -320±20 cm^-1/kbar, E ⊥ c: dv?_⊥/dp = -270±20 cm^-1/kbar. These values are discussed in the context of the known functional relationship (for ambient conditions) between v? and R.     

Optical anisotropy of orthorhombic InS

The optical anisotropy of InS single crystals in the range of photon energy from 1.8 to 3.5 eV has been studied by absorption, electroreflectance and wavelength-derivative reflectance measurements. These systematic optical measurements for the polarizations, E//a and E//b, have revealed that the transition at the fundamental absorption edge of InS is allowed for E//b, and there exist three distinct doublet transitions having different selection rules in the photon energy region from 2 to 3.5 eV; Bo and B^'₀doublet allowed only for E//b, A₀ and A^'₀ allowed only for E//a, and E₁ and E^'₁ allowed for both polarizations. The observed results are discussed based on the anisotropic nature of two chemical bonds in InS, cation-cation and cation-anion.     

Luminescence of exciton in GeS

The luminescence of one free and four bound excitons has been investigated in the layer compound GeS. Up to six phonon replicas of the bound excitons are observable. The energies of these phonons are in reasonable agreement with Raman- and IR reflectivity measurements. The luminescence is highly anisotropic and is only seen in the polarization E ∥ a which confirms that the transitions E ∥ b are forbidden. Measurements with E ∥ c were inconclusive because of the difficulties in the sample preparation. Time resolved measurements revealed decay times between 20 nsec and 1.5 μsec for the different bound excitons. One exciton has been identified as bound to a Si impurity. This is the first observation of intentional doping of GeS. Thermal dissociation energies for the bound excitons lie between 6.5 and 20 meV.     

Rotational excitation of HD by collisions with He

The information theoretic surprisal analysis is employed to characterise the recent quantal close-coupling computations of rotational excitation rates by Green. The analysis is based on comparing the actual rates to the priors k⁰ which depend only on the temperature and the reduced “energy defect” ΔE_R/kT. The surprisal representation of the computed rates as k=k⁰ x exp (-I₀ - θ_R6ΔE_R6/kT is accurate throughout the temperature range considered by Green and is found to reduce in the low and high temperature limits to functional forms previously employed to characterise the rotational energy transfer rates in H₂.     

Infrared lattice vibration spectra of tetragonal ZnP2

Infrared reflectivity spectra of tetragonal ZnP₂ are measured in the frequency range from 40 to 600 cm^-1 for both polarization directions E ⊥ c and E 6 c. The parameters of 9 E modes and 4 A₂ modes are determined by a dispersion analysis of the spectra. Three additional A₂ modes are detected by infrared transmission measurements. The results obtained are compared with previous Raman scattering and two-phonon combination mode spectra.     

A new dioxime ligand and its trinuclear copper(II) complex: Synthesis, characterization and optical properties

The synthesis and characterization of a new dioxime ligand, (H₂L), (III) and its trinuclear copper(II) complex, [Cu₃L₂(H₂O)₂](ClO₄)₂, (V) is described. IR spectra show that the ligand acts in a tetradentate manner and coordinates N₄ donor groups of H₂L to copper(II) ion. The structure of the metal chelate is clarified with the help of elemental analysis, magnetic moment, conductometric and spectroscopic measurements. The optical absorption studies reveal that the transition is direct with band gap energy values are calculated. The optical constants such as refractive index and dielectric constant of the compound were determined. The refractive index dispersion curves of the films obey the single-oscillator model and oscillator parameters. Optical dispersion parameters E₀ and E_d developed by Wemple-DiDomenico were calculated.     

Calculation of HELAS amplitudes for QCD processes using graphics processing unit (GPU)

We use a graphics processing unit (GPU) for fast calculations of helicity amplitudes of quark and gluon scattering processes in massless QCD. New HEGET (HELAS Evaluation with GPU Enhanced Technology) codes for gluon self-interactions are introduced, and a C++ program to convert the MadGraph generated FORTRAN codes into HEGET codes in CUDA (a C-platform for general purpose computing on GPU) is created. Because of the proliferation of the number of Feynman diagrams and the number of independent color amplitudes, the maximum number of final state jets we can evaluate on a GPU is limited to 4 for pure gluon processes (gg→4g), or 5 for processes with one or more quark lines such as $q\overline{q}\rightarrow 5g$ and qq→qq+3g. Compared with the usual CPU-based programs, we obtain 60–100 times better performance on the GPU, except for 5-jet production processes and the gg→4g processes for which the GPU gain over the CPU is about 20.     

Effect of an intense laser field on the magnon damping in free carrier magnetic semiconductors

The influence of an intense radiation fieldE₀ on the magnon damping in free carrier magnetic semiconductors is discussed. It is shown that the effect of the intense field is to give a drift velocity v₀ = eE₀/mΩ to the carriers such that when v₀ exceeds the phase velocity of the spin waves the electrons are more able to emit magnons than they absorb and as a consequence the magnon population grows with time.     

Tensor methods for the exceptional group E6

We present a tensor formalism to describe irreducible representations of the exceptional group E₆. Irreducible tensors are characterized by covariant and contravariant indices associated with the irreducible representation 27, and a third (orthogonal-type) index associated with the 78; contractions of these indices with a set of invariant tensors are required to vanish for irreducibility. The formalism is applied to the reduction of Kronecker products of E₆ irreducible representations. As a further illustration of the method, we construct explicitly the Higgs potential for scalar fields in the E₆ representations 27, 78, 351, 351′.     

The absorption edges of GeS and Urbach's rule

The low-energy absorption tail of the E∥a exciton in GeS obeys Urbach's rule over at least three orders of magnitude in absorption coefficient for 4.2 ? T ? 240 K. The E∥b polarization (for which no exciton is observed) does not obey Urbach's rule. The E∥a Urbach edge is caused by interactions between the excitons and a 8.7 meV rigid-layer vibrational mode. Our results are consistent with Sumi and Toyazawa's theory of the Urbach edge, and inconsistent with the models of Dow, Redfield and Skettrup. The absorption edge of GeS is confirmed as a direct edge.     

Effective Hamiltonian for the Fermi resonance between the and , states of molecules of symmetry

The effective correlation-free Hamiltonian and corresponding matrix elements for interacting degenerate fundamental v_t(E) and combination v_n(A₁)+v_t^′(E) states in C_3v molecules are derived. The Hamiltonian terms H₃₀, H₃₁, H₃₂ and the recommended set of parameters following from the appropriate reduction are presented.     

Single crystal magnetization studies of DySb

High resolution magnetization measurements in single crystal-spherical DySb samples have been performed versus T in fields to 23.6 kOe. Measurements with H along principal crystallographic and 〈11$\text{2}$〉 directions are interpreted in terms of the intermediate metamagnetic phase having the HoP structure. Magnetization components parallel and perpendicular to the applied field for field rotations in (110) and (111) crystallographic planes have been measured and are interpreted in terms of a simple model with a single critical field. For H ∥ 〈110〉, M and H are collinear. The (M - H - T) phase diagram has been determined for H ∥ 〈110〉. The metamagnetic transition is 1st order below a critical point P_c = (8.5 K, 14.7 kOe) becoming 2nd order above. Field induced order for T >T_N is observed in agreement with the results of Brun et al. The absence of hysteresis in M_∥(θ) for H in (110) and (111) planes is interpreted as evidence for the tunneling model in DySb.     

Theoretical studies of ground and excited states in a series of Zn(II) complexes,derived from thiourea and thiosemicarbazide

Theoretical studies for a series of mono- and binuclear zinc (II) complexes Zn(CH₃COO)₂(H₂L)₂ [H₂L = N-2-propenyl-N ^′-2-pyridinylthiourea] (A), Zn₂(CH₃COO)₂(H₃L-a)₂ [H₃L-a = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-phenylcarbothioamide] (B), and Zn(H₃L-b)₂ [H₃L-b = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-(2-propenyl)carbothioamide] (C) have been performed on their structures and excited-state absorption spectra. The singlet ground-state geometries are fully optimised at three DFT levels, i.e., B3LYP, B3PW91, and M06. Different geometries, i.e., strongly distorted tetrahedral coordination environment in complex A, distorted square-pyramidal environment in complex B, and irregular octahedral mode in complex C are identified. Consequently, the spectroscopic properties are calculated by means of time-dependent density functional theory (TDDFT) with the Polarisable Continuum Model (PCM) based on the optimised gas-phase geometries. Three absorption peaks are identified for every complex, which are in good agreement with the experimental ones. For complex A, all three absorption peaks centered at 280.33 nm, 268.09 nm, and 250.87 nm, respectively, are ascribed to the (p,π) → π* transition with a mixed intraligand charge-transfer (ILCT)/ligand-ligand charge-transfer (LLCT) character. The composition of frontier orbitals involved in major absorption bands for the three complexes shows similarities, which results in the almost homologous transition attributions and characteristics. A remarkable bathochromic shift in the lowest-lying absorption band is observed for complexes B and C as compared with complex A, which is attributed to the decreased H (HOMO)-L (LUMO) energy gap (ΔE |HOMO-LUMO|) by the formation of conjugate metallocycles in complexes B and C.     

Photon electrodynamics and photon structure as a bunch of one of many possible states of electromagnetic field

Fundamental laws of conservation are used to show that electromagnetic field is generally represented (even in vacuum at ρ = 0 and j = 0) using four vectors D, E, B, and H with different equations of state (material equations) that are linear for electromagnetic waves and nonlinear for photons and particles. An equation that describes different states of electromagnetic field (i.e., different but not arbitrary relationships of field vectors E, H, D, and B) is derived. It is shown that electromagnetic wave and photon are different states of electromagnetic field that exhibit different dependences of energy density on field vectors. Partial analytical solutions are obtained for a photon (spatially localized bunch of electromagnetic field energy) that propagates at a velocity of light along a single (as distinct from electromagnetic wave) direction.