O. G. Kharlanov

CPT and Lorentz violation effects in hydrogenlike atoms

Within the framework of Lorentz-violating extended electrodynamics, the Dirac equation for a bound electron in an external electromagnetic field is considered assuming the interaction with a CPT-odd axial vector background bμ. The quasirelativistic Hamiltonian is obtained using a 1∕c-series expansion. Relativistic Dirac eigenstates in a spherically symmetric potential are found accurate up to the second order in b0. b0-induced CPT-odd corrections to the electromagnetic dipole moment operators of a bound electron are calculated that contribute to the anapole moment of the atomic orbital and may cause a specific asymmetry of the angular distribution of the radiation of a hydrogen atom.Within the framework of Lorentz-violating extended electrodynamics, the Dirac equation for a bound electron in an external electromagnetic field is considered assuming the interaction with a CPT-odd axial vector background bμ. The quasi-relativistic Hamiltonian is obtained using a 1/c-series expansion. Relativistic Dirac eigenstates in a spherically-symmetric potential are found accurate up to the second order in b0. b0-induced CPT-odd corrections to the electromagnetic dipole moment operators of a bound electron are calculated that contribute to the anapole moment of the atomic orbital and may cause a specific asymmetry of the angular distribution of the radiation of a hydrogen atom.

Casimir effect within D = 3+1 Maxwell-Chern-Simons electrodynamics

Within the framework of the (3+1)-dimensional Lorentz-violating extended electrodynamics including the CPT-odd Chern-Simons term, we consider the electromagnetic field between the two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. We also show that the tachyon-induced vacuum instability vanishes when the separation between the plates is sufficiently small though finite. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the two different methods, the zeta function technique and the transformation of the discrete sum into a complex plane integral via the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one obtained in [M. Frank and I. Turan, Phys. Rev. D 74, 033016 (2006)], using the misinterpreted equations of motion. Compared to the experimental data, our result places a constraint on the absolute value of the Chern-Simons term.

Analytical treatment of long-term observations of the day-night asymmetry for solar neutrinos

The Earth’s density distribution can be approximately considered piecewise continuous at the scale of two-flavor oscillations of neutrinos with energies about 1 MeV. This quite general presumption appears to be enough to analytically calculate the day-night asymmetry factor. Using the explicit time avergaing procedure, we show that, within the leading-order approximation, this factor is determined by the electron density immediately before the detector, i.e. in the Earth’s crust. Within the approximation chosen, the resulting asymmetry factor does not depend either on the properties of the inner Earth’s layers or on the substance and the dimensions of the detector. For beryllium neutrinos, we arrive at the asymmetry factor estimation of about −4 × 10, which is at least one order of magnitude beyond the present experimental resolution, including that of the Borexino experiment.The Earth’s density distribution can be approximately considered piecewise continuous at the scale of two-flavor oscillations of neutrinos with energies about 1 MeV. This quite general assumption appears to be enough to analytically calculate the day-night asymmetry factor. Using the explicit time averaging procedure, we show that, within the leadingorder approximation, this factor is determined by the electron density immediately before the detector, i.e. in the Earth’s crust. Within the approximation chosen, the resulting asymmetry factor does not depend either on the properties of the inner Earth’s layers or on the substance and the dimensions of the detector. For beryllium neutrinos, we arrive at the asymmetry factor estimation of about −4 × 10 4 , which is at least one order of magnitude beyond the present experimental resolution, including that of the Borexino experiment.

Numerical study of strongly-nonlinear regimes of steady premixed flame propagation. The effect of thermal gas expansion and finite-front-thickness effects

Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based on fixed-point iterations and uses simple (Picard) iterations or the Anderson acceleration method that facilitates separation of different solutions. Using these techniques, we scan the parameter space of the problem so as to study various effects governing formation of curved flames. These include the thermal gas expansion and the finite-front-thickness effects, namely flame stretch, curvature, and compression. In particular, flame compression is demonstrated to have a profound influence on the flame, strongly affecting the dependence of its propagation speed on the channel width b. Specifically, the solutions found exhibit a sharp increase of flame speed with channel width. Under weak flame compression, this increase commences at b/λc ≈ 2  ∼  3, where λc is the cutoff wavelength, but this ratio becomes significantly larger as the flame compression grows. The results obtained are also used to identify limitations of the analytical approach based on the weak-nonlinearity assumption, and to revise the role of noise in flame evolution.

Peculiar seasoning in the neutrino day-night asymmetry: where and when to look for spices?

We analyze the peculiar seasonal effects in the day-night asymmetry of solar neutrinos, namely those connected with the neutrino nighttime flux anomaly near the winter solstice. We show that, for certain placements of the neutrino detector, such effects may be within the reach of next-generation detectors.

On the question of the magnitude of day-night asymmetry for solar neutrinos

The effect of flavor day-night asymmetry is considered for solar neutrinos of energy about 1 MeV under the assumption that the electron-density distribution within the Earth is approximately piecewise continuous on the scale of the neutrino-oscillation length. In this approximation, the resulting asymmetry factor for beryllium neutrinos does not depend on the structure of the inner Earth’s layers or on the properties of the detector used. Its numerical estimate is on the order of −4 × 10−4, which is far beyond the reach of present-day experiments.

Casimir effect within (3 + 1) D Maxwell-Chern-Simons electrodynamics

Within the framework of the Lorentz-violating (3 + 1)-dimensional extended electrodynamics including the Lorentz-violating CPT-odd Chern-Simons term, we consider the electromagnetic field between two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one calculated in [1] and based on wrong equations of motion. Compared with the experimental data, our result places a constraint on the absolute value of the Chern-Simons term.

Electromagnetic radiation of quantum systems under conditions of Lorentz-invariance and CPT violation

Solutions to the Dirac equation for an electron moving in a central electrostatic and a constant uniform magnetic field are considered within extended electrodynamics (in the presence of Lorentz-invariance violation of the minimal CPT-odd form). On the basis of these solutions, the features of electromagnetic radiation from a hydrogen-like atom and the features of electron synchrotron radiation are calculated, and possible observable effects caused by the assumed Lorentz-invariance violation are described.

CPT and Lorentz Invariance Violation in Hydrogen-Like Atoms

We analyze an approximate solution to the Dirac equation for an electron in a central potential, in particular, in a Coulomb potential, when Lorentz invariance is violated. A quasi-relativistic approximation for the Dirac equation in an external field has been derived. The directivity pattern of spontaneous emission for a polarized hydrogen atom has been found to be asymmetric.