Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in the QED$_{2+1}$ at the finite chemical potential, find the imaginary part of this Green function and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem to be likely to be revealed in a monolayer graphene sample in the presence of external constant uniform magnetic field $B$ perpendicular to it.Comment: 9 pages, 2 references are delete

Plane density of induced vacuum charge in a supercritical Coulomb potential

An expression for the density of a planar induced vacuum charge is obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in this potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. The behavior of the obtained vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulomb impurity in graphene is briefly discussed. We calculate the real vacuum polarization charge density that acquires the quantum electrodynamics vacuum in the supercritical Coulomb potential due to the so-called real vacuum polarization. It is shown that the vacuum charge densities essentially differ in massive and massless cases. We expect that our results can, as a matter of principle, be tested in graphene with a supercritical Coulomb impurity.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1601.0766

Induced current in the presence of magnetic flux tube of small radius

The induced current density, corresponding to the massless Dirac equation in (2+1) dimensions in a magnetic flux tube of small radius is considered. This problem is important for graphene. In the case, when an electron can not penetrate the region of nonzero magnetic field, this current is the odd periodical function of the magnetic flux. If the region inside the magnetic tube is not forbidden for penetration of electron, the induced current is not a periodical function of the magnetic flux. However in the limit $R\to 0$, where $R$ is the radius of magnetic flux tube, this function has the universal form which is independent of the magnetic field distribution inside the magnetic tube at fixed value of the magnetic flux.Comment: 5 pages, 1 figur

Vortex Interferometric Microscopy with Laguerre-Gaussian Beams

In the present research, we discuss the results of analysis of coherent light beams carrying an optical vortex and propagating through the isotropic medium with a complex surface microrelief and its application to super resolution microscopy. It was shown, that phase analysis of singular beam with single charged centered optical vortex allow to retrieve information about sample surface relief. High spatial resolution caused by vortex helical phase sensitivity to disturbances in wave front after reflection or spreading through studying sample, which can be optically transparent or have a reflecting surface. This method applicable for non-destructive testing of live cells and biological tissues in real-time regime with exceeding optical diffraction limit. Vertical resolution of a microscope based on the phase singularity of Laguerre-Gaussian beams of low order can be achieved down to 5,27 nm for helium-neon laser source for optically transparent and reflecting surfaces. Keywords: optical vortex, phase, microscopy, singularit

On the M87 jet structure near the central engine

At present, there is no doubt that relativistic jets observed in active galactic nuclei pass from highly magnetized to weakly magnetized stage, which is observed as a break in the dependence on their width $d_{\rm jet}(z)$ on the distance $z$ to the central engine. In this paper, we discuss the possibility of observing another break, which should be located at shorter distances. The position of this break can be associated with the region of formation of the dense central core near the jet axis which was predicted both analytically and numerically more than a decade ago, but has not yet received sufficient attention. In this case, the observed width should be determined by the dense core, and not by the total transverse size of the jet. The calculations carried out in this paper, which took into account both the transverse electromagnetic structure of the jet and the change in the spectrum of emitting particles along its axis, indeed showed such behaviour. We also found the evidence of the predicted break in the jet expansion profile using stacked 15 GHz VLBA image of M87 radio jet and constrain the light cylinder radius.Comment: 11 pages, 6 figures. Accepted by MNRAS 2024 February 7. In original form 2023 September 2

Effects of pyrocatechol on neuromuscular transmission

Effects of pyrocatechol on neuromuscular transmission were studied both in the frog pectoral-cutaneous muscle and in the mouse phrenic-diaphragmatic preparation by means of extracellular microelectrode recording of synaptic signals. Pyrocatechol applied in a concentration of 0.05 mM increased the frequency of miniature end-plate currents (MEPC) and the amplitude of end-plate current (EPC) by increasing its quantum content. Pyrocatechol also increased the duration of presynaptic response. When voltage-dependent potassium channels had been blocked, pyrocatechol affected neither the EPC quantum content nor the duration of presynaptic response. It is suggested that the pyrocatechol-induced enhancement of transmitter release results from modulatory effects of pyrocatechol on voltage-dependent potassium current in the membrane of a nerve terminal. © 1995 Plenum Publishing Corporation

Simulation of thermophysical processes in residential storey buildings

© Research India Publications.Performing thermophysical modeling of processes of heatwind conditions in urban design allows setting the amount of convective-radiative heat flow, which comes from heating of the active surface and goes into the air. Knowing these values allows the possibility of taking appropriate design considerations in the human breathing zone for creating conditions for thermal comfort