Bound states of scalar particles in the presence of a short range potential

We analyze the behavior of the energy spectrum of the Klein-Gordon equation in the presence of a truncated hyperbolic tangent potential. From our analysis we obtain that, for some values of the potential there is embedding of the bound states into the negative energy continuum, showing that, in opposition to the general belief, relativistic scalar particles in one-dimensional short range potentials can exhibit resonant behavior and not only the Schiff-Snyder effect.Comment: To appear in Modern Physics Letters

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

Planar Dirac Electron in Coulomb and Magnetic Fields

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong magnetic fields, we present the exact recursion relations that determine the coefficients of the series expansion of wave functions, the possible energies and the magnetic fields. It is found that analytic solutions are possible for a denumerably infinite set of magnetic field strengths. This system thus furnishes an example of the so-called quasi-exactly solvable models. A distinctive feature in the Dirac case is that, depending on the strength of the Coulomb field, not all total angular momentum quantum number allow exact solutions with wavefunctions in reasonable polynomial forms. Solutions in the nonrelativistic limit with both attractive and repulsive Coulomb fields are briefly discussed by means of the method of factorization.Comment: 18 pages, RevTex, no figure

Induced Current and Aharonov-Bohm Effect in Graphene

The effect of vacuum polarization in the field of an infinitesimally thin solenoid at distances much larger than the radius of solenoid is investigated. The induced charge density and induced current are calculated. Though the induced charge density turned out to be zero, the induced current is finite periodical function of the magnetic flux $\Phi$. The expression for this function is found exactly in a value of the flux. The induced current is equal to zero at the integer values of $\Phi/\Phi_0$ as well as at half-integer values of this ratio, where $\Phi_0=2\pi\hbar c/e$ is the elementary magnetic flux. The latter is a consequence of the Furry theorem and periodicity of the induced current with respect to magnetic flux. As an example we consider the graphene in the field of solenoid perpendicular to the plane of a sample.Comment: 3 pages, 1 figure, version accepted to Phys. Rev.

Hydrogen sulfide inhibits giant depolarizing potentials and abolishes epileptiform activity of neonatal rat hippocampal slices

© 2016 IBROHydrogen sulfide (H2S) is an endogenous gasotransmitter with neuroprotective properties that participates in the regulation of transmitter release and neuronal excitability in various brain structures. The role of H2S in the growth and maturation of neural networks however remains unclear. The aim of the present study is to reveal the effects of H2S on neuronal spontaneous activity relevant to neuronal maturation in hippocampal slices of neonatal rats. Sodium hydrosulfide (NaHS) (100 μM), a classical donor of H2S produced a biphasic effect with initial activation and subsequent concentration-dependent suppression of network-driven giant depolarizing potentials (GDPs) and neuronal spiking activity. Likewise, the substrate of H2S synthesis L-cysteine (1 mM) induced an initial increase followed by an inhibition of GDPs and spiking activity. Our experiments indicate that the increase in initial discharge activity by NaHS is evoked by neuronal depolarization which is partially mediated by a reduction of outward K+ currents. The subsequent decrease in the neuronal activity by H2S appears to be due to the rightward shift of activation and inactivation of voltage-gated Na+ currents, thus preventing network activity. NaHS also reduced N-methyl-D-aspartate (NMDA)-mediated currents, without essential effect on AMPA/kainate or GABAA-mediated currents. Finally, H2S abolished the interictal-like events induced by bicuculline. In summary, our results suggest that through the inhibitory action on voltage-gated Na+ channels and NMDA receptors, H2S prevents the enhanced neuronal excitability typical to early hippocampal networks

Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

Anisotropic Pressures in Very Dense Magnetized Matter

The problem of anisotropic pressures arising as a consequence of the spatial symmetry breaking introduced by an external magnetic field in quantum systems is discussed. The role of the conservation of energy and momentum of external fields as well as of systems providing boundary conditions in quantum statistics is considered. The vanishing of the average transverse momentum for an electron-positron system in its Landau ground state is shown, which means the vanishing of its transverse pressure. The situation for neutron case and Strange Quark Matter (SQM) in $\beta$-equilibrium is also briefly discussed. Thermodynamical relations in external fields as well as the form of the stress tensor in a quantum relativistic medium are also discussed. The ferromagnetic symmetry breaking is briefly discussed.Comment: 10 page

Theoretical evaluation of rheological state of sand cement composite systems with polyoxyethylene additive using topological dynamics concept

© 2016 Trans Tech Publications, Switzerland.Presents the results of studies of contemporary materials in the field of rheological state. The topological mortar structure has been provided by theoretical evaluation of the rheological state of the cross-linked solutions and the experimental viscosity data of the sand cement mortar which has been modified by water-soluble additive – polyoxyethylene. The general model has been made for the structure of non-Newtonian liquideous systems including dilatant, pseudoplastic bodies with two main rheological active components in their structure – rigid and viscous phases. It is shown that in pseudoplastic systems, as the shear stress increases, the viscous phase grows because of the reduction of rigid phase content. In dilatant systems the converse situation has been observed. Furthermore, these phases are not clearly distinguishable, but to the contrary they are spatially interconnected in a complex way. The structure modeling has been made for non-Newtonian bodies using the Shklovskii-de Gennes model. The studies have found that the construction composite sand cement system is defined as the pseudoplastic body where cement and sand act as the rigid phase, water solution of polyoxyethylene – as the viscous phase. These findings can be used to prove the influence of polymer powder on the workability of dry mortar