Plasmon decay to a neutrino pair via neutrino electromagnetic moments in a strongly magnetized medium

We calculate the neutrino luminosity of a degenerate electron gas in a strong magnetic field via plasmon decay to a neutrino pair due to neutrino electromagnetic moments and obtain the relative upper bounds on the effective neutrino magnetic moment.Comment: 3 pages, submitted to the Proceedings of the 16th Lomonosov Conference on Elementary Particle Physics, Moscow State University, Moscow, Russia, August 201

Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold case

We consider a pair of adjacent quantum waveguides, in general of different widths, coupled laterally by a pair of windows in the common boundary, not necessarily of the same length, at a fixed distance. The Hamiltonian is the respective Dirichlet Laplacian. We analyze the asymptotic behavior of the discrete spectrum as the window distance tends to infinity for the generic case, i.e. for eigenvalues of the corresponding one-window problems separated from the threshold

Magnetoelectric properties of 500 nm Cr2O3 films

The linear magnetoelectric effect was measured in 500 nm Cr2O3 films grown by rf sputtering on Al2O3 substrates between top and bottom thin film Pt electrodes. Magnetoelectric susceptibility was measured directly by applying an AC electric field and measuring the induced AC magnetic moment using superconducting quantum interference device magnetometry. A linear dependence of the induced AC magnetic moment on the AC electric field amplitude was found. The temperature dependence of the magnetoelectric susceptibility agreed qualitatively and quantitatively with prior measurements of bulk single crystals, but the characteristic temperatures of the film were lower than those of single crystals. It was also possible to reverse the sign of the magnetoelectric susceptibility by reversing the sign of the magnetic field applied during cooling through the N\'eel temperature. A competition between total magnetoelectric and Zeeman energies is proposed to explain the difference between film and bulk Cr2O3 regarding the cooling field dependence of the magnetoelectric effect.Comment: accepted at Physical Review

Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $b$ located on the opposite walls and the Dirichlet boundary condition on the remaining part of the boundary of the strip. We prove that such a system exhibits discrete eigenvalues below the essential spectrum for any $a,b>0$. When $a$ and $b$ tend to the infinity, the asymptotic of the eigenvalue is derived. A comparative analysis with the one-window case reveals that due to the additional possibility of the regulating energy spectrum the anticrossing structure builds up as a function of the inner radius with its sharpness increasing for the larger outer radius. Mathematical and physical interpretation of the obtained results is presented; namely, it is derived that the anticrossings are accompanied by the drastic changes of the wave function localization. Parallels are drawn to the other structures exhibiting similar phenomena; in particular, it is proved that, contrary to the two-dimensional geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure

Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum