On entanglement in neutrino mixing and oscillations

We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, and then for the case of Quantum Field Theory.Comment: 14 pages, 2 figures. Presented at "Symmetries in Science Symposium - Bregenz 2009"

Entanglement, local measurements, and symmetry

A definition of entanglement in terms of local measurements is discussed. Viz, the maximum entanglement corresponds to the states that cause the highest level of quantum fluctuations in all local measurements determined by the dynamic symmetry group of the system. A number of examples illustrating this definition is considered.Comment: 10 pages. to be published in Journal of Optics

Stein's Method and Characters of Compact Lie Groups

Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the trace into irreducible components. This is illustrated for Lie groups of classical type and Dyson's circular ensembles. The approach in this paper will be useful for the study of higher dimensional characters, where normal approximations need not hold.Comment: 22 pages; same results, but more efficient exposition in Section 3.

Measurement of the Absolute Differential Cross Section for np Elastic Scattering at 194 MeV

A tagged medium-energy neutron beam has been used in a precise measurement of the absolute differential cross section for np back-scattering. The results resolve significant discrepancies within the np database concerning the angular dependence in this regime. The experiment has determined the absolute normalization with 1.5% uncertainty, suitable to verify constraints of supposedly comparable precision that arise from the rest of the database in partial wave analyses. The analysis procedures, especially those associated with evaluation of systematic errors in the experiment, are described in detail so that systematic uncertainties may be included in a reasonable way in subsequent partial wave analysis fits incorporating the present results.Comment: 22 pages, 21 figures, submitted for publication in Physical Review

Dynamics of a Bose-Einstein condensate in a symmetric triple-well trap

We present a complete analysis of the dynamics of a Bose-Einstein condensate trapped in a symmetric triple-well potential. Our classical analogue treatment, based on a time-dependent variational method using SU(3) coherent states, includes the parameter dependence analysis of the equilibrium points and their local stability, which is closely related to the condensate collective behaviour. We also consider the effects of off-site interactions, and how these "cross-collisions" may become relevant for a large number of trapped bosons. Besides, we have shown analytically, by means of a simple basis transformation in the single-particle space, that an integrable sub-regime, known as twin-condensate dynamics, corresponds in the classical phase space to invariant surfaces isomorphic to the unit sphere. However, the quantum dynamics preserves the twin-condensate defining characteristics only partially, thus breaking the invariance of the associated quantum subspace. Moreover, the periodic geometry of the trapping potential allowed us to investigate the dynamics of finite angular momentum collective excitations, which can be suppressed by the emergence of chaos. Finally, using the generalized purity associated to the su(3) algebra, we were able to quantify the dynamical classicality of a quantum evolved system, as compared to the corresponding classical trajectory.Comment: 22 pages, 10 figure

Measurement of the Absolute np Scattering Differential Cross Section at 194 MeV

We describe a double-scattering experiment with a novel tagged neutron beam to measure differential cross sections for np back-scattering to better than 2% absolute precision. The measurement focuses on angles and energies where the cross section magnitude and angle-dependence constrain the charged pion-nucleon coupling constant, but existing data show serious discrepancies among themselves and with energy-dependent partial wave analyses (PWA). The present results are in good accord with the PWA, but deviate systematically from other recent measurements.Comment: 4 pages, 4 figure

Russian Higher Education as Influenced by COVID-19 Pandemic

Цель настоящей концептуальной статьи – проанализировать тенденции, проявившиеся в российском высшем образовании в период пандемии коронавируса. Рассматриваются основные проблемы, с которыми столкнулись российские вузы при переходе на дистанционное обучение студентов. Особое внимание уделяется проблеме «цифрового неравенства», актуализировавшейся в условиях перехода вузов на дистант и онлайн-режим обучения. Показано, что «цифровое неравенство» не сводится к дифференциации студентов по наличию у них технических возможностей учиться дистанционно. Вопросы «цифрового неравенства» исследуются на уровне регионов, вузов, преподавателей и студентов. Также авторами обосновывается тезис о том, что в рамках действующей модели бюджетного финансирования решить проблему динамичного развития российской системы высшего образования не удастся, и предлагаются подходы к ее изменению.The purpose of this article is to analyze trends in Russian higher education development during the coronavirus pandemic. The paper considers main problems faced by Russian universities in their students’ transition to distance learning. Particular attention is paid to the problem of the «digital inequality», which became urgent in the conditions of online teaching organization. It is shown that the «digital inequality» does not only mean differentiating students by their having necessary equipment to study remotely. The issues of «digital inequality» are being investigated at the levels of regions, universities, teachers and students. At the same time, the authors substantiate the thesis that it will not be possible to solve the problem of the dynamic development of the Russian higher education system within the framework of the current model of budget financing, and thus propose approaches to its change.Статья подготовлена в рамках выполнения научно-исследовательской работы государственного задания РАНХиГС.The article was prepared as part of the research work of the state assignment of the RANEPA

Growing smooth interfaces with inhomogeneous, moving external fields: dynamical transitions, devil's staircases and self-assembled ripples

We study the steady state structure and dynamics of an interface in a pure Ising system on a square lattice placed in an inhomogeneous external field. The field has a profile with a fixed shape designed to stabilize a flat interface, and is translated with velocity v_e. For small v_e, the interface is stuck to the profile, is macroscopically smooth, and is rippled with a periodicity in general incommensurate with the lattice parameter. For arbitrary orientations of the profile, the local slope of the interface locks in to one of infinitely many rational values (devil's staircase) which most closely approximates the profile. These ``lock-in'' structures and ripples dissappear as v_e increases. For still larger v_e the profile detaches from the interface which is now characterized by standard Kardar-Parisi-Zhang (KPZ) exponents.Comment: 4 pages, 4 figures, published version, minor change

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold