Mechanism of formation of the equilibrium domain structure in crystals undergoing thermoelastic phase transitions

The mechanism of formation of the equilibrium domain structure during a thermoelastic phase transition is proposed. This mechanism is related to long-range elastic strain fields created by “elastic charges” at the free crystal surface. It is assumed that, during a phase transition, there appears not only the nonzero primary (antiferromagnetic, martensitic) order parameter in the crystal but also an internal (quasi-plastic) stress rigidly related to the order parameter. The orientation of this stress with respect to the crystallographic axes can be changed by external fields. Elastic charges arise due to those components of the internal stress tensor whose flux across the crystal surface is nonzero. The nonlocal destressing energy is found. It is shown that, for a certain shape of a sample, an inhomogeneous distribution of the primary order parameter (a domain structure) is energetically more favorable. The characteristic field at which a sample becomes a single domain is shown to be dependent on the shape of the crystal.     

Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source

It was shown recently that the basic properties of a fluctuating electromagnetic beam can be derived from knowledge of a 2 x 2 cross-spectral density matrix of the electric field in the source plane. However, not every such matrix represents a source that will generate a beamlike field. We derive conditions that the matrix must satisfy for the source to generate an electromagnetic Gaussian Schell-model beam.     

Non-Linear Electrodynamics in Blandford–Znajek Energy Extraction

Non-linear electrodynamics (NLED) is a generalization of Maxwell's electrodynamics for strong fields. It has significant implications for the study of black holes and cosmology and has been extensively studied in the literature, extending from quantum to cosmological contexts. In this work, two new ways to investigate these non-linear theories are investigated. First, the Blandford-Znajek mechanism is analyzed in light of this promising theoretical context, providing the general form of the extracted power up to second order in the black hole spin parameter a. It is found that, depending on the NLED model, the emitted power can be extremely increased or decreased, and that the magnetic field lines around the black hole seem to become vertical quickly. Considering only separated solutions, it is found that no monopole solutions exist and this could have interesting astrophysical consequences (not considered here). Last but not least, it is attempted to confine the NLED parameters by inducing the amplification of primordial magnetic fields (“seeds”), thus admitting non-linear theories already during the early stages of the Universe. However, the latter approach proves to be useful for NLED research only in certain models. These (analytical) results emphasize that the behavior of non-linear electromagnetic phenomena strongly depends on the physical context and that only a power-law model seems to have any chance to compete with Maxwell.     

Magnetization of type-ii superconductors in the range of fields H c 1 ≤ H ≤ H c 2Variational Method

A variational method is proposed to find the magnetic field dependence of the magnetization of type-II superconductors in the mixed state by a self-consistent technique. This model allows for suppression of the order parameter to zero at the centers of Abrikosov vortices and also for the magnetic field dependence of the order parameter. The results can be applied to the entire range of fields H _c 1 ≤ H ≤ H _c 2 for any values of the Ginzburg-Landau parameter $\kappa > 1/\sqrt 2$ . It is shown that in weak fields where κ ? 1 the behavior of the magnetization can be described exactly in the London approximation provided that the correct value of H _c 1 is used. Near the second critical field this dependence shows good agreement with the well-known Abrikosov result. It is also shown that using the concept of isolated vortices and applying the principle of superposition of the fields and currents generated by these vortices to calculate the magnetization gives inaccurate quantitative results even in fairly weak fields. By going beyond these concepts, it was possible to allow more accurately for the influence of the vortex cores on the magnetization behavior in the intermediate range of fields H _c 1 ?H ? H _c 2 and to identify the range of validity of various approximations used widely in the literature.     

No black holes: A gravitational gauge theory possibility

The most general lowest order lagrangian that can be formed from gauge-derived vierbein invariants is constrained by the hypothesis that the speed of light as measured by conventional rods and clocks of atomic constitution is independent of direction in a gravitational field. It is shown that the standard weak field observational tests of general relativity serve to eliminate all possible combinations of parameters in this constrained lagrangian except two. One parameter choice gives the isotropic Schwarzchild black hole metric of the general theory of relativity. The other allowable choice leads to an exponential metric of the class proposed by Yilmaz, corresponding in strong fields to large red shifts without black hole formation.     

Entangled Two Two-Level Atom in the Presence of External Classical Fields

In this contribution, we investigate a TTLAs (two two-level atoms) in interaction with an electromagnetic field in presence of the external classical fields. The general solution of the time evolution operator is obtained and used to derive the density matrix operator. The temporal evolution of the atomic inversion, the degree of entanglement measured by the negativity, as well as the single atom entropy squeezing are discussed. We consider the atomic system at either the upper or Bell states, while the field in the coherent state. It has been shown that the coupling parameter g (the coupling of the external classical fields) gets more effective for the case in which the g is not equal to zero. Also for a strong coupling parameter g the superstructure phenomenon can be reported. The results shown that for increase the value of the classical external fields parameter leads to the entanglement between the atoms and the fields gets stronger. Also it has shown that for specific value of the classical external fields the system never reaches the pure state except during the revival periods.     

Spinor fields at spacelike infinity

The concept of a spinor structure at spacelike infinity is introduced for space-times which are asymptotically flat. It is shown how zero-rest-mass fields on space-time acquire smooth limits on this structure and that these limits satisfy certain differential equations characterized by the helicity and regularity of the field. The geometry of the limits of twistor fields is also discussed, and it seems possible that one can define the momentum and angular momentum of an asymptotically flat space-time in terms of a twistor space at spacelike infinity.     

K-essential covariant holography

Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used, for example, to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld possesses a 4D de Sitter induced metric and is asymptotically flat despite the presence of a negative bulk cosmological constant, a novel and interesting peculiarity that contrasts with previously known models. It turns out that universal scalar fields can be localized in this expanding braneworld if their bulk mass obeys an upper bound, otherwise the scalar fields delocalize: The dynamics of the scalar field is governed by a Schrödinger equation with an analog quantum mechanical potential of modified Pöschl–Teller type. This potential depends on the bulk curvature of the braneworld system as well as on the value of the bulk scalar field mass. For masses satisfying a certain upper bound, the potential displays a negative minimum and possesses a single massless bound state separated from the Kaluza–Klein (KK) massive modes by a mass gap defined by the Hubble (expansion scale) parameter of the 3-brane. As the bulk scalar field mass increases, the minimum of the quantum mechanical potential approaches a null value and, when the bulk mass reaches certain upper bound, it becomes positive (eventually transforming into a potential barrier), leading to delocalization of the bulk scalar field from the brane. We present analytical expressions for the general solution of the Schrödinger equation. Thus, the KK massive modes are given in terms of general Heun functions as well as the expression for the massless zero mode, giving rise to a new application of these special functions.     

A curiosity concerning the role of coherent states in quantum field theory

In the usual Fock quantisation of fields in Minkowski space-time, one has the result that the expectation value of the quantum Hamiltonian in any coherent state equals the energy of the classical field at which the state is peaked. It is shown that this property can be used tocharacterise the usual Fock representation. It is also pointed out that the entire analysis goes through for a substantially more general class of systems including, in particular, Bose fields in arbitrary stationary space-times.     

Golden Oldie

A form of initial value problem is considered in which the initial hypersurface is not spacelike but null. This approach has the striking advantage over the more usual Cauchy problem that all constraints (initial data equations) are eliminated from the theory, for a wide class of interacting fields in special relativity and also for general relativity. The theory is most naturally described in terms of the two-component spinor calculus, for which an elementary introduction is given here. A general scheme for interacting fields, which holds both in special and general relativity, is presented which describes all fields in terms of sets of irreducible spinors. The concept of an exact set of such spinors is introduced and it is shown that this concept is the appropriate one for an initial value problem on a null cone without constraints. The initial data can be expressed in the form of a complex number, called a null datum, defined at each point of the null cone, one corresponding to each spinor. There is the curious feature of these null data that apparently it is sufficient here, to have onehalf as much information per point as in the corresponding Cauchy problem. The classical Maxwell-Dirac theory and the Einstein-Maxwell theory are two examples that can be put into the form of exact sets. The Einstein empty-space equations are also of particular note, and in this case the null datum describes essentially the intrinsic geometry of the null cone. The argument given here as applied to a general exact set is incomplete in two important respects. Firstly it depends on the null data being analytic, and secondly the initial hypersurface must be a cone. However, both these restrictions are removed in the case of certain elementary fields called basic free fields, examples of which are the Weyl neutrino field, the free Maxwell field, and the linearized gravitational field. For these cases a simple explicit formula is introduced which expresses the field at any point in terms of the null datum, as an integral taken over the intersection of the initial null hypersurface with the null cone of the point.This article originally appeared in 1963 in Aerospace Research Laboratories 63-56 (P.G. Bergmann). It is an important and oft-cited work, but as it has never been published in a widely distributed journal, it is generally inaccessable to the relativity community. This regrettable situation is hereby rectified-Ed.This work was done while the author was at Princeton, Syracuse, and Cornell Universities, visiting under a NATO Fellowship administered by the Department of Scientific and Industrial Research in London. The work at Syracuse was supported by the Aeronautical Research Laboratory and at Cornell by the National Science Foundation.     

First-order invariant Einstein-Cartan variational structures

A first-order invariant Einstein-Cartan structure is a Lagrangian structure on a differential manifold defined by a generally invariant Lagrangian depending on a metric field, a connection field, and the first derivatives of these fields. Moreover, it is assumed that the metric and connection fields satisfy the so-called compatibility condition. In this paper the problem of finding all such invariant Einstein-Cartan structures is discussed. It is shown that each Lagrangian of these structures depends only on certain tensors constructed from the metric and the connection fields, which means that all the Lagrangians can be described within the framework of the classical theory of invariants. The maximal number of functionally independent Lagrangians is determined as a function of the dimension of the underlying manifold.     

Unphysical and physical(?) solutions of the Lorentz-Dirac equation

A simple proof of a weak version of Eliezer's theorem on unphysical solutions of the Lorentz-Dirac equation is given. This version concerns a free particle scattered by a spatially localized electric field in one space dimension. (The solutions are also solutions in three space dimensions.) It establishes that for certain physically reasonable localized fields, all solutions which are free (i.e., unaccelerated) before they enter the field have unbounded proper acceleration and velocity asymptotic to that of light in the future. For any given initial velocity, the fields yielding this unphysical behavior can be arbitrarily weak. The result is then extended to a class of static fields which need not be spatially localized, including Coulomb fields. For this case the same conclusion is obtained omitting the assumption that the particle be free in the past.The rest of the paper discusses solutions to the localized field problem which are assumed free in the future rather than the past. Some strange features of these solutions are noted. The possibility of experimentally detecting deviations from the Coulomb law for a particle obeying the Lorentz-Dirac equation is discussed.     

Lagrangian dynamics of spinning particles and polarized media in general relativity

The general form of the Lagrangian equations of motion is derived for a spinning particle having arbitrary multipole structure in arbitrary external fields. It is then shown how these equations, together with the complete system of field equations can be recovered from a fourdimensional action integral representing a polarized dustlike medium interacting with an arbitrary set of fields. These general results are then specialized to the case of Einstein-Maxwell fields in order to obtain the general-relativistic extension of Lorentz's dielectric theory.     

Influence of atomic defect generation on the propagation of elastic waves in laser-excited solid layers

The mechanical behavior of solid layers subjected to laser irradiation is investigated by a dynamical model that is based on coupled evolution equations for the elastic displacement of the medium and lattice defect-density fields. The evolution of defect-density is governed by the (i) generation of defects by irradiation, (ii) their diffusion and recombination and (iii) diffusion induced by strain field. The strain field associated with lattice dilatation due to atomic defects is shown to couple with deformation fields of the layer. Frequency equations corresponding to the symmetric and anti-symmetric modes of vibration of the layer are obtained. It is found that coupling between diffusion and strain fields cause dispersion of the general waveform. Explicit expressions are defined for the wave velocity, and the attenuation (amplification) coefficients which characterize these waves.     

Entanglement and classical polarization states

We identify classical light fields as physical examples of nonquantum entanglement. A natural measure of degree of polarization emerges from this identification, and we discuss its systematic application to any optical field, whether beamlike or not.     

Level-splitting effects in resonant four-wave mixing

Resonant spectral structures of four-wave mixing (FWM) in molecular sodium are investigated. For a double- ? configuration with strong-weak-strong-weak fields, split components in FWM spectra induced by the strong pump fields are observed. It is shown that the split components merge into a single peak for a certain ratio of the strong field intensities. A correlation between the level-splitting effects and the saturation behavior of the FWM signal is experimentally demonstrated.     

Paraxial Approximation of Modern Radiometry for Beamlike Wave Propagation

A new approach to the construction of a system of the generalized radiometric quantities expressed in terms of the cross-spectral density function of the wave field is proposed. The key distinction of this approach lies in the fact that the initial hypothesis of beamlike wave propagation allows to invoke the paraxial approximation when deducing the generalized radiant flux. Within the framework of this approach the new expressions for the generalized radiant emittance, the generalized radiant intensity and the generalized radiance are derived. All the proposed generalized radiometric characteristics represent physically measurable quantities and, hence, may be used in practical radiometry. The results obtained in this paper can be regarded as a particular case of the modern radiometry theory in paraxial approximation for beamlike wave propagation.On leave from Kiev Polytechnic Institute, Ukraine.     

Weyl-Dirac geometry and dark matter

Weyl proposed a geometry that differed from Riemannian geometry, which underlies general relativity, in that it contained a vector that could be interpreted as describing the electromagnetic field. Dirac modified this geometry to remove certain difficulties and based it on a variational principle which gave satisfactory field equations for gravitation and electromagnetism. However, by changing the value of a parameter appearing in his variational principle one gets, instead of electromagnetism, a field of massive particles of spin 1, which can be assumed to interact with ordinary matter only through gravitation. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe.     

Dynamics of Bell-nonlocality of two-mode squeezed vacuum fields interacting with atoms

We consider a system of two separated cavities with the cavity fields initially prepared in a two-mode squeezed vacuum state (TMSVS). We investigate the short time evolution of Bell-nonlocality of the fields interacting with one or two atoms. It is shown that the Bell-inequality violation of the fields can be fully destroyed in a finite time and reappears in the later time. After Bell-nonlocality sudden death (BNSD) in some cases, Bell-nonlocality of the fields almost but does not totally return to its initial value when the squeezing parameter for the fields is small. The pattern of Bell-nonlocality evolution is dependent on the squeezing parameter of the fields, the detuning between the atomic transition and field frequency and the differences between atom-field couplings.     

Positioning of the arc discharge channel in vacuum arc facilities

The behavior of an electric arc in a magnetic field is studied theoretically and experimentally. It is found that the arc behavior can be governed by the ponderomotive interaction of the arc with current-carrying elements. In a nonuniform magnetic field, the behavior of the arc depends on the Hall currents and the diamagnetic properties of its plasma. It is shown that the position of the arc channel between the end faces of cylindrical electrodes can be controlled by nonuniform magnetic fields. The methods and devices considered in this paper allow one, in particular, to control arc heat sources used in the heat treatment of metals.