First observation of electronic structure of the even parity boron acceptor states in diamond

We use electronic Raman scattering for studying the band structure of the ns$\mathrm{n}s$ boron acceptor states in diamond. For the first time, the spin–orbit splitting of these acceptor states and the 1s→ns$1s\to \mathrm{n}s$ Lyman series of transitions are observed. The spin–orbit splitting linearly increases with n number. Lyman series exhibit fine structure consisting of four bands each. The energy spacing between series is equal to ∼13 meV$\sim 13\text{meV}$. Evolution of Raman spectra of the boron-doped diamond with increasing boron concentration is shown. Mott transition is revealed in Raman spectrum. Correct values of Luttinger parameters for diamond are specified.     

Lyman transitions of high rovibrationally excited H2, HD and D2 molecules

Energies and probabilities of Lyman transitions of high rovibrationally excited H₂, HD and D₂ molecules have been measured and compared with calculations. The experimental results are obtained from laser-induced fluorescence spectra that have been recorded in the spectral range from 60 500 to 83 500 cm⁻¹, covering 2/3 of the hydrogen Lyman band system. The necessary vacuum-UV radiation is produced by stimulated anti-Stokes Raman scattering, providing a widely tunable radiation source with narrow spectral bandwidth to resolve single Lyman transitions. The highest internal energies of detected hydrogen isotopologues are close to the dissociation limit. This extends the available data base of Lyman transitions from and to higher rotational states (J > 10) of HD and D₂.     

Matter-wave solitons in the presence of collisional inhomogeneities: Perturbation theory and the impact of derivative terms

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrödinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.     

Nonlinear diffusion of indirect excitons in an ideal bilayer with an in-plane harmonic trap

The nonlinear diffusion of the spatially indirect excitons in an ideal bilayer with an in-plane harmonic trap is investigated based on the theories developed by Ivanov [A.L. Ivanov, Europhys. Lett. 59 (2002) 586; A.L. Ivanov, J. Phys.: Condens. Matter 16 (2004) S3629] and Rapaport et al. [R. Rapaport, G. Chen, S. Simon, O. Mitrofanov, L. Pfeiffer, P.M. Platzman, Phys. Rev. B 72 (2005) 075428]. A nonlinear equation for the diffusion of the indirect excitons in this structure is established. The two-dimensional density of the indirect excitons in this structure is calculated. The calculations show that the density adjacent to the trap center for different exciton temperatures can remain very high even long after the photo-excitation because of the confinement of the in-plane harmonic trap, and that the indirect excitons gather several tens of μm away from the trap center. The calculations are in good agreement qualitatively with the experimental results of Voros et al. [Z. Voros, D.W. Snoke, L. Pfeiffer, K. West, Phys. Rev. Lett. 97 (2006) 016803] and prove that an in-plane harmonic trap can indeed keep an exciton gas dense near its center.     

New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation

New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation are constructed by means of the Darboux transformation with constant seed solution. The new positon, negaton and complexiton solutions are analytical or singular and given out both analytically and graphically.     

Potential symmetry and invariant solutions of Fokker-Planck equation in cylindrical coordinates related to magnetic field diffusion in magnetohydrodynamics including the Hall current

Lie groups involving potential symmetries are applied in connection with the system of magnetohydrodynamic equations for incompressible matter with Ohm's law for finite resistivity and Hall current in cylindrical geometry. Some simplifications allow to obtain a Fokker-Planck type equation. Invariant solutions are obtained involving the effects of time-dependent flow and the Hall-current. Some interesting side results of this approach are new exact solutions that do not seem to have been reported in the literature.     

Cross Soliton-Like Waves for the （2＋1）-Dimensional Breaking Soliton Equation

We construct a two-soliton-like solution for the （2＋1）-dimensionai breaking soliton equation. The obtained solution contains two arbitrary functions and hence can model various cross soliton-like waves including the two-solitary waves. We show the evolution of some special cross soliton-like waves diagrammatically.     

Numerical Solution of the Three-Dimensional Helmholtz Equation

We apply the homotopy analysis method to solve the nonhomogeneous multidimensional partial differential equation model problem. The analytic solutions are calculated in terms of convergent series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling ＂noise＂ terms whose sum vanishes in the limit. Numerical results clearly reveal the complete reliability and efficiency of the proposed algorithm.     

Consistent determination of photoluminescence quantum efficiency for phosphors in the form of solution, plate, thin film, and powder

We have developed an improved method for easily determining the photoluminescence quantum efficiencies of transparent materials, such as solutions, glass plates, and thin films on a substrate, having various absorbances from ca. 0.05 to 1.0 at the excitation wavelength when reabsorption is negligible. The estimated accuracy for emitting semiconductor nanocrystals is ±5% for solutions. The efficiencies of non-transparent material, such as powder, together with the above-mentioned transparent materials were measured using the traditional integrating sphere method. Comparison of the two values showed that the traditional integrating sphere method usually underestimates the efficiency of powder samples ca. 10-20% depending on the optical density of the powder. This is because the emissions from more than ca. 0.2 mm deep do not leave the powder sample due to internal scattering. We also developed a method to overcome this problem.     

Characterization, global analysis and integrability of a family of Poisson structures

An n-dimensional solution family of the Jacobi equations is characterized and investigated, including the global determination of its main features: the Casimir invariants, the construction of the Darboux canonical form and the proof of integrability for the related Poisson systems. Examples are given and include novel Poisson formulations.