Conformal Evolution of Waves in the Yang-Mills Condensate: The Quasi-Classical Approach

We have constructed a consistent system of equations for the Yang-Mills quantum-wave fluctuations in the classical Yang-Mills condensate based on canonical quantization in the Heisenberg representation. Such a quasi-classical system has been thoroughly analyzed in the conformal limit in the linear and quasi-linear approximations, both analytically and numerically. We have found that interaction between waves and condensate triggers a significant transfer or swap of energy from the condensate to the wave modes in the SU(2) gauge theory. Remarkably, a similar energy swap effect has been found in the maximally-supersymmetric N=4 Yang-Mills theory, as well as in the two-condensate SU(4) gauge theory. Such a generic feature of Yang-Mills dynamics opens up vast phenomenological implications in ultra-relativistic Yang-Mills plasma physics.

Quantum Gravity in Heisenberg Representation and Self-Consistent Theory of Gravitons in Macroscopic Spacetime

The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically equivalent to the operator equations of quantum theory of gravity with canonical rules of quantization of the gravitational and ghost fields. In its operator formulation, the theory can be used to calculate the graviton S-matrix as well as to describe the quantum evolution of macroscopic system of gravitons in the non-stationary Universe or in the vicinity of relativistic objects. In the S-matrix case, the standard results are obtained. For problems of the second type, the original Heisenberg equations of quantum gravity are converted to a self-consistent system of equations for the metric of the macroscopic space time and Heisenberg operators of quantum fields. It is shown that conditions of the compatibility and internal consistency of this system of equations are performed without restrictions on the amplitude and wavelength of gravitons and ghosts. The status of ghost fields in the various formulations of quantum theory of gravity is discussed.

Macroscopic Effect of Quantum Gravity: Graviton, Ghost and Instanton Condensation on Horizon Scale of Universe

We discuss a special class of quantum gravity phenomena that occur on the scale of the Universe as a whole at any stage of its evolution, including the contemporary Universe. These phenomena are a direct consequence of the zero rest mass of gravitons, conformal non-invariance of the graviton field, and one-loop finiteness of quantum gravity, i.e. it is a direct consequence of first principles only. The effects are due to graviton-ghost condensates arising from the interfereence of quantum coherent states. Each of coherent states is a state of gravitons and ghosts of a wavelength of the order of the horizon scale and of different occupation numbers. The state vector of the Universe is a coherent superposition of vectors of different occupation numbers. One-loop approximation of quantum gravity is believed to be applicable to the contemporary Universe because of its remoteness from the Planck epoch. To substantiate the reliability of macroscopic quantum effects, the formalism of one-loop quantum gravity is discussed in detail. The theory is constructed as follows: Faddeev-Popov path integral in Hamilton gauge → factorization of classical and quantum variables, allowing the existence of a self-consistent system of equations for gravitons, ghosts and macroscopic geometry → transition to the one-loop approximation, taking into account that contributions of ghost fields to observables cannot be eliminated in any way. The ghost sector corresponding to the Hamilton gauge automatically ensures of one-loop finiteness of the theory off the mass shell. The Bogolyubov-Born-Green-Kirckwood-Yvon (BBGKY) chain for the spectral function of gravitons renormalized by ghosts is used to build a self-consistent theory of gravitons in the isotropic Universe. It is the first use of this technique in quantum gravity calculations. We found three exact solutions of the equations, consisting of BBGKY chain and macroscopic Einstein’s equations. It was found that these solutions describe virtual graviton and ghost condensates as well as condensates of instanton fluctuations. All exact solutions, originally found by the BBGKY formalism, are reproduced at the level of exact solutions for field operators and state vectors. It was found that exact solutions correspond to various condensates with different graviton-ghost compositions. Each exact solution corresponds to a certain phase state of graviton-ghost substratum. We establish conditions under which a continuous quantum-gravity phase transitions occur between different phases of the graviton-ghost condensate.

Structure and dielectric properties of (1-x)Na_(0.5)Bi_(0.5)TiO_(3-x)Na_(0.5)K_(0.5)NbO_(3)

The solid solutions of the(1-x)Na_(0.5)Bi_(0.5)TiO_(3-x)Na_(0.5)K_(0.5)NbO_(3) system were produced by the conventional ceramic technology using mechanical activation of the synthesized product.It was found that in the(1-x)Na_(0.5)Bi_(0.5)TiO_(3-x)Na_(0.5)K_(0.5)NbO_(3) system at room temperature,a number of morphotropic phase transitions occur:rhombohedral!cubic!tetragonal!monoclinic phases.The introduction of a small amount of Na_(0.5)K_(0.5)NbO_(3) leads to an increase in the temperature stability of the dielectric properties of ceramics.A change in the relaxor properties of the solid solutions of the(1-x)Na_(0.5)Bi_(0.5)TiO_(3-x)Na_(0.5)K_(0.5)NbO_(3) system was shown.The increase in energy density and energy efficiency was found at additive 10 mol.%of Na_(0.5)K_(0.5)NbO_(3).

Microstructure, domain structure, ferroelectric and piezoelectric properties of textured bismuth-containing ceramics

In this report,the processes of texture formation in grain-oriented ferroelectric ceramics based on layer-structured ferroelectric Bi_(4)Ti_(3)O_(12)(LSBT)prepared by hot forging method are considered.The microstructural and X-ray methods revealed the axial textured formation in ferroelectric ceramic that are used to estimate the orientation factor of ceramics.For the first time,the domain structure changes when poling the anisotropic ferroelectric ceramics are investigated.The anisotropy of electromechanical,piezoelectric and ferroelectric properties of ferroelectric ceramics due to the crystal texture existence in it is studied.The aim of this study is to study the processes of crystalline texture formation in polycrystalline BLSF and to establish the dependence of the electrophysical properties of ceramics on the degree of texturing.Ceramics were textured using the hot stamping(HS)method developed at the Research Institute of Physics.The mechanism of the method is that the workpiece is subjected to uniaxial pressure and free radial deformation occurs due to the plastic flow of the material until the workpiece fills the free volume of the mold,which is created by placing the workpiece in the mold with a gap.The study of the microstructure of ceramics showed that an increase in the firing temperature in the range 950-1050℃ causes a sharp decrease in porosity and increases the density to 7.95 g/cm^(3),which is 98%of theoretical.An X-ray analysis was performed and microstructural studies were carried out,which revealed the formation of an axial texture in ceramics.The features of the switching processes of textured ceramics are revealed.The characteristics of the polarization switching of ceramics in the directions parallel and perpendicular(⊥)of the pressure axis during hot processing were obtained from the dielectric hysteresis P(E)loops,i.e.,axis axial texture.The⊥-cut ceramics are characterized by a more complete polarization switching,which is associated with the additional orientation of the(001)crystallographic planes in the textured material,as well as the presence of a threshold switching field.In the temperature range from-196 to+600℃,the anisotropy of the electro physical properties of ceramics due to the presence of a crystalline texture in it was studied.The dielectric constant,electrical conductivity,piezoelectric and elastic coefficients were measured for sections of ceramics of different orientations relative to the axis of the texture.The anisotropy of the dielectric constant and electrical conductivity manifests itself weakly at room temperature and increases sharply when approaching the Curie temperature.In the temperature range+20-400℃,the high thermal stability of the piezoelectric module d_(33),measured by the quasistatic method,was established.

Parameter of dielectric loss distribution in the new model for complex conductivity based on Havriliak-Negami formula

This paper is focused on the comparison of the results of various approximation models describing the frequency dependences of the dielectric constanε'/ε_(0)(f)andε"/ε_(0)(f),the tangent of the loss angle tgδ(f)T and the electrical conductivityγ'(f)T andγ"(f)T of nonlinear dielectrics.The classic ferroelectric material of the PZT system with x=0.50 was chosen as the object of study.Based on the analysis of temperature-frequency dependences of the“empirical”parametersαandβ,a regularity has been revealed that allows them to be calculated.A new relationship has been established through the parameterα,which allows to relate the temperature and frequency dependences of the complex electrical conductivity asω→∞and asω→0 in the Havriliak-Negami approximation models and in the new model for the description of the complex electrical conductivityγ*.It is shown thatαis a parameter of the temperature-frequency distribution of dielectric losses.Using the obtained expressions,a new theoretical description of experimental spectra having a relaxation character was proposed.It has been proven that the use of the new model makes it possible to accurately describe the set of studied spectra,including the high and low frequencies,in the frequency range from 10^(-3) to 10^(8) Hz.

Microstructure features of the BST/(Mg,Ln)-ceramic

Solid solutions of the composition Ba_(1-x-y)(Mg,Ln)_(x)SryTiO_(3)(x=0.01;0.025;0.04;y=0.20;0.50;0.80;Ln=La,Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Er,Tu,Yb)were prepared by two-stage solid-phase synthesis followed by sintering using conventional ceramic technology.The influence of rare-earth elements on the microstructure of the prepared ceramic samples was investigated.It was found that regardless of the type of modifiers introduced,the grain landscape of the studied solid solutions with different amounts of SrTiO_(3)is refined(in the initial system,the average grain size,d,at x=0.20 is 6μm;at x=0.50 is 4μm;at x=0.80 is 18μm)to crystallite sizes not exceeding(2-3)μm,and compacted.The using of mechanical activation procedures leads to an even greater decrease in the size and an increase in the density of ceramics.The increasing in the concentration of modifiers in each group(within the considered range of dopant variation)against the background of such a fine-grained structure has little effect on the dynamics of changes in d.It is concluded that it is advisable to use the data obtained in the development of functional materials based on BST/(Mg,Ln)and devices with the participation of these compositions.

Grain landscape and dielectric properties of ceramics based on sodium,calcium,strontium niobates,depending on the synthesis and sintering conditions,and mechanical processing

The properties studying results of ceramics based on strontium,calcium and sodium niobates,which vary from the conditions of synthesis,sintering,and mechanical processing,are presented.The evolution of the grain structure of objects is traced depending on their phase filling during concentration changes in the composition and thermodynamic prehistory(preparation conditions).

Phase states and electrophysical properties of multicomponent perovskite solid solutions on the base of PMN-PT and PZT systems

Phase diagrams were constructed(at room temperature),the dielectric,piezoelectric,elastic and reversible properties of the Gemodified xPbTiO_(3)-yPbZrO_(3)-zPbNb_(2/3)Mg_(1/3)O_(3) multicomponent system ceramics were studied.The data obtained are compared with the results of studies of solid solutions of basic binary systems,as well as with the results obtained previously for other sections of the system under consideration.A significant increase in the width of the morphotropic region,diffusion of the concentration dependences of the electrophysical characteristics,and an increase in stability under the influence of constant bias fields in the solid solutions of the studied system were established.

Crystal structure,microstructure,electrophysical properties,and thermally induced aging of PZT-CdNb_(2)O_(6)ceramics

Solid solution samples of the three-component system(1−x)Pb(Ti_(0.5)Zr_(0.5))O_(3)−xCdNb_(2)O_(6)with x=0.0125-0.0500,Δx=0.0125 were obtained by solid phase synthesis followed by sintering using conventional ceramic technology.The crystal structure,microstructure,electrophysical,and thermophysical properties of these ceramics have been studied.It is shown that all studied solid solutions can be divided into two groups(with x=0.0125 and with x>0.0125),characterized by different characteristics of the change in properties with variations in external influences.This is probably due to the transition from a perovskite-type structure with a tetragonal(T)unit cell to inhomogeneous solid solutions consisting of a series of T-phases with similar cell parameters.A conclusion is made about the expediency of using the data obtained in the development of similar materials for devices based on them.

Studying of dielectric spectra of YCu_(0.15)Mn_(0.85)O_(3)solid solution with the use of complex conductivity

This work presents the results of studying the electrophysical properties of the YCu_(0.15)Mn_(0.85)O_(3)solid solution in the range of temperatures of T=26-400°C and frequency range of f=102-105 Hz.A model description of the revealed dispersion of dielectric parameters in the material is made.The nonclassical modified Havriliak-Negami model written for complex electrical conduc-tivity was used as an approximation model.It is shown that the application of this model almost exactly describes the frequency behavior of the dielectric constantε′/ε0(f),the dielectric loss tangent tgδ(f)as well as the real and imaginary parts of complex conductivityγ′(f)andγ′′(f).The results of this work are an important step in identifying the opportunities and understanding the applications of this model.

Peculiarities of the dependences of the dielectric properties of solid solutions of multicomponent systems on the electronegativity of their constituent cations

Solid solutions(SS)of 3-and 4-component systems based on lead titanate-zirconate were prepared by the method of solid-phase reactions and uniaxial hot pressing.The dependences of the relative permittivity of polarized samples on the electronegativity(EN)of their constituent cations have been studied.The ferro-hardness of the SS(the stability of the domain structure to external influences)is shown to be directly dependent on the EN of elements B in the corresponding oxidation states,i.e.,the degree of covalence of the B-O bond.The deviation from this dependence in SS with Ni and Cd is explained by their individual features,which result in changes in the degree of bond covalence in both cationic sublattices.The conducted crystal-chemical analysis made it possible to choose promising SS when creating ferroelectric materials,including textured piezoelectric ceramic materials for piezoelectric transducers for various purposes:Piezotransformers,piezoelectric motors,ultrasonic emitters,filter devices,ultrasonic flaw detectors,accelerometers,etc.

Low-and high-field electromechanical responses of relaxor-based multicomponent ceramics for application in multiregime actuators

The electromechanical responses of multicomponent solid solutions Pb_(0.95)Ba_(0.05)(Mg_(1/3)Nb_(2/3))_(0.471)(Zn_(1/3)Nb_(2/3))_(0.102)(Ni_(1/3)Nb_(2/3))_(0.152)Ti_(0.275)O_(3)in low and high electric fields were studied.In both cases,significant electromechanical responses are observed.In particular,the maximum values of the large-signal piezoelectric coefficient d_(33)reach 1600 m/V at very low values of the electric field(≈5 kV/cm).The observed features of the electromechanical responses of the studied ceramics are advantages in terms of their possible application in actuators.

Thermophysical properties of BiFeO_(3)/REE multiferroics in a wide temperature range

The paper presents the results of a comprehensive study of the thermophysical properties(thermal conductivity,thermal diffusivity,heat capacity)of high-temperature multiferroic BiFeO_(3) modified with rare-earth elements(REEs)(La,Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Er,Tm,Lu).The regularities of the formation of the mentioned characteristics were established.The assumptions about the nature of the observed phenomena were suggested.

Structure and dielectric properties of solid solutions Bi_(7−2x)Nd_(2x)Ti_(4)NbO_(21)(x=0.0,0.2,0.4,0.6,0.8,1.0)

The electrophysical and structural characteristics of bismuth titanate oxides of a number of phases of solid solutions of the Aurivillius phases Bi_(7−2x)Nd_(2x)Ti_(4)NbO_(21)(x=0.0,0.2,0.4,0.6,0.8,1.0)having a layered structure of the perovskite type have been investigated.According to the XRD data,all studied compounds are single-phase and have a mixed-layer structure of Aurivillius phases(m=2.5)with a rhombic crystal lattice(space group I2cm,Z=2).A relationship has been established between changes in the chemical composition of solid solutions and orthorhombic and tetragonal distortions of perovskite-like layers.The temperature dependences of the relative permittivityε/ε_(o)(T)are measured.It was found that the change in the phase transition temperature-Curie temperature T_(C)synthesized Aurivillius phases Bi_(7−x)Nd_(2x)Ti_(4)NbO_(21)(x=0.0,0.2,0.4,0.6,0.8,1.0)has a close to linear dependence on the change in the parameter x.The activation energies of charge carriers in different temperature ranges were calculated.It was found that three clearly defined temperature ranges with different activation energies can be distinguished,which is associated with the different nature of charge carriers in the studied solid solutions of the perovskite type.The effect of substitution of Nd^(3+)ions for Bi3+ions is investigated.

Dielectric properties of bismuth-containing pyrochlores:A comparative analysis

The comparative analysis of the dielectric properties of bismuth-containing pyrochlores with different manifestation of atomic order/disorder was carried out.We examined the dielectric properties(including behavior in electric fields)of two pyrochlore compounds:BZN(presumably a composition close to Bi_(1.5)Zn_(0.5)Nb_(1.5)O_(6.5))ceramics with chemical disorder in both A and B cation sublattices and Bi_(2)Ti_(2)O_(7)single crystal with fully chemical ordered structure.The fundamental differences between the dielectric properties of the BZN ceramics and Bi_(2)Ti_(2)O_(7)single crystal were shown.In particular,in the dielectric relaxation behavior(which cannot be described via Arrhenius law in the Bi_(2)Ti_(2)O_(7))or in the influence of the electric fields on the dielectric permittivity(split-ting of the field-cooled and zero-field-cooled behaviors was observed for Bi_(2)Ti_(2)O_(7)below estimated freezing temperature).The results of this study highlights the special role of Bi_(2)Ti_(2)O_(7)as a candidate material for studying aspects of geometric frustration related with pyrochlore structure in non-magnetic medium and specifies the future directions of research.

Crystal structure and dielectric properties of layered perovskite-like solid solutions Bi_(3-x)Gd_(x)TiNbO_(9)(x=0,0.1,0.2,0.3)with high Curie temperature

The Aurivillius phases(APs)[Bi_(2)O_(2)]2t[A_(m-1)B_(m)O_(3m+1)]2-are well-known ferroelectrics with high Curie temperatures.Hightemperature piezoceramics Bi_(3-x)Gd_(x)TiNbO_(9)(BiGdTiNb,x=0,0.1,0.2,0.3)were prepared by a solid-state reaction method.The structural and electrophysical characteristics of BiGdTiNb ceramics have been studied.According to the data of powder X-ray diffraction,all the compounds are single-phase with the structures of two-layer APs(m=2)with the orthorhombic crystal lattice(space group A21am).The temperature dependence of the relative permittivityε/ε_(0)(T)of the compounds was measured and showed that the Curie temperature of perovskite-like oxides Bi_(3-x)Gd_(x)TiNbO_(9) increases linearly with an increase in the substitution parameter x to T_(C)=950℃.The activation energies of charge carriers have been found in different temperature ranges.

Structure and dielectric properties of solid solutions Bi_(7)Ti_(4+x)WxNb_(1-2x-0.1)V_(0.1)O_(21)(x=0.1-0.4)

The structural and electrophysical characteristics of a number of solid solutions of layered oxides of the perovskite-type Bi_(7)Ti_(4+x)WxNb_(1-2x-0.1)V_(0.1)O_(21)(x=0.1-0.4)are studied.According to X-ray powder diffraction data,all the compounds studied are single-phase and have the structure of Aurivillius phases(m=2.5)with a rhombic crystal lattice(space group I2 cm,Z=2).Changes in tetragonal and rhombic distortions of perovskite-like layers in compounds were considered depending on their chemical composition.The temperature dependences of the relative permittivityε(T)were measured.It was shown that the Curie temperature T_(C) of the perovskite-type oxides Bi_(7)Ti_(4+x)WxNb_(1-2x-0.1)V_(0.1)O_(21)(x=0.1-0.4)linearly decreases with increasing parameter x.The activation energies of charge carriers were obtained in different temperature ranges.It was found that there are three temperature regions with very different activation energies due to the different nature of the charge carriers in the studied compounds.The effect of substitution of Nb^(5+) ions by V^(5+) ions is investigated.It was found that for a number of compounds,the substitution of niobium ions by vanadium ions led to an increase in the dielectric constant and a decrease in the dielectric loss tangent.

Effect of lithium carbonate modification on the ferroelectric phase transition diffusion in lead ferroniobate ceramics

The paper discusses the features of the effect of modification with lithium carbonate on the dielectric dispersion of lead ferroniobate ceramics.The modifier has been previously shown to change the ways of the recrystallization sintering and therefore reduce the sintering temperature of the ceramics,increase their average grain size,and improve their dielectric and piezoelectric properties.In this study,the emphasis is placed on the analysis of the diffusion effects of the ferroelectric phase transition upon such mod-ification considered from the standpoint of the chemical specifics of the modifier and its location in the structure of the parent compound.

Colossal dielectric response and complex impedance analysis of LaFeO_(3)ceramics

The present investigations mainly focused on the colossal dielectric response and complex impedance analysis of LaFeO3 ceramics.The studied sample was prepared by a citrate gel method.Structural and microstructural properties are analyzed from the XRD pattern and SEM micrograph.The anomalies in the dielectric constant versus temperature plots are analyzed on the basis of polarization induced by the Maxwell-Wagner mechanisms and ferromagnetic interaction between the Fe3+ions driven by the oxygen vacancy mediated Fe^(3+)-Vo-Fe3+exchange interaction A giant dielectric permittivity in the order of~105 was observed in the sample even at the room temperature for 100 Hz.The colossal dielectric constant in LaFeO3 is mainly driven by the internal barrier layer capacitor(IBLC)formation.The formation of IBLC was explained on the basis of highly insulating grain boundary and less resistive/semiconducting grain,which was confirmed from both the resistance and capacitance of grain and grain boundary from the impedance analysis.The non-Debye-type relaxation process associated with the grain and grain boundary effect was investigated from the broad and asymmetric relaxation peak.The relaxation time for both the grain and grain boundary effect was also calculated.In addition to this,we have also analyzed the normalized bode plot of imaginary part of impedance and electrical modulus which suggests the relaxation process dominated by the short-range movement of charge carriers.