Neutrinos with Mixing in Twisting Magnetic Fields

Transitions in a system of neutrinos with vacuum mixing and magnetic moments, propagating in matter and transverse magnetic field, are considered. It is shown that in the realistic case of magnetic field direction varying along the neutrino path qualitatively new phenomena become possible: permutation of neutrino conversion resonances, appearance of resonances in the neutrino-antineutrino ($\nu_{lL}\leftrightarrow\bar{\nu}_{lR}$) transition channels, neutrino-antineutrino resonant conversion, large amplitude $\nu_{lL}\leftrightarrow\bar{\nu}_{lR}$ oscillations, merging of different resonances (triple resonances). Possible phenomenological implications of these effects are briefly discussed.Comment: LaTeX, 35 pages, 4 figures (not included but available upon request). In memoriam of Ya.A. Smorodinsky. SISSA-170/92/E

Constructing infinitely many smooth structures on small 4-manifolds

The purpose of this article is twofold. First we outline a general construction scheme for producing simply-connected minimal symplectic 4-manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain irreducible symplectic 4-manifolds homeomorphic but not diffeomorphic to \CP#(2k+1)\CPb for $k = 1,...,4$, or to 3\CP# (2l+3)\CPb for $l =1,...,6$. Secondly, for each of these homeomorphism types, we show how to produce an infinite family of pairwise nondiffeomorphic nonsymplectic 4-manifolds belonging to it. In particular, we prove that there are infinitely many exotic irreducible nonsymplectic smooth structures on \CP#3\CPb, 3\CP#5\CPb and 3\CP#7\CPb.Comment: 23 pages, 3 figure

Beta decay and other processes in strong electromagnetic fields

We consider effects of the fields of strong electromagnetic waves on various characteristics of quantum processes. After a qualitative discussion of the effects of external fields on the energy spectra and angular distributions of the final-state particles as well as on the total probabilities of the processes (such as decay rates and total cross sections), we present a simple method of calculating the total probabilities of processes with production of non-relativistic charged particles. Using nuclear beta-decay as an example, we study the weak and strong field limits, as well as the field-induced beta-decay of nuclei stable in the absence of the external fields, both in the tunneling and multi-photon regimes. We also consider the possibility of accelerating forbidden nuclear beta-decays by lifting the forbiddeness due to the interaction of the parent or daughter nuclei with the field of a strong electromagnetic wave. It is shown that for currently attainable electromagnetic fields all effects on total beta-decay rates are unobservably small.Comment: LaTeX, 30 pages, 2 figures. Invited contribution to the special issue of Yadernaya Fizika dedicated to the centennial anniversary of birthday of A.B. Migdal. V2: references adde

New Physics and Neutrino Oscillation

Description of neutrino oscillation in the case of Non-Standard neutrino Interaction (NSI) is briefly presented. The NSI causes the entanglement between internal degrees of freedom of neutrinos (mass, spin, flavour) and other accompanying particles in the production and detection processes. In such case neutrinos are mostly in the mixed states. Role of the density matrix in description of neutrino oscillation process is shortly explained.Comment: 3 pages. Talk given at NOW 2010: Neutrino Oscillation Workshop, Conca Specchiulla (Otranto), Lecce, Italy, 4-11 Sep 201

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

Uzbekistan 's foreign policy for the implementation of our national interests

Today, the term "New Uzbekistan" is accepted in the international arena not only as a new concept, but also as a real social phenomenon. Such achievements and results, which are the result of the enormous legal opportunities created by our Constitution, certainly give us great pride and honor. It should be noted that the Constitution is an encyclopedic document that defines the independence of our people, the peaceful and peaceful life, the restoration of our national values, history and culture, as well as the guarantees of human rights and freedoms. At the same time, our Constitution is the sum of our national interests, which embodies the development of our country, ensuring the welfare and security of our people, strengthening our sovereignty, our country's activity as an equal subject in international relations. In addition, radical changes and large-scale reforms in all spheres of state and public life, including the strengthening of the rule of law and human rights, the development of an economy based on free market relations and the priority of private property, cooperation with far and near abroad. Our Constitution serves as an important basis for the establishment of mutually beneficial relations

An infrared origin of leptonic mixing and its test at DeepCore

Fermion mixing is generally believed to be a low-energy manifestation of an underlying theory whose energy scale is much larger than the electroweak scale. In this paper we investigate the possibility that the parameters describing lepton mixing actually arise from the low-energy behavior of the neutrino interacting fields. In particular, we conjecture that the measured value of the mixing angles for a given process depends on the number of unobservable flavor states at the energy of the process. We provide a covariant implementation of such conjecture, draw its consequences in a two neutrino family approximation and compare these findings with current experimental data. Finally we show that this infrared origin of mixing will be manifest at the Ice Cube DeepCore array, which measures atmospheric oscillations at energies much larger than the tau lepton mass; it will hence be experimentally tested in a short time scale.Comment: 14 pages, 1 figure; version to appear in Int.J.Mod.Phys.

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