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

Quantum field theoretic approach to neutrino oscillations in matter

We consider neutrino oscillations in non-uniform matter in a quantum field theoretic (QFT) approach, in which neutrino production, propagation and detection are considered as a single process. We find the conditions under which the oscillation probability can be sensibly defined and demonstrate how the properly normalized oscillation probability can be obtained in the QFT framework. We derive the evolution equation for the oscillation amplitude and discuss the conditions under which it reduces to the standard Schr\"odinger-like evolution equation. It is shown that, contrary to the common usage, the Schr\"odinger-like evolution equation is not applicable in certain cases, such as oscillations of neutrinos produced in decays of free pions provided that sterile neutrinos with $\Delta m^2\gtrsim 1$ eV$^2$ exist.Comment: LaTeX, 24 pages + 16 pages of appendices, 1 figure. V2: typos correcte

Black Hole Motion in Entropic Reformulation of General Relativity

We consider a system of black holes -- a simplest substitute of a system of point particles in the mechanics of general relativity -- and try to describe their motion with the help of entropic action: a sum of the areas of black hole horizons. We demonstrate that such description is indeed consistent with the Newton's laws of motion and gravity, modulo numerical coefficients, which coincide but seem different from unity. Since a large part of the modern discussion of entropic reformulation of general relativity is actually based on dimensional considerations, for making a next step it is crucially important to modify the argument, so that these dimensionless parameters acquire correct values.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

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

A diagrammatic treatment of neutrino oscillations

We present a covariant wave-packet approach to neutrino flavor transitions in vacuum. The approach is based on the technique of macroscopic Feynman diagrams describing the lepton number violating processes of production and absorption of virtual massive neutrinos at the macroscopically separated space-time regions ("source" and "detector"). Accordingly, the flavor transitions are a result of interference of the diagrams with neutrinos of different masses in the intermediate states. The statistically averaged probability of the process is representable as a multidimensional integral of the product of the factors which describe the differential flux density of massless neutrinos from the source, differential cross section of the neutrino interaction with the detector and a dimensionless factor responsible for the flavor transition. The conditions are analyzed under which the last factor can be treated as the flavor transition probability in the usual quantum-mechanical sense.Comment: 27 pages,7 figures, iopart class. Includes minor corrections made in proofs. References update

Mass hierarchy, 2-3 mixing and CP-phase with Huge Atmospheric Neutrino Detectors

We explore the physics potential of multi-megaton scale ice or water Cherenkov detectors with low ($\sim 1$ GeV) threshold. Using some proposed characteristics of the PINGU detector setup we compute the distributions of events versus neutrino energy $E_\nu$ and zenith angle $\theta_z$, and study their dependence on yet unknown neutrino parameters. The $(E_\nu - \theta_z)$ regions are identified where the distributions have the highest sensitivity to the neutrino mass hierarchy, to the deviation of the 2-3 mixing from the maximal one and to the CP-phase. We evaluate significance of the measurements of the neutrino parameters and explore dependence of this significance on the accuracy of reconstruction of the neutrino energy and direction. The effect of degeneracy of the parameters on the sensitivities is also discussed. We estimate the characteristics of future detectors (energy and angle resolution, volume, etc.) required for establishing the neutrino mass hierarchy with high confidence level. We find that the hierarchy can be identified at $3\sigma$ -- $10\sigma$ level (depending on the reconstruction accuracies) after 5 years of PINGU operation.Comment: 39 pages, 21 figures. Description of Fig.3 correcte

Casimir effect for massless minimally coupled scalar field between parallel plates in de Sitter spacetime

Casimir effect for massless minimally coupled scalar field is studied. An explicit answer for de Sitter spacetime is obtained and analized. Cosmological implications of the result are discussed.Comment: 7 pages, 2 figure

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

On the physical meaning of the Unruh effect

We present simple arguments that detectors moving with constant acceleration (even acceleration for a finite time) should detect particles. The effect is seen to be universal. Moreover, detectors undergoing linear acceleration and uniform, circular motion both detect particles for the same physical reason. We show that if one uses a circularly orbiting electron in a constant external magnetic field as the Unruh--DeWitt detector, then the Unruh effect physically coincides with the experimentally verified Sokolov--Ternov effect.Comment: 7 pages, 0 figures references added, small changes in text. To be published JETP Lett