Volume 10, Issue 2

In this review, some benchmark works by Han and coworkers on the stereodynamics of typical chemical reactions, triatomic reactions H + D2, Cl + H2 and O + H2 and polyatomic reaction Cl+CH4/CD4, are presented by using the quasi-classical, quantum and mixed quantum-classical methods. The product alignment and orientation in these A+BC model reactions are discussed in detail. We have also compared our theoretical results with experimental measurements and demonstrated that our theoretical results are in good agreement with the experimental results. Quasi-classical trajectory (QCT) method ignores some quantum effects like the tunneling effect and zero-point energy. The quantum method will be very time-consuming. Moreover, the mixed quantum-classical method can take into account some quantum effects and hence is expected to be applicable to large systems and widely used in chemical stereodynamics studies.

We review and compare two models recently used to describe electronic transport in polymer fibers/nanotubes and carbon nanotubes including graphene nanoribbons, namely, variable range hopping (VRH) in different versions and their modifications on the one hand and electric-field-induced phonon-assisted tunneling (PhAT) on the other hand. The VRH model is mainly approved on behalf of the results of temperature dependences. However, the field dependencies of the conductivity in the framework of this model remain practically unexplained. At the same time, the PhAT model describes properly not only temperature dependence of conductivity measured in a wide temperature range, but also conductivity/current dependences on field strength using the same set of parameters characterizing the materials

We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of “fuzzy” and “free-flight” sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called “times.”

In this paper a model of targeted drug delivery by means of active (motor-driven) axonal transport is developed. The model is motivated by recent experimental research by Filler et al. (A.G. Filler, G.T. Whiteside, M. Bacon, M. Frederickson, F.A. Howe, M.D. Rabinowitz, A.J. Sokoloff, T.W. Deacon, C. Abell, R. Munglani, J.R. Griffiths, B.A. Bell, A.M.L. Lever, Tri-partite complex for axonal transport drug delivery achieves pharmacological effect, Bmc Neuroscience 11 (2010) 8) that reported synthesis and pharmacological efficiency tests of a tri-partite complex designed for axonal transport drug delivery. The developed model accounts for two populations of pharmaceutical agent complexes (PACs): PACs that are transported retrogradely by dynein motors and PACs that are accumulated in the axon at the Nodes of Ranvier. The transitions between these two populations of PACs are described by first-order reactions. An analytical solution of the coupled system of transient equations describing conservations of these two populations of PACs is obtained by using Laplace transform. Numerical results for various combinations of parameter values are presented and their physical significance is discussed.

The UV-VIS absorption property and the structural modification of PVA membranes gamma irradiated were investigated by XRD, UV-VIS and Raman spectroscopies. The increase of UV absorbance is observed after irradiation. This behavior is correlated with the scission effect and local ordering of the polymeric chain induced by irradiation. These effects were probed by XRD and Raman spectroscopy.

In this work, we study parametric excitations in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric excitations (oscillations of the BEC width). Regular oscillations disappear when one of the competing factors, i.e. the strength of harmonic trap or the strength of optical lattice, dominates. Parametric instabilities (chaotic dynamics) arise for large variations in the strength of the optical lattice.

Analytical results for the spatial dependence of the correlation functions for all meson excitations in perturbative Quantum Chromodynamics, the lowest order, are calculated. The meson screening mass is obtained as a large distance limit of the correlation function. Our analysis leads to a better understanding of the excitations of Quark Gluon Plasma at sufficiently large temperatures and may be of relevance for future numerical calculations with fully interacting Quantum Chromodynamics.

The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states based on both methods are discussed, and it is found that generally there are significant differences between the two approaches. As an illustration of the applications and the features of these formulas, S-matrix elements and energy corrections in two quantum field theoretical models are calculated using (generalized) old-fashioned perturbation theory. The two methods are found to give equivalent results.

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C s from the valence energy spectrum of particle and also for pseudospin symmetry constant C ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.

A dynamical system governed by equations with derivatives of non-integer order, such as the fractional oscillator, can be considered as an open (non-isolated) system with memory. Fractional equations of motion are obtained from the interaction between the system and the environment with power-law spectral density.

We study the scaling properties of Fisher’s information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher’s measure I and encounter that, from the concomitant operating rules, several interesting, albeit known, results can be derived. This entails that such results can be regarded as pre-configured by the conjunction of scaling and information theory. The central notion to be arrived at is that scaling entails that I must obey a certain partial differential equation (PDE). These PDE-solutions have properties that enable the application of a Legendre-transform (LT). The conjunction PDE+LT leads one to obtain several quantum results without recourse to the Schrödinger’s equation.

The relationship between Jacobi’s last multiplier and the Lagrangian of a second-order ordinary differential equation is quite well known. In this article we demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonians of certain well known first-order systems of differential equations arising in biology.

The aim of the paper is to use the recurrence relations with respect to both indices of the associated Legendre functions for the extraction of the Dirac quantization condition and dynamical symmetry group U(1, 1) corresponding to the highest Landau levels on the hyperbolic plane with uniform magnetic field B. Irreducible representations of the su(2) algebra are obtained by the ladder differential operators which change B by 1/2 unit and mode number by one unit. Two different classes of the irreducible representations of SU(1, 1) with the even and odd boson numbers 2B − 1/2 are extracted for the Bargmann indices 1/4 and 3/4, respectively. Finally, we show that shape invariance symmetry is realized by the ladder operators which shift only the magnetic field B by 1/2 unit.

Path and path deviation equations for neutral, charged, spinning and spinning charged test particles, using a modified Bazanski Lagrangian, are derived. We extend this approach to strings and branes. We show how the Bazanski Lagrangian for charged point particles and charged branes arises à la Kaluza-Klein from the Bazanski Lagrangian in 5-dimensions.

We present a new independent scheme of SO(3) group transformations suitable for the N particle system, composed of N − 1 and 1 particle subsystems, where N − 1 particles have their own intrinsic clusterization. The simple expressions for corresponding four-particle harmonic-oscillator transformation brackets are presented, as well as their simplifications for the special values of mass ratio parameters d = 0, d → ∞ and d 1 = 0, d 1 → ∞.

Two-dimensional and one-dimensional models are used to evaluate the seashore effects of the tsunami generated by an asteroid hitting the deep water in the Eastern region of the Black Sea. The shallow water theory has been used to describe tsunami propagation. The distance between the impact point and the nearest coast is about 150 km. The effects on the coastal regions depend on many factors among which the most important is asteroid size. The tsunami generated by a 250 m asteroid reaches the nearest dry land location in 20 minutes and needs about two hours to hit all over the Black Sea coast. The horizontal inundation length is also known as run-in or run-off distance, according to the direction of water movement. The run-up values may be up to 39 m in the Eastern basin and a more than ten times smaller in theWestern region. The Northern part of the Black Sea coast is not affected by the tsunami. The run-in values of a tsunami generated by a 1000 m diameter asteroid are sensibly larger than the similar values associated to a 250 m diameter asteroid. The run-in strongly depends on the distance from the impact position to the shore and on coastal topographical profile. For instance, the run-in distance in case of a tsunami generated by a 250 m size asteroid is 0.1 km (at Varna), 0.5 km (Ordu), 0.7 km (Yalta) and 1.4 km (Sochi). In case of the 1000 m diameter asteroid the run-in distance is 0.7 km (at Varna) and 2.9 km (Yalta). The results accuracy is also discussed.

The work presents measurements of the length stability of Zerodur glass ceramic with temperature change. Measurement of this thermal characteristic is necessary for determination of the optimal temperature at which the Zerodur glass ceramic has a coefficient of thermal expansion close to zero. The principle of the measurement is to monitor the length changes using an optical resonator with a cavity mirror spacer made from the Zerodur material to be studied. The resonator is placed inside a vacuum chamber with a temperature control. A tunable laser diode is locked to a certain optical mode of the resonator to monitor the optical frequency of this mode. A beat-note signal from optical mixing between the laser and a stabilized femtosecond frequency comb is detected and processed. The temperature dependence of the glass ceramics was determined and analyzed. The resolution of the length measurement of the experimental set-up is on the order of 0.1 nm.

We focus on a comparison between the classical and quantum descriptions of the degree of polarization of an optical field. A quantum field containing photons with various states of polarization and which propagate in the same direction in free space one after another (a so called photon beam) is analyzed. We show that the formulated definition of degree of polarization for this quantum field leads to a measurable quantity. The concept of a thought experiment is presented.

We have derived and analyzed the wavefunctions and energy states for an asymmetric double quantum well (ADQW), broadened due to interdiffusion or other static interface disorder effects, within a known discreet variable representative approach for solving the one-dimensional Schrodinger equation. The main advantage of this approach is that it yields the energy eigenvalues, and the eigenvectors, in semiconductor nanostructures of different shapes as well as the strengths of the optical transitions between them. The behaviour of ADQW states for the different mutual widths of coupled wells, for the different degree of broadening, and under increasing external electric field is investigated. We have found that interface broadening effects change and shift energy levels, not monotonously, but the resonant conditions near an energy of sub-band coupling regions do not strongly distort. Also, it is shown that an external electric field may help to achieve resonant conditions for inter-sub-band inverse population by intrawell emission of LO-phonons in diffuse ADQW.

Fine particles of ZnFe2O4 were synthesized by a wet chemical method in the (80 wt.% Fe2O3 + 20 wt.% ZnO) system. The morphological and structural properties of the mixed system were investigated by scanning electron microscopy, X-ray diffraction, inductively coupled plasma atomic emission, and X-ray photoelectron spectroscopy. The major phase was determined to be the ZnFe2O4 spinel with particle size of 11 nm. The magnetic properties of the material were investigated by ferromagnetic resonance (FMR) in the temperature range from liquid helium to room temperature. A very intense, asymmetric FMR signal from ZnFe2O4 nanoparticles was recorded, which has been analyzed in terms of two Callen-lineshape lines. Temperature dependence of the FMR parameters was obtained from fitting the experimental lines with two component lines. Analysis of the FMR spectra in terms of two separate components indicates the presence of strongly anisotropic magnetic interactions.

Un-doped and Mn-doped ZnO nanoparticles were successfully synthesized in an ethanolic solution by using a sol-gel method. Material properties of the samples dependence on preparation conditions and Mn concentrations were investigated while other parameters were controlled to ensure reproducibility. It was observed that the structural properties, particle size, band gap, photoluminescence intensity and wavelength of maximum intensity were influenced by the amount of Mn ions present in the precursor. The XRD spectra for ZnO nanoparticles show the entire peaks corresponding to the various planes of wurtzite ZnO, indicating a single phase. The diffraction peaks of doped samples are slightly shifted to lower angles with an increase in the Mn ion concentration, signifying the expansion of the lattice constants and increase in the band gap of ZnO. All the samples show the absorption in the visible region. The absorbance spectra show that the excitonic absorption peak shifts towards the lower wavelength side with the Mn-doped ZnO nanoparticles. The PL spectra of undoped ZnO consist of UV emission at 388 nm and broad visible emission at 560 nm with varying relative peak intensities. The doping of ZnO with Mn quenches significantly the green emission while UV luminescence is slightly affected.

The longitudinal optical (LO) phonon energy in AlGaN/GaN heterostructures is determined from temperature-dependent Hall effect measurements and also from Infrared (IR) spectroscopy and Raman spectroscopy. The Hall effect measurements on AlGaN/GaN heterostructures grown by MOCVD have been carried out as a function of temperature in the range 1.8-275 K at a fixed magnetic field. The IR and Raman spectroscopy measurements have been carried out at room temperature. The experimental data for the temperature dependence of the Hall mobility were compared with the calculated electron mobility. In the calculations of electron mobility, polar optical phonon scattering, ionized impurity scattering, background impurity scattering, interface roughness, piezoelectric scattering, acoustic phonon scattering and dislocation scattering were taken into account at all temperatures. The result is that at low temperatures interface roughness scattering is the dominant scattering mechanism and at high temperatures polar optical phonon scattering is dominant.

Well oriented KYb(WO4)2 and KTb0.2Yb0.8(WO4)2 single crystals have been investigated for their magnetic and optical properties using the Raman and EPR techniques. The registered EPR signal is dominated by three lines ascribed to ytterbium ions: one main and two satellites. Tb ions, although non-paramagnetic, distinctly modify magnetic properties of the KYb(WO4)2 single crystal. Basic parameters of the spin Hamiltonian, including Zeeman and hyperfine terms (g and A matrices) as well the spatial orientation between principal and crystallographic axes systems were determined for both crystals.

Growth conditions and electron paramagnetic resonance investigations of two well oriented KSm(WO4)2 and KEr(WO4)2 single crystals have been presented and discussed. Hyperfine structure of Sm3+ ion was detected and analyzed for angular and temperature dependences. EPR spectra of KEr(WO4)2 and its angular dependence showed the presence of 5 magnetically nonequivalent Er centers in the crystal. A change in the type of magnetic interactions was analyzed using mixed (Gaussian and Lorentzian) fits of the EPR spectra.

Single crystals of lithium-sodium-tetragermanate, a member of the solid solution series Li2−xNaxGe4O9 with x=0.28, pure and slightly doped with Cr3+ ions (0.03 mol.% and 0.1 mol.%), were grown in ambient atmosphere by the Czochralski technique from stoichiometric melt. The crystals with dimensions up to 20 mm in diameter and 50 mm in length were obtained. The crystal structure has been determined by means of X-ray diffraction. Phase analysis and structural refinement of the Li1.72Na0.28Ge4O9 crystals were performed by X-ray powder diffraction using Ni-filtered Cu Kα radiation with a Siemens D5000 diffractometer. The absorption, excitation and photoluminescence spectra of the crystals were measured in the UV-VIS and IR range at low temperatures. EPR investigations were performed using a conventional X-band Bruker ELEXSYS E 500 CW-spectrometer operating at 9.5 GHz with 100 kHz magnetic field modulation. Temperature and angular dependences of the EPR spectra of the crystal samples were recorded in the 3–300 K temperature range.

A series of new red phosphors, MZr2(PO4)3:Eu3+; Bi3+ (M=Na; K), were synthesized using the solidstate reaction method, and their photoluminescence spectra were measured. The MZr2(PO4)3:Eu3+; Bi3+ (M=Na; K) phosphors were efficiently excited by an ultraviolet (UV; 395 nm) source, and showed intense orange-red emission at 595 nm. Further investigation of the concentration-dependent emission spectra indicated that the MZr2(PO4)3:Eu3+; Bi3+ (M=Na; K) phosphors exhibit the strongest luminescence intensity when y = 0.01 in NaZr2(0:95−y)(PO4)3:Eu0.103+, Bi2y 3+ and y = 0.09 in NaZr2(0.95−y)(PO4)3:Eu0.103+, Bi2y 3+, whereas the relative PL intensity decreases with increasing Bi3+ concentration due to concentration quenching. The addition of Bi3+ widens the excitation band of NaZr2(0.95−y)(PO4)3:Eu0.103+, Bi2y 3+ around 320 nm, which provides the useful idea of broadening the excitation band around 300–350 nm to fit the ultraviolet chip.

Lithium-indium oxide is a high-density (5.9 g·cm−3), wide band-gap semiconductor with promising applications for scintillating detection of solar neutrinos as well as for efficient phosphorescence when doped with Er3+ or Sm3+ ions. In this report, we demonstrate visible upconversion emission of Er3+-doped LiInO2 synthesized by a simple solid-state chemistry procedure and discuss mechanisms responsible for pumping the Er3+ ions to upper levels. Intense upconversion emission is observed in the green and red spectral regions under near-infrared excitation, and it is greatly enhanced by co-doping with Yb3+ ions. We also examined the upconversion intensity change as a function of temperature, and, consequently, possible applications of this material as a low-temperature sensor.

Absorption and photoluminescence (PL) spectra, PL quantum efficiency, and PL lifetime have been investigated on bis(8-hydroxyquinoline) zinc (Znq2) and magnesium (Mgq2) in solutions and powder. Znq2 and Mgq2 have the lowest-energy absorption band at 376 and 396 nm in acetonitrile solution, respectively, and emission band with peak at 555 and 480 nm. The PL quantum efficiency is 0.03 and 0.45 for Znq2 and Mgq2 in the solution, respectively, while 0.45 and 0.36 in powder. Unlike the case of powders, two PL lifetimes are obtained in solutions. The longer lifetime is attributed to molecule having interaction with its neighboring molecule, while the shorter one to the isolated single molecule.

This article describes our attempts to produce ”nonexcimer” polymer systems by means of rigid fixation of chromophore groups positioned between two vinyl bonds. Divinylbenzene and methylmethacrylate copolymers were chosen as such systems. Study of the optical properties of synthesized copolymers showed their constancy in a wide region of specific concentrations of chromophore groups. The absence of luminescent properties modification in a wide concentrations range proves the possibility of eliminating the intrasystem energy traps by means of rigid fixation of chromophores in polymer.

Recent experiments show that mRNAs and proteins can be localized both in prokaryotic and eukaryotic cells. To describe such situations, I present a 3D mean-field kinetic model aimed primarily at gene expression in prokaryotic cells, including the formation of mRNA, its translation into protein, and slow diffusion of these species. Under steady-state conditions, the mRNA and protein spatial distribution is described by simple exponential functions. The protein concentration near the gene transcribed into mRNA is shown to depend on the protein and mRNA diffusion coefficients and degradation rate constants.