Nonlinear theory of multiphonon relaxation of excited rare-earth ions in laser crystals

A general formula for the probability of multiphonon nonradiative transitions between J multiplets of 4f ^N states of trivalent rare-earth ions in a crystal derived for a nonlinear mechanism is discussed. A technique is developed for calculating the quantities involved in this formula. Particular attention is given to calculating the spectral density J ^(p)(Ω), which is the Fourier transform (at the transition frequency) of the pth power of the correlation function K(t) of host ion displacements. Based on the central limit theorem from probability theory, an approximation is proposed for the spectral density J ^(p)(Ω). The theoretical values of nonradiative multiphonon transition rates are compared with experimental ones.     

Generalized density expansion in the kinetic theory and the resistivity of liquid metals

For the system of electrons and immovable interacting centers an exact equation for averaged electron Green's function is formulated. The expansion of self-energy part over the one-particle t-matrices and explicit Green's functions is derived. It represents a kind of a generalized density series containing the correlation functions of the centres. In the low approximation over t-matrix, the transition probability (t)²S in the kinetic equation is obtained (S = the structure factor of centers).     

Temperature-dependent photoluminescence in La2/3Ca1/3MnO3

Visible photoluminescence and its temperature dependence of La_2/3Ca_1/3MnO₃ in the temperature range 138-293 K were measured. It was observed that the main broad band centered at ∼1.77 eV with the shoulders at ∼1.57 and ∼1.90 eV existed in the entire temperature range. It can be well fitted by three Gaussian curves B₁, B₂ and B₃ centered at ∼1.52, ∼1.75 and ∼1.92 eV, respectively. The intensities of the peak B₁ and B₂ vary as temperature increases. In the entire temperature range, the intensity of B₁ increases with increasing temperature, whereas that of B₂ decreases. The photoluminescence mechanisms for La_2/3Ca_1/3MnO₃ are presented based on the electronic structures formed by the interactions among spin, charge and lattice, in which B₁ was identified with the charge transfer excitation of an electron from the lower Jahn-Teller split e_g level of a Mn³⁺ ion to the e_g level of an adjacent Mn⁴⁺ ion, B₂ is assigned to the transition between the spin up and spin down e_g bands separated by Hund's coupling energy E_J and B₃ is attributed to the transition, determined by the crystal field energy E_C, between a t_2g core electron of Mn³⁺ to the spin up e_g bands of Mn⁴⁺ by a dipole allowed charge transfer process.     

Transient bi-fractional diffusion: space-time coupling inducing the coexistence of two fractional diffusions

Anomalous diffusion is researched within the framework of the coupled continuous time random walk model, in which the space-time coupling is considered through the correlated function g(t) ~ t ^γ , 0 ≤ γ< 2, and the probability density function ω(t) of a particle’s transition time t follows a power law for large t: ω(t) ~ t ^{? (1 + α)},1 <α< 2. The bi-fractional generalized master equation is derived analytically which can be applied to describe the transient bi-fractional diffusion phenomenon which is induced by the space-time coupling and the asymptotic behavior of ω(t). Numerical results show that for the transient bi-fractional diffusion, there is a transition from one fractional diffusion to another one in the diffusive process.     

Drag exerted on dislocation kinks in solid solutions

The theory of drag exerted on dislocation kinks by statistical density fluctuations of impurity atoms is generalized to the case of solid solutions. The conditions of the transition to anomalous kink drift, which is characterized by a nonlinear time (t) dependence of the displacement x (x ～ t ^δ, δ < 1), are obtained. The related consequences for the dislocation mobility and the plastic flow of a solid solution are derived. The theory is illustrated through calculating the concentration dependence of the deforming stress in a Ge_1?c Si _c solid solution.     

First principles study of structural, electronic and vibrational properties of heavily boron-doped diamond

The structural, electronic and vibrational properties of a series of heavily B-doped diamond models have been investigated using the density functional theory within a local density approximation. The doped models C_64 − nB_n (n=1-3) were constructed using supercell techniques. The structural and electronic calculations confirmed that the B dimers are always energetically stable and electrical inactive. The superconducting transition temperature TC is not only decided by the B concentration, but also by the lattice configurations of boron atoms. The vibrational frequencies and eigenmodes were determined using the linear response approach, while Raman intensities were obtained by the second response method. The Raman analysis in terms of atomic vibrations found that the “500 cm⁻¹” and “1230 cm⁻¹” bands are both superposed bands including not only C vibrations but also B-B vibrations and B-C vibrations, respectively. The calculated Raman spectra with isotopic substitutions are in excellent agreement with corresponding experimental results. The reasonable explanation was provided for no obvious Raman shift of main bands from ¹⁰B¹²C to ¹¹B¹²C model.     

A comment on the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T.D. Frank

The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and nonlinear Fokker-Planck equations, Physica A 331 (2004) 391]. Our comment centers on the claims of a “non-linear Markov process” and a “non-linear Fokker-Planck equation.” First, memory in transition densities is misidentified as a Markov process. Second, the paper assumes that one can derive a Fokker-Planck equation from a Chapman-Kolmogorov equation, but no proof was offered that a Chapman-Kolmogorov equation exists for the memory-dependent processes considered. A “non-linear Markov process” is claimed on the basis of a non-linear diffusion pde for a 1-point probability density. We show that, regardless of which initial value problem one may solve for the 1-point density, the resulting stochastic process, defined necessarily by the conditional probabilities (the transition probabilities), is either an ordinary linearly generated Markovian one, or else is a linearly generated non-Markovian process with memory. We provide explicit examples of diffusion coefficients that reflect both the Markovian and the memory-dependent cases. So there is neither a “non-linear Markov process”, nor a “non-linear Fokker-Planck equation” for a conditional probability density. The confusion rampant in the literature arises in part from labeling a non-linear diffusion equation for a 1-point probability density as “non-linear Fokker-Planck,” whereas neither a 1-point density nor an equation of motion for a 1-point density can define a stochastic process. In a closely related context, we point out that Borland misidentified a translation invariant 1-point probability density derived from a non-linear diffusion equation as a conditional probability density. Finally, in the Appendix A we present the theory of Fokker-Planck pdes and Chapman-Kolmogorov equations for stochastic processes with finite memory.     

Metal-insulator transition induced by the magnetic field in n-type GaSb

The metal-insulator (MI) transition induced by a magnetic field was evidenced for the first time in compensated n-type GaSb layers grown by molecular beam epitaxy. The free electron densities were in the low 10¹⁶ cm⁻³ range or even slightly lower, so that the zero-field 3D electron gas was degenerate and, at the B_MI magnetic field of the MI transition, it populates only the spin-split 0⁽⁺⁾ Landau level (extreme quantum limit). On the metallic side of the MI transition a T^1/3 dependence of the conductivity was assumed to fit the low-T data and to estimate the B_MI value, which resulted of 9.1 T in the purest sample. The MI transition manifests in a strong increase of the diagonal resistivity with the magnetic field, but not of the Hall coefficient, suggesting that the apparent electron density is practically constant, whereas the mobility varies strongly. The evidence of a maximum in the temperature dependence of the Hall coefficient has been explained through a two channels transport mechanism involving localized and extended states.     

Franck-Condon factors and absolute transition probabilities for the if (B3Π0+-X1Σ+) transition

Improved spectroscopic constants have been used to calculate Rydberg-Klein-Rees (RKR) potentials and Franck-Condon factors for the IF(B³Π₀₊-X¹Σ⁺) transition. The Franck-Condon factors are generally in good agreement with previously calculated values, but differ by as much as 30% for transitions from higher levels of the B-state. Several experimentally measured relative transition moment functions have been evaluated and the best scaled, so that the total transition probability calculated for each B-state vibrational level, A(v'), matched measured values. The scaled function was then used to calculate individual transition probabilities, A(v',v), for the vibronic transitions.     

Weak isoscalar response of 11B

Weak-interaction responses of ¹¹B were studied by measuring the ¹¹B(³He, t) and ¹¹B(p, p′) reactions. Obtained nuclear transition matrix elements B(GT), B(στ), and B(σ) were compared with the shell-model calculations. The shell-model calculations, which explained the isovector parts B(GT) and B(στ) reasonably well if the quenching factors of 0.5–0.7 were taken into account, did not describe the isoscalar part B(σ).     

Relaxation Kinetics of the Microhardness of KDP Crystals after Their Exposure to a Magnetic Field

It has been shown that potassium dihydrogen phosphate crystals change their microhardness reversibly after their exposure to a magnetic field of B = 0.8 or 1.2 T for t_m = 7–90 min. It has been found that the magnetic effect can be conveniently characterized by the quantity B²t_m, because the variation of the parameters conserving B²t_m=const does not change the result. At B²t_m < 10 T² min, the effect is almost absent. Above this threshold, the amplitude of changes in the microhardness increases and approaches a constant value of ~10% at B²t_m ≈ 19 T² min. The responses of samples of the same crystal from the faces of the prismatic and pyramidal growth sectors to exposure are different. In the former case, they soften; in the latter case, the hardening stage follows the softening stage. However, in both cases, the microhardness returns to the initial value. At B²t_m values from 19 to 37 T² min, the amplitudes and durations of the effect do not change, but in the narrow range of 37–43 T² min, the lifetime of the modified state increases sharply with transition to a new level: “sharp” peaks with a half-width of ~2 days are transformed to trapezoids with the width of the horizontal side of ~1–2 weeks. A physical scheme of the observed effects has been proposed.     

Space use by foragers consuming renewable resources

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: (i) the high-order moments, ?x(t) ^q ? for q > 2 and the probability density of the process exhibit multiscaling; (ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; (iii) positive order moments satisfying standard scaling does not imply an exact scaling property of the probability density.     

Phase transformation and elastic behavior of MgX (X=S, Se, Te) alkaline earth chalcogenides

Pressure induced structural aspects of NaCl-type (B1) to CsCl-type (B2) structure in alkaline earth chalcogenides (AECs) magnesium chalcogenides (MgX; X=S, Se, and Te) are presented. An effective interionic interaction potential (EIoIP) with long-range Coulomb interactions and the Hafemeister and Flygare type short-range overlap repulsion extending up to the second neighbor ions and the van der Waals (vdW) interaction is developed. The vdW coefficients are evaluated following the Slater-Kirkwood variational method, as both the ions are polarizable. The present calculations have revealed reasonably good agreement with the available experimental data on structural transition (B1-B2 structure), the phase transition pressures P_t of 167 (MgS), 170 (MgSe), and 176 (MgTe) GPa as well the elastic properties. The calculated values of the volume collapses [ΔV(P)/V(0)] are also closer to their observed data. Further, the variations of the second and third order elastic constants with pressure have followed a systematic trend, which are almost identical to those exhibited by the observed data measured for other semiconducting compounds with rocksalt (B1) type crystal structure. The Born and relative stability criteria is valid in Mg monochalcogenides.     

Random Renormalization Group Operators Applied to Stochastic Dynamics

Let X(t) be a fixed point the renormalization group operator (RGO), R _p,r X(t)=X(rt)/r ^p . Scaling laws for the probability density, mean first passage times, finite-size Lyapunov exponents of such fixed points are reviewed in anticipation of more general results. A generalized RGO, $\mathcal{R}_{P,n}$ where P is a random variable, is introduced. Scaling laws associated with these random RGOs (RRGOs) are demonstrated numerically and applied to subdiffusion in bacterial cytoplasm and a process modeling the transition from subdiffusion to classical diffusion. The scaling laws for the RRGO are not simple power laws, but are a weighted average of power laws. The weighting used in the scaling laws can be determined adaptively via Bayes?? theorem.     

Axial vector meson production

Recently available differential cross section and density matrix information on π^?p → B^?p at 4 GeV/c are successfully described in terms of t channel exchanges and s channel absorptive effects. The s channel helicity amplitude which is dominant at small |t| (zero net helicity flip ω exchange) is found to have a zero at ?t = 0.2 GeV². SU(3) and higher symmetries are used to predict cross sections for further axial vector meson production processes, in particular non-diffractive A₁ production. The importance of these processes with regard to Regge phenomenology and meson spectroscopy is emphasized.     

Nonlinear electrostatic response of strongly correlated one-dimensional electron systems

We investigate the nonlinear response of the strongly correlated one-dimensional electron systems to the static electric field with using the one-dimensional Hubbard model in the half-filled case. We adopt the variational Monte Carlo method with the Gutzwiller wave function to describe the strong correlation effects. In the weak correlation region U/t≤4, where U is the one-site Coulomb repulsion energy and t is the transfer integral between the nearest neighbor sites, the response can be described within the band picture, and the third order nonlinear susceptibility χ⁽³⁾ increases slowly with increasing U/t. For U/t≤4, χ⁽³⁾ increases rapidly with increasing U/t, and χ⁽³⁾ at U/t=10 is more than ten times larger than that at U/t=2. This large value of χ⁽³⁾ originates from the exotic properties of carriers in the strongly correlated one-dimensional electron systems.     

Structural and optical properties of lithium borobismuthate glasses

Glasses with compositions 25Li₂O-(75−x)Bi₂O₃-x B₂O₃, with 0?x?30 mol%, have been prepared using the melt quenching technique. The density and the molar volume have been determined. IR spectroscopy is used as a structural probe of the nearest neighbor environment in the glass network. The optical transmittance and reflectance spectrum of the glasses have been recorded in the wavelength range 400-1100 nm. The values of the optical band gap E_g^opt for indirect transition and refractive index have been determined for 0?x?30 mol%. The average electronic polarizability of the oxide ion α_o²⁻ and the optical basicity have been estimated from the calculated values of the refractive indices. Variations in the different physical parameters such as the density, molar volume, optical band gap, refractive index, average electronic polarizability of the oxide ion and optical basicity with B₂O₃ content have been analyzed and discussed in terms of the changes in the glass structure.     

Monte Carlo simulation of film growth in a phase separating binary alloy model

Using a kinetic Monte Carlo method, we simulate binary film (A_0.5B_0.5/A) growth on an L×L square lattice with the focus on the domain growth behaviour. We compute the average domain area, A(t), as a measure of domain size. For a sufficiently large system, we find that A(t) grows with a power law in time with A(t)∼t^2/3 after the initial transient time. This implies that the dynamic exponent for domain growth with non-conserved order parameter is z=3, a value which was theoretically predicted for the conserved order parameter case. Further analysis reveals that such a power-law behaviour emerges because the order parameter is approximately conserved after the early stage of growth.     

IR and Raman investigation on the structure of (100-x)B2O3-x[0.5 BaO-0.5 ZnO] glasses

Glasses with molar composition of (100-x)B₂O₃-x[0.5 BaO-0.5 ZnO], x=40, 50, 60, 70 were prepared from the melts of ZnO, BaCO₃ and H₃BO₃ mixture. The structure and thermal behavior were characterized by IR and Raman spectroscopy, DSC and Dilatometer. The investigation shows that the transition of the structural unit [BO₄] (B^IV) to [BO₃] (B^III) happens when BaO and ZnO content x increases in the borate glass, resulting in fewer B^III-O-B^IV bonds and more B^III-O-B^III bonds. At the same time, the diborate groups, which are found to be the predominant structural group of the glass with high B₂O₃ content, gradually changes into ring-type metaborate, pyro- and orthoborate groups. With increasing ZnO and BaO content x, the glass transition temperature (T_g) and the softening point (T_f) decreases, while linear expansion coefficient (α) increases, that comes from the weakening of the glass network.