Structure analysis of multiphase systems by anomalous small-angle X-ray scattering

The theory of small-angle scattering is reviewed with special attention paid to the anomalous scattering and multiphase systems. A general equation is derived that describes the scattering of a multiphase system as a sum of scattering functions of each of the phases, as if it scattered alone in a two-phase system, and interphase interference scattering functions. These scattering functions depend only on the spatial distribution of the phase boundaries, but not on the scattering density. Contrast variation techniques are most rewarding when the scattering density of only one phase can be varied. For anomalous small-angle X-ray scattering (ASAXS), this means the most favourable is the case in which resonant atoms are contained in one phase only. The general equation involves n(p ? 1) unknown partial atomic number density differences, where p is the number of phases and n the number of the different atom types in the sample. These partial atomic number density differences can be found if a suitable structure model is applied to calculate the phase scattering functions. Then, the phase compositions and densities can be calculated by solving a system of linear equations incorporating the atom number conservation law. The partial structure factors formalism is also reviewed. Corresponding equations for a system of n types of atoms and p phases are derived. The number of independent partial structure factors is p(p ? 1)/2 and depends on the number of phases, but not on the number of the types of the atoms in the sample, as in the case of wide-angle scattering.     

A probabilistic model for tracer distribution in multiphase spatially inhomogeneous transport systems

A probabilistic model describing tracer transport in multiphase spatially inhomogeneous transport (plug-flow) systems is presented. The properties of the trajectories are completely described by a two-component Markov process with absorbing boundaries. The first component is continuous, the second discrete. Infinitesimal conditions are given. Probabilities associated with the process are derived.     

Coarsening in inhomogeneous systems

This article is a brief review of coarsening phenomena occurring in systems where quenched features—such as random field, varying coupling constants or lattice vacancies—spoil homogeneity. We discuss the current understanding of the problem in ferromagnetic systems with a non-conserved scalar order parameter by focusing primarily on the form of the growth law of the ordered domains and on the scaling properties.     

Domain growth and aging scaling in coarsening disordered systems

We explore the electronic and transport properties out of a biased multilayer hexagonal boron nitride (h-BN) by first-principles calculations. The band gaps of multilayer h-BN decrease almost linearly with increasing perpendicular electric field, irrespective of the layer number N and stacking manner. The critical electric filed (E ₀) required to close the band gap decreases with the increasing N and can be approximated by E ₀ = 3.2 / (N ? 1) (eV). We provide a quantum transport simulation of a dual-gated 4-layer h-BN with graphene electrodes. The transmission gap in this device can be effectively reduced by double gates, and a high on-off ratio of 3000 is obtained with relatively low voltage. This renders biased MLh-BN a promising channel in field effect transistor fabrication.     

Slow coarsening in a class of driven systems

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating the various growing domains are macroscopically smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions. Received 3 April 2000     

On the anomalous skin effect in an inhomogeneous bounded plasma

The possibility of penetration of a variable transverse field into a bounded plasma when the skin depth is small in comparison with the plasma thickness is discussed.     

Exchange and correlation in inhomogeneous electron systems

An exchange-correlation functional with a nonlocal density dependence is proposed. It fulfills a sum rule stating that the exchange-correlation hole should contain on electron, atom. We have used this functional as well as an earlier proposed approximation to calculate the exchange energy of atoms. The errors in the local density approximation are reduced by an order of magnitude, indicating that these improved functionals should be very useful for more complicated systems.     

Diffusion in multiphase systems with nonstationary boundaries

In this work the problem of diffusion in the definite diffusion field whose one boundary is fixed and the other — interphase boundary — moves in time according to the parabolic law. The mathematical problem is solved exactly by means of thermal potentials of a double layer. The solution of the diffusion equation in the proximity to the boundary was derived and the concentration gradients on these boundaries were calculated. The numerical procedure of determining the diffusion characteristics from experimental concentration gradients on the phase boundaries was presented. As the zero approximation the result of calculations according to Wagner’s solution was used. Theory. Numerical calculations.     

Entanglement in spatially inhomogeneous many-fermion systems

We investigate entanglement of strongly interacting fermions in spatially inhomogeneous environments. To quantify entanglement in the presence of spatial inhomogeneity, we propose a local-density approximation (LDA) to the entanglement entropy, and a nested LDA scheme to evaluate the entanglement entropy on inhomogeneous density profiles. These ideas are applied to models of electrons in superlattice structures with different modulation patterns, electrons in a metallic wire in the presence of impurities, and phase-separated states in harmonically confined many-fermion systems, such as electrons in quantum dots and atoms in optical traps. We find that the entanglement entropy of inhomogeneous systems is strikingly different from that of homogeneous systems.     

Kinetic theory of runaway breakdown in inhomogeneous thundercloud electric field

Kinetic theory of runaway breakdown in inhomogeneous thunderstorm electric field is developed. The kinetic equation, boundary and initial conditions are formulated. Spectrum of X-ray emission generated by runaway electrons is calculated. It has quite a specific form: a sharp maximum at energies 50–60 keV and a rapid fall both to the smaller and higher energies. The intensity of the emission is growing effectively with the relation E_m/E_c (of maximal electric field E_m to critical field E_c) and falling down sharply with the distance near the point z where electric field E(z) is equal to critical field E_c.     

Optical resonance in inhomogeneous parity-time symmetric systems

We show that inhomogeneous waveguides of slowly varied parity-time(PT) symmetry support localized optical resonances.The resonance is closely related to the formation of exceptional points separating exact and broken PT phases. Salient features of this kind of non-Hermitian resonance, including the formation of half-vortex flux and the discrete nature,are discussed. This investigation highlights the unprecedented uniqueness of field dynamics in non-Hermitian systems with many potential adaptive applications.     

Magnetoexciton light absorption in inhomogeneous quasi-two-dimensional systems

The problem of exciton light absorption in quasi-two-dimensional inhomogeneous systems in a strong transverse magnetic field H is analyzed. We assume that a random Gaussian field (“white noise”) acting separately on an electron and a hole is due to (1) fluctuations in the quantum well thickness or (2) fluctuations in the concentrations of the solid solution components. The problem of a magnetoexciton in a random Gaussian white noise field has been reduced to the problem of the motion in an H-dependent effective field of a single particle with the effective magnetic mass of the exciton, which is a function of the magnetic field and parameters of the quantum wells, in a field characterized by “colored noise,” whose correlation function is different from that of the white noise field. In this approximation, the problem of a magnetoexciton in isolated and coupled quantum dots is considered. In the coherent-potential approximation, the exciton absorption in random fields of the first and second type in single and coupled quantum wells has been calculated. The absorption decreases as H increases in the range of strong magnetic fields, which is in agreement with experimental data. Zh. éksp. Teor. Fiz. 114, 1451–1465 (October 1998)     

Critical dynamics and stability of elastically coupled systems at marginal dimensionalities

Static and dynamic behavior of an-component classical model atd=4 has been investigated assuming a coupling to a fluctuating lattice displacement field. Solutions of renormalization-group (RG) equations are given for elastically isotropic and anisotropic systems, and the temperature dependences of elastic constants and of the corresponding damping coefficients are calculated. For isotropic and weakly anisotropic systems it is found that forn<4 the critical regime can be split into a rigid regimet>t _s , and a compressible regimet<t _s , wheret=(T–T _c )/T _c andt _s is a crossover temperature. In the rigid regime, the logarithmic correction factors characterizing deviations from Landau theory have the same form as in systems without elastic coupling; in the compressible regime the exponents are renormalized by the coupling. Forn4 rigid behavior prevails at all temperatures; similarly only rigid behavior is found for strongly anisotropic systems for alln. The thermodynamic stability of the system is investigated by evaluating the contribution of ring diagrams for the casen=1. It is thus shown that under constant hydrostatic pressure a first-order transition occurs in both isotropic and anisotropic systems, and the corresponding equations for the transition temperature and the value of the order parameter atT _c are derived.     

On the connection between off-equilibrium response and statics in non disordered coarsening systems

The connection between the out of equilibrium linear response function and static properties established by Franz, Mezard, Parisi and Peliti for slowly relaxing systems is analyzed in the context of phase ordering processes. Separating the response in the bulk of domains from interface response, we find that in order for the connection to hold the interface contribution must be asymptotically negligible. How fast this happens depends on the competition between interface curvature and the perturbing external field in driving domain growth. This competition depends on space dimensionality and there exists a critical value d _c = 3 below which the interface response becomes increasingly important eventually invalidating the connection between statics and dynamics as the limit d = 1 is reached. This mechanism is analyzed numerically for the Ising model with d ranging from 1 to 4 and analytically for a continuous spin model with arbitrary dimensionality. Received 10 July 2001     

Anomalous heat conduction and anomalous diffusion in one-dimensional systems

We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is =2Dt(alpha)(01) implies anomalous heat conduction with a divergent thermal conductivity (beta>0). More interestingly, subdiffusion (alpha<1) implies anomalous heat conduction with a convergent thermal conductivity (beta<0), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results.     

Electrogradient EMF and volt-ampere characteristics of inhomogeneous systems

This paper studies the manifestation of electrogradient effects in the shape of the voltampere characteristics (VAC) of inhomogeneous conducting sandwich structures of the SSS and MSM types (S stands for n-type semiconductor, and M for metal) during the passage of a current perpendicular to the interfaces between the materials. It is shown that on the ohmic portion of the VAC the Peltier effect in the general case causes the conductivity of the sandwich system to drop. In the region of heating currents the VAC displays segments that are quadratic with respect to the current. The case when the VAC remains linear in the region of heating currents is considered.