Nonthermal radiation from black holes

We consider particle production by charged and rotating black holes. A simple derivation is presented for the leading term (n=1) in the Schwinger formula for pair creation by a constant electric field. The same approach is then applied to charged-particle production by a charged black hole. The effect is due to the tunneling of created particles through an effective Dirac gap. Nonthermal radiation from a rotating black hole can also be explained in an analogous way. In the leading semiclassical approximation, this approach is applicable to bosons as well.     

Pair creation by a photon in an electric field

The process of pair creation by a photon in a constant and homogeneous electric field is investigated basing on the polarization operator in the field. The total probability of the process is found in a relatively simple form. At high energy the quasiclassical approximation is valid. The corrections to the standard quasiclassical approximation (SQA) are calculated. In the region of relatively low photon energies, where SQA is unapplicable, the new approximation is used. It is shown that in this energy interval the probability of pair creation by a photon in electric field exceeds essentially the corresponding probability in a magnetic field. This approach is valid at the photon energy much larger than the “vacuum” energy in electric field: ω?eE/m. For smaller photon energies the low energy approximation is developed. At ω?eE/m the found probability describes the absorption of soft photon by the particles created by an electric field.     

Schwinger Effect in a Robertson-Walker Space-Time

The problem of particle creation from vacuum in a flat Robertson-Walker space-time in the presence of a varying electric field is studied. The Klein Gordon equation is exactly solved when the scale factor is a(η)=A+Btanh(λη). The canonical method based on Bogoliubov transformation is applied. The pair creation probability and the density number of created particles are calculated. The particular case of radiation dominated universe is considered where the total probability is written as a Schwinger-like series. It is shown that the electric field amplifies gravitational particle creation.     

Creation of vector bosons by an electric field in curved spacetime

We investigate the creation rate of massive spin-1 bosons in the de Sitter universe by a time-dependent electric field via the Duffin–Kemmer–Petiau (DKP) equation. Complete solutions are given by the Whittaker functions and particle creation rate is computed by using the Bogoliubov transformation technique. We analyze the influence of the electric field on the particle creation rate for the strong and vanishing electric fields. We show that the electric field amplifies the creation rate of charged, massive spin-1 particles. This effect is analyzed by considering similar calculations performed for scalar and spin-1/2$1/2$ particles.     

What is the effective stress energy of particles created from the vacuum?

When spontaneous particle creation occurs in a strong gravitational field, it seems clear on physical grounds that the particle creation must back-react on the gravitation field. It is generally believed that in the semiclassical approximation this effect can be described by assigning an effective stress energy to the created particles, which acts as a source of the gravitational field via Einstein's equation. In this essay, I discuss an axiomatic approach for determining the renormalized value of this effective stress energy.This essay was awarded the third prize for 1977 by the Gravity Research Foundation.     

On the Mutual Excitation of Embedded Circular Chains of Small Plasmonic Particles

To solve the problems of the repeated scattering of electromagnetic waves at ensembles of dielectric particles taking into account their conductivity, the interaction between collective optical modes of 2D embedded chains of small spherical plasmonic particles, which are characterized by electric dipole coupling, is analytically described on the basis of the quasi-separable T-scattering operator approach. It is assumed that the polarization vector of the electric field of an incident wave is oriented perpendicular to the plane of particle chains. The mutual influence of currents is demonstrated using a regular triangle whose vertices and center of symmetry contain particles and two embedded square chains with eight particles located at their vertices.     

Density matrix of a quantum field in a particle-creating background

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark–gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.     

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

The present study attempts to develop a detailed numerical approach and a simulation procedure to predict the motion of gas, ions and particles inside a simple parallel plate channel containing a single corona wire. A hybrid Finite Element (FEM)-Flux Corrected Transport (FCT)-Finite Volume (FVM) method is used: the FEM–FCT numerical algorithm is applied for modeling the steady-state corona discharge, while the turbulent gas flow and the particle motion under electrostatic forces are modeled using the commercial CFD code FLUENT. Calculations for the gas flow are carried out by solving the Reynolds-averaged Navier–Stokes equations and turbulence is modeled using the k–? turbulence model. An additional source term is added to the gas flow equation to include the effect of the electric field, obtained by solving a coupled system of the electric field and charge transport equations using User-Defined Functions (UDFs). The particle phase is simulated based on the Lagrangian approach, where a large number of particles is traced with their motion affected by the gas flow and electrostatic forces using the Discrete Phase Model (DPM) in FLUENT. The developed model is useful to gain insight into the particle collection phenomena that take place inside an ESP.     

Effects of strong electric fields in a polyacetylene chain

In this work, we study the effects related to the creation of electron/hole pairs via application of an external electric field that acts on a pristine trans-polyacetylene molecular chain at zero-temperature. This phenomenon is termed Schwinger–Landau–Zener (SLZ) effect and arises when a physical system, which can even be the vacuum, is under the action of a strong, static and spatially homogeneous electric field. Initially, we investigate how the electrical conductivity of the polyacetylene changes with the applied field, by considering the carriers production as well as the variation of the interband gap according to certain ab initio models. Next, we analyse the competition between the SLZ effect and another one associated with the incidence of an uniform electric field on one-dimensional crystals – the Bloch oscillations. We evaluate the conditions in which these latter can be destroyed by the particles created through the same field that induces them, and verify the possibility of occurrence of the Bloch oscillations inside the trans-polyacetylene with frequencies equal to or higher than the terahertz scale.     

Creation of particles and the effective Lagrangian in the quasi-Euclidean model of the universe with an electro-magnetic field

A calculation of the number of scalar and spinor particles created in the quasi-Euclidean cosmological model with an electric field is carried out. The inverse effect of the created particles on the electric field is investigated. It is shown that for large times the creation of particles leads to a decrease of the electric field. The imaginary part of the effective action in quasi-Euclidean space with constant electric and magnetic fields is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 12–16, May, 1982.     

Dynamical view of pair creation in uniform electric and magnetic fields

Pair creation in a uniform classical electromagnetic field (Schwinger mechanism) is studied focusing on the time evolution of the distribution of created particles. The time evolution of the distribution in time-dependent fields is also presented as well as effects of back reaction. Motivated by the Glasma flux tube, which may be formed at the initial stage of heavy-ion collisions, we investigate effects of a magnetic field parallel to an electric field, and find that the magnetic field makes the evolution of a fermion system faster.     

On particle creation by black holes

Hawking's analysis of particle creation by black holes is extended by explicitly obtaining the expression for the quantum mechanical state vector ψ which results from particle creation starting from the vacuum during gravitational collapse. (Hawking calculated only the expected number of particles in each mode for this state.) We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. In agreement with previously known results, we find that we are led to a unique quantum scattering theory which is completely well behaved mathematically provided a certain condition is satisfied by the operators which describe the scattering of classical positive frequency solutions. In terms of these operators we derive the expression for the state vector describing particle creation from the vacuum, and we prove that S-matrix is unitary. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. There is some ambiguity in the theory in this case arising from freedom involved in defining what one means by “positive frequency” at the future event horizon. However, it is proven that the expression for the density matrix formed from ψ describing the emission of particles to infinity is independent of this choice, and thus unambiguous predictions for the results of all possible measurements at infinity are obtained. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail (i.e., not only in expected number of particles) with black body emission.     

Gluon transport equations,plasma oscillations,and screening

The gluon transport equations (Phys. Lett. 177B (1986) 402) are reconsidered to derive a consistent semiclassical limit. Introducing the color current of gluon fluctuations around a classical mean field, we calculate the color permeability function of a collisionless gluon plasma in linear response approximation. The dispersion relations and electric screening length agree with one-loop high temperature QCD results. We find no magnetic screening atO(g ²) and predict transverse magnetic plasma oscillations similar to electric ones. The extension to include particle production by a mean color field is shortly described.     

Magnetic fluid in ionizing electric field

This article describes influence of strong (ionizing) electric field on sprayability of magnetic fluid containing colloid particles with size in the range from 10 to 20 nm of magnetite Fe₃O₄. Magnetic fluids can be based for example on both transformer oil and physiological solution for application in medical using (in human medical science research), that supports a fluid colloidal system. Further component of magnetic fluid is surfactant. It is acting as surface-active substance that prevents from nanometric dimension particle settlement. Magnetic fluid gets off nozzle with diameter in range 0.3–1.0 mm from container in surroundings of ionizing (i.e. strong) electric field (E > 10⁷ V m^?1). As a consequence of action of electric field it gives out suppression surface tension in fluid what leads onwards to decomposition of magnetic fluid ligament at the end of nozzle. The diameter of nozzle oneself respects basic theoretical calculations in regards of fluid concentration and thereinbefore its selected size. Magnetic fluid in dependency on its used liquid base has weak-polar till polar orientation polarization character. It gives out sprayability in non-homogeneous electric field E in combination with magnetic field of intensity H. Orientation of vectors Ê and ?, resp. induction of magnetic field B is defined by parallel or vertical direction. Results are confronted with measurements realized explicitly only at action of electric field (variable B = 0). In the case of magnetic field applications with permanent magnet together with electric non-homogeneous field it gives out unconventional dynamics of electrical charging particles of macroscopic dimension. Orientation particle track is influenced by orientation of field vector combinations. This phenomenon develops magneto-dielectric anisotropy, which oneself manifests behaviour of electrophysical quantities characterizing examination system. In consideration of technology utilization of this method it is very important to respect applied magnetic fluid concentration. Electrical characteristics were examined for volume concentration of magnetite particles in the range from 0.125% to 18%. Nevertheless efficiency optimization of given media suggests to boundary concentration of magnetic fluid of 4.0%, when it is in the regions of weak polar till polar material. Electrophysical research refers to exploitation of applied magnetic layer technology on dielectric insulating substances with inorganic origin as well as thin layer technology coating plastic foils created from macromolecular organic substance.     

Pair production in time-dependent electric fields

The particle production problem in a general time-dependent electric field is formulated by path integrals. The creation of charged scalar particles and electron-positron pairs is studied in detail for an exponentially decaying electric field. Some other exactly solvable cases are also considered.     

Fermionic Particle Production by Varying Electric and Magnetic Fields

Creation of fermionic particles by a time-dependent electric field and a space-dependent magnetic field is studied with the Bogoulibov transformation method. Exact analytic solutions of the Dirac equation are obtained in terms of the Whittaker functions and the particle creation number density depending on the electric and magnetic fields is determined.     

Dressing up a Reissner naked singularity

Spontaneous pair creation in the field of a large Reissner singularity (a point-like charge e whose mass M is such that $\text{MG}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< e}$) is here considered. Using as a guide the definition of the positive and negative energy states of a classical particle in this field, a particular basis of quantum states is chosen which contains resonance states — these are interpreted by invoking particle creation. Extremely energetic particles are shown to burst out to infinity whereas the antiparticles dress up and neutralize the singularity. This result is contrasted with the process of pair production by black holes and compared with the isotropization of the early universe by creation of matter.     

Relativistic charged particles in the field of an electromagnetic plane wave in a medium

Solutions of the Klein-Gordon and Dirac equation for a charged particle in the field of an electromagnetic plane wave in a medium with a constant refractive index n are discussed. Generally, for n² < 1, spontaneous pair creation from the vacuum, and for n² > 1, energy bands are observed. The interplay of Compton and Cherenkov scattering is discussed. Some doubts are formulated as to the physical relevance of calculating pair creation in a homogeneous electric field as it is usually done.     

Particle creation in a time-dependent electric field revisited

We adopt the general formalism for analyzing evolution of gaussian states of quantized fields in time-dependent backgrounds in the Schrodinger picture (presented in detail in Mahajan and Padmanabhan [G. Mahajan, T. Padmanabhan, Gen. Rel. Grav. 40 (2008) 661]) to study the example of a spatially uniform electric field background (in a time-dependent gauge) which is kept turned on for a finite duration of time. In particular, we study the time-dependent particle content, defined in terms of the concept of instantaneous eigenstates, and describe how it captures the time evolution of the quantized field modes. The actual particle creation process occurs over a relatively short interval in time, and the particle content saturates rather quickly. We also compare the power spectrum of the field modes, computed in the asymptotic limit, with the corresponding situation in a cosmological de Sitter background. Particle creation under the influence of a spiked electric field localized in time, as a particular limiting case of the above general model, is also considered.