Properties of renormalized spectrum of interacting with polarization phonons localized quasiparticle with degenerated excited state

Abstract

The quantum theory of renormalized energy spectrum of the system of localized two-level quasiparticle, with degenerated spectrum, interacting with polarization phonons, being the model of multilayered nanostructure, is developed within the modified Feynman-Pines diagram technique. Effectively taking into account the multi-phonon processes, the theory is valid in a wide range of energies which contains the main states and the satellite groups of energies produced by the resonant bound-to-phonons states of quasiparticle in the vicinity of the threshold energies of their radiation. The properties of renormalized spectrum of the system are analyzed and dependences of the widths of groups of energy levels (main and satellite) on the magnitudes of inter-level coupling constants are obtained.     

Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals

The nonstandard theory of X-ray scattering in a deformed crystal has been generalized. The vector of atomic-plane displacement is introduced into the crystal polarizability model like in the generalized Takagi dynamic theory. The solution to the wave equation is sought for using the procedure of expanding the field amplitude and vector operators in the Fourier components of polarizability χ _H in a series according to the multiscale method. It is shown that considering lattice strain generally calls for introducing various characteristic spatial regions for the diffraction equation, which is in complete agreement with the main concept of the multiscale method. A particular case of a strain field depending on one scale is considered. If a relative change in strain occurs at a length on the order of the extinction length, one can obtain equations generalizing the Takagi equations to the case of arbitrary diffraction geometries.     

Nematic-isotropic phase transition in polar liquid crystals. 2. Role of dispersion interactions

The present study furthers the development of the theory of the nematic-isotropic phase transition in the system of rodlike particles with large longitudinal dipoles. The effect of dispersion interactions between single molecules (monomers) and molecular pairs (dimers) on the transition temperature is considered. The crucial point of the approach used is existence of dimers in the system. Dispersion interactions are estimated within the framework of the model in which molecules consist of spherical blocks interacting according to the Lennard-Jones law. The direct pair-correlation functions are approximated by spherical invariants forming a complete system of functions. Then, these correlation functions are varied in order to study the behavior of the phase-transition temperature depending on the choice of the molecular model. It is shown that, depending on the molecule shapes, dimers can either destroy or stabilize the nematic order. It is also shown that the presence of dimers in the system decelerates an increase of the transition temperature (and, in many instances, can even reduce it) with an increase in the value of the molecular dipole.     

Evolution of the magnetic excitation spectra of the YbB12 kondo insulator under variations in temperature

The results obtained from experiments on inelastic neutron scattering in the YbB₁₂ Kondo insulator are discussed. The structure of the magnetic excitation spectra and their evolution under variations in temperature are interpreted in the framework of a simple phenomenological model with due regard for the crystal field effects renormalized as a result of the influence of the intermediate valence state.     

Dynamical Threshold Behavior of A Sliding Charge Density Wave

It is argued that the existence of a dynamical threshold field [i.e. the value of the electric field such that when the applied field is reduced to this value the charge density wave (CDW) stops sliding] requires that the sliding of the CDW at low center of mass velocity occurs as local sudden jumping motion reminiscent of “stick-slip” friction. Using this model, it is argued in the weak impurity limit that the static threshold field is greater than the dynamic threshold field.     

Polyacetylene and Relativistic Field Theory Models

Connections between continuum, mean-field, adiabatic Peierls-fröhlich theory in the half-filled band limit and known field theory results are discussed. Particular attention is gi en to the Φ⁴ model and to the solvable N +2 Gross-Neveu model. The later is equivalent to the Peierls system at a static, semi- classical level. Based on this equivalence we note the prediction of both kink and polaron solitions in models of trans-(CH)_x. Polarons in cis-(CH) are compared with those in the trans isomer. Optical absorption from polarons is described, and general experimental consequences of polarons in (CH)_x and other conjugated polymers is discussed.     

Analytische Untersuchungen zum Small-Scale-Yielding-Problem

In connection with the asymptotic solution of HUTCHINSON for the small scale yielding problem in a power-law hardening material a second approximation is given by a perturbation theory. The method used makes it possible to estimate further approximations in a successive manner. For this purpose an expression is formulated representing the exponents of these approximations.     

Dopant concentration profile in a Czochralski flow of liquid metal in a vertical or a horizontal magnetic field

Dopant concentration profiles are obtained for a Czochralski flow of liquid metal in a static crucible under either an axisymmetric vertical magnetic field or a horizontal uniform magnetic field. The latter magnetic field inevitably requires fully three-dimensional cylindrical coordinate model equations, which are successfully solved for the representative parameters Gr = 10⁷, Pr = 0.01, Re = 1620 and Ha 1000. Asymmetric concentration profiles are obtained. The average heat flux decreased with the Hartmann number. The circumferential rotational direction was found to be reversed in a lower regime against that of a top rotating crystal rod in a strong lateral magnetic field. In a vertical magnetic field, the concentration profile approached the pure diffusion state.     

Numerical Simulation of a Liquid Drop Freely Oscillating

Free oscillations of a viscous liquid drop surrounded by a dynamically inactive ambient gas, in zero gravity, are investigated numerically using FIDAP^TM package in the axisymmetrical case. The full Navier‐Stokes equations with appropriate interfacial conditions are solved by using Galerkin/Finite element technique along with the spine method for the advection of the free boundary are used. The aim of this preliminary study is to demonstrate the ability of the package to accurately solve nonlinear free surface problems. Oscillations of viscous drops released from an initial static deformation of small‐ to large‐amplitude proportional to the second spherical harmonic, without initial internal circulation, are considered. Accuracy is attested by demonstrating that (i) the drop volume remains constant, (ii) dynamic response to small and moderate amplitudes agrees well with linear and weakly non‐linear perturbation theories, (iii) large amplitude oscillations compare well with some numerical and experimental published results.     

Theory of X-Ray diffuse scattering from a crystal with pores in the form of triangular prisms

A theory of X-ray diffuse scattering (XRDS) from a crystal with pores in the form of triangular prisms has been developed. Solutions for the static Debye-Waller factor, intrinsic correlation function, and the correlation volume (which characterizes the XRDS angular distribution in reciprocal space) are obtained within this model. A numerical simulation of reciprocal space maps of X-ray diffuse scattering is performed. The influence of pore-size fluctuations on the formation of XRDS intensity isolines is demonstrated.     

CdX2(X=Cl、Br):Ni2+晶体的吸收光谱和EPR谱的统一解释

本文考虑3d电子和轨道局域性差异和配体旋-轨耦合作用的影响,在晶体场理论和电子顺磁共振理论基础上,采用d轨道模型,推导出了3d2/d8电子组态在D3d对称下的广义能量矩阵,利用双共价因子双旋-轨耦合EPR谱高阶微扰公式,统一解释了CdX2(X=Cl、Br):Ni2+晶体的吸收光谱和EPR谱.     

Computer Simulation Studies of Anisotropic Systems,III. Two-Dimensional Nematic Liquid Crystals

We have studied a two-dimensional ensemble of cylindrically symmetric particles interacting via a weak anisotropic potential using the Monte Carlo technique of computer simulation. The calculation is simplified by confining the particles to the sites of a triangular lattice. The internal energy, specific heat, second rank orientational order parameter and second rank orientational pair correlation function were calculated at various temperatures. The variation of the order parameter and pair correlation function shows that the system exhibits a transition from an orientationally disordered to a partially ordered phase. The temperature dependence of the specific heat suggests that the transition is second order or higher.

The possibility of the existence of order-disorder transitions in two dimensions is discussed. The results of the simulation are then compared with the predictions of a molecular field theory of orientational phase transitions. As expected the theory is found to be in poor agreement with the calculations.     

Molecular organization in liquid crystals: A comparative computational analysis

A comparative computational analysis of molecular organization in four-nematogenic acids (nOCAC) having two, four, six, and eight carbon atoms in the alkyl chain is carried out with respect to translatory and orientational motions. The evaluation of the atomic charge and dipole moment at each atomic center is performed through the complete neglect differential overlap (CNDO/2) method. The Rayleigh-Schrödinger perturbation theory, along with the multicentered-multipole expansion method, is employed to evaluate the long-range interactions, while the “6-exp” potential function is assumed for short-range interactions. The total interaction-energy values obtained through these computations are used to calculate the probability of each configuration at the phase transition temperature via the Maxwell-Boltzmann formula. Further, the flexibility of various configurations is studied in terms of variation of probability due to small departures from the most probable configuration. A comparative picture of molecular parameters, such as the total energy, binding energy, and total dipole moment, is given. An attempt is made to explain the nematogenic behavior of these liquid crystals in terms of their relative order and, thereby, to develop a molecular model for the liquid crystallinity.     

Theoretical investigation of phantom controlled crystal growth: Equations and model without surface tension

A general model with one free operator is described for growing a crystal of a given shape. We give basic equations and investigate a simple model without surface tension.     

The glass transition of Pd40Ni10Cu30P20 studied by temperature-modulated calorimetry

The frequency dependence of the heat capacity in the glass-transition region of Pd₄₀Ni₁₀Cu₃₀P₂₀ was studied by temperature-modulated differential scanning calorimetry (TMDSC) during slow heating and cooling. Such data for low frequencies between 0.1 and 0.01 Hz are not available, especially for metallic glasses. A crossover between mixed static/dynamic and purely dynamic response signals was observed for the lowest frequencies between 1/80 and 1/100 s⁻¹, which allows a direct determination of the average relaxation time at a given cooling rate during the static glass transition. Further, these results were used to evaluate the experimental parameters necessary to truly separate the static and dynamic response in low-frequency modulation calorimetry experiments to obtain the moduli of the dynamic specific heat.     

The strain energy density of cubic epitaxial layers

We obtain a compact exact expression for the strain energy density of a cubic epitaxial medium in the limit of linear elasticity theory. Only the result for 001 is identical to the isotropic case: the greatest departure from isotropic theory occurs for 111. We have evaluated this difference for a large number of cubic media and have obtained an estimate of its impact on epilayer critical thickness t_c for [001] oriented growth. We suggest that it tends to lower t_c for [001] oriented growth relative to that given by isotropic theory: by 15%–30% for common semiconductors and by up to a factor of 3 for metals.     

Dark field microscopy for diffraction analysis of amorphous carbon solids

Diffraction methods for determining structure in non-crystalline materials often rely solely on the determination of pair correlation functions, extracted from measurements of the diffracted intensity. A dark field image of a non-crystalline solid taken with a conventional transmission electron microscope contains phase information lost in the measurement of the diffracted intensity which can be accessed by evaluating a variance function. This variance function is defined in terms of spherical averages of the diffracted intensity and the mean square of the diffracted intensity. The latter contains higher order correlation information derived from correlations between two pairs of atoms. We examine the sensitivity of the variance function, to subtle atomic structural differences between carbon network structures. The structures have similar pair correlations, but different levels of diamond like bonding. The variance function is shown to give improved discrimination between the networks.     

Systematic Solution of the Mean Field Equation for Liquid Crystals

Starting with a pairwise, spatially and orientationally dependent intermolecular potential of the Kobayashi-McMillan form, we carry out a systematic solution of the mean field equation for liquid crystals. The mean field equation, presented as first of a hierarchy of BBGKY equations, is first reduced to a set of coupled integrodifferential equations by means of expanding the distribution function f (r, δ) and In f (r, δ) in Legendre polynomials and the reciprocal lattice space. In the first level of approximation, the expansion retains only the lowest-order coefficients, permitting a complete decoupling of the equations. In the second level of approximation, the leading coefficient which couples spatial order to orientational order is included. In the third level of approximation two more higher order coefficients are included. At each level, the free energy functional is evaluated to determine the equilibrium phase at given temperatures and chainlengths of a homologous series. It is shown that the expansion converges very rapidly, the second level of approximation being entirely sufficient. This lends support to our earlier variational calculation which contained only three variational parameters.     

Contribution to the determination of the entropy production for steady state eutectic growth

In order to find a generalized entropy production for steady-state eutectic growth the entropy production per unit time and volume is to be determined. A relationship which expresses the entropy production per unit time and volume as a function of KRUPKOWSKI 's equations is shown. It is in a qualitative accuracy with LESOULT -TURPIN 's theory. The above quantity is to be integrated over a distinguished volume of the unidirectionally solidified eutectic structure. A correlation between this volume and entropy production is discussed.     

An analysis of dielectric relaxation using the fractional master equation of the stochastic Ising model

In this paper, we begin introducing some basic definitions and mathematical preliminaries of the fractional calculus theory. By using the fractional calculus technique (that is, calculus of derivatives and integrals of any arbitrary real or complex order) a solution of the fractional master equation derived from the stochastic Ising model of Glauber has been obtained and the result is applied to an analysis of the dielectric relaxation processes. From the solution of the equation, the Cole-Cole dispersion relation, KWW (Kohlrausch-William-Watts) equation and algebraic decay relaxation functions are obtained easily. Then these functions are compared with Bozdemir's earlier analysis of the stochastic Ising model.