Floquet theory of neutrino oscillations in the earth

We review the Floquet theory of linear differential equations with periodic coefficients and discuss its applications to neutrino oscillations in matter of periodically varying density. In particular, we consider parametric resonance in neutrino oscillations which can occur in such media, and discuss implications for oscillations of neutrinos traversing the earth and passing through the earth's core.Comment: LaTeX, 28 pages, 8 eps figures. Contribution to the special issue of Yad. Fiz. dedicated to the memory of A.B. Migda

Comment on the Surface Exponential for Tensor Fields

Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e. in tensors of rank 2), we suggest a non-trivial but multi-parametric exponential ${\cal E}(B|I|t_\gamma)$, which can serve as an interesting multi-directional evolution operator in the case of higher ranks. To emphasize the most important aspects of the story, construction is restricted to backgrounds $I_{ijk}$, associated with the structure constants of {\it commutative} associative algebras, what makes it unsensitive to topology of the 2d surface. Boundary effects are also eliminated (straightfoward generalization is needed to incorporate them).Comment: 6 page

Exotic smooth structures on 4-manifolds with zero signature

For every integer $k\geq 2$, we construct infinite families of mutually nondiffeomorphic irreducible smooth structures on the topological $4$-manifolds $(2k-1)(S^2\times S^2)$ and (2k-1)(\CP#\CPb), the connected sums of $2k-1$ copies of $S^2\times S^2$ and \CP#\CPb.Comment: 6 page

Comments on QED with background electric fields

It is well known that there is a total cancellation of the \emph{factorizable} IR divergences in unitary interacting field theories, such as QED and quantum gravity. In this note we show that such a cancellation does not happen in QED with background electric fields which can produce pairs. There is no factorization of the IR divergences.Comment: 14 pages, 1 figur

Resonant neutrino spin-flavor precession and supernova shock revival

A new mechanism of supernova shock revival is proposed, which involves resonant spin--flavor precession of neutrinos with a transition magnetic moment in the magnetic field of the supernova. The mechanism can be operative in supernovae for transition magnetic moments as small as $10^{-14}\mu_B$ provided the neutrino mass squared difference is in the range $\Delta m^2 \sim (3 \;{\rm eV})^2-(600 \;{\rm eV})^2$. It is shown that this mechanism can increase the neutrino--induced shock reheating energy by about 60\%.Comment: 16 pages, latex, 2 figures. added few reference

Supernova prompt neutronization neutrinos and neutrino magnetic moments

It is shown that the combined action of spin-flavor conversions of supernova neutrinos due to the interactions of their Majorana-type transition magnetic moments with the supernova magnetic fields and flavor conversions due to the mass mixing can lead to the transformation of \nu_e born in the neutronization process into their antiparticles \bar{\nu}_e. Such an effect would have a clear experimental signature and its observation would be a smoking gun evidence for the neutrino transition magnetic moments. It would also signify the leptonic mixing parameter |U_{e3}| in excess of 10^{-2}.Comment: LaTex, 25 pages, 3 figures. v4: Discussion section expanded, references added. Matches the published versio

Surface superconducting states in yttrium hexaboride single crystal in a tilted magnetic field

We present the results of an experimental study of the nucleation of superconductivity at the surface of a single crystal YB$_6$ in a tilted dc magnetic field. A recently developed experimental technique allowed us to determine $H_{c3}$ at each side of the sample as a function of the angle between the dc magnetic field and the surface. Experiment shows that the ratio $H_{c3}/ H_{c2}\approx 1.28$ in the direction perpendicular to the surface dc field while according to the theory this ratio should be equal to 1. This sharp distinction cannot be ascribed to the surface roughness.Comment: 6 pages, 8 figure

On the Perturbative Stability of Quantum Field Theories in de Sitter Space

We use a field theoretic generalization of the Wigner-Weisskopf method to study the stability of the Bunch-Davies vacuum state for a massless, conformally coupled interacting test field in de Sitter space. We find that in $\lambda \phi^4$ theory the vacuum does {\em not} decay, while in non-conformally invariant models, the vacuum decays as a consequence of a vacuum wave function renormalization that depends \emph{singularly} on (conformal) time and is proportional to the spatial volume. In a particular regularization scheme the vacuum wave function renormalization is the same as in Minkowski spacetime, but in terms of the \emph{physical volume}, which leads to an interpretation of the decay. A simple example of the impact of vacuum decay upon a non-gaussian correlation is discussed. Single particle excitations also decay into two particle states, leading to particle production that hastens the exiting of modes from the de Sitter horizon resulting in the production of \emph{entangled superhorizon pairs} with a population consistent with unitary evolution. We find a non-perturbative, self-consistent "screening" mechanism that shuts off vacuum decay asymptotically, leading to a stationary vacuum state in a manner not unlike the approach to a fixed point in the space of states.Comment: 36 pages, 4 figures. Version to appear in JHEP, more explanation

Study of the properties of Plessey's electrocardiographic capacitive electrodes for portable systems

Cardiac diseases are still most widely spread in all regions of the world. And more and more devices are invented to satisfy increasing requirements of the patients. One of the perspective technologies in cardiac diagnostics is capacitive sensing ECG electrodes