The wave operator representation of quantum and classical dynamics

The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator representation of quantum dynamics, and explore its connection to standard methods of quantum dynamics. This method takes as its central object the square root of the density matrix, and consequently enjoys several unusual advantages over standard representations. By combining this with purification techniques imported from quantum information, we are able to obtain a number of results. Not only is this formalism able to provide a natural bridge between phase and Hilbert space representations of both quantum and classical dynamics, we also find the waveoperator representation leads to novel semiclassical approximations of both real and imaginary time dynamics, as well as a transparent correspondence to the classical limit. This is demonstrated via the example of quadratic and quartic Hamiltonians, while the potential extensions of the waveoperator and its application to quantum-classical hybrids is discussed. We argue that the wave operator provides a new perspective that links previously unrelated representations, and is a natural candidate model for scenarios (such as hybrids) in which positivity cannot be otherwise guaranteed

Wigner phase space distribution as a wave function

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.Comment: 6 pages and 2 figure

Innovative Development of the IT Sphere in Ukraine

The development of strategic guidelines in the IT sphere deserves considerable attention in view of the efficiency and long-term consequences that certain decisions and actions have for the development of IT business in the country. Strategic management of innovation activities in the IT sphere should involve policies and procedures available for implementation in the conditions of specific companies that ensure the protection of the assets of the entity, efficiency and effectiveness of management. The above requires the definition of basic forms of implementation of the IT development strategy in Ukraine, which indicates the relevance of this study. Among researchers of the innovation process today, the prevailing belief is that innovations in the modern economic environment arise and be spread in the networks that connect individual actors. This position is formed on the basis of the evolution of views on the problems of the course of innovation processes and finds expression in the conception of feedback models, integrated models, as well as the concept of «open innovation environment». The researchers have also identified the following components of innovation development: social activity, creative activity, intellectual capital and entrepreneurial initiative. At the same time, studies of the problems of implementing the innovation process in the IT sphere in the reviewed works relate primarily to the micro level and much less to the macro level, that is, taking into account the need to solve the problems of development of this sphere and the economy of the country as a whole. The creation, assimilation and dissemination of innovations in the modern economic environment should be implemented in the form of a certain development strategy, within which it is possible to manage, control and stimulate the course of this process. The article is aimed at substantiating strategic guidelines for innovative development of the IT sphere in Ukraine under current conditions, under the influence of factors of the business environment and specifics of the national innovation system. The informational basis of the carried out study is the normative legal acts of Ukraine on the issues of conducting economic activity of enterprises, the implementation of innovation activity; scientific publications of leading foreign and domestic scientists. The study uses general scientific and special methods: induction, deduction, analysis, synthesis; dialectical method – in identifying specific features of strategic innovative development of the IT sphere in Ukraine; abstraction, generalization, system, functional methods – when developing a strategy for the development of the IT sphere in Ukraine and the forms of its practical implementation. Based on the results of the study, the authors conclude that the strategic management of innovation activities in the IT sphere should use instruments available for implementation in the conditions of specific companies that ensure the protection of the assets of an economic entity, efficiency and effectiveness of management. The configuration of such instrumentarium is formed taking into account the problems of development of the IT sphere, country-specific development factors, global trends in the development of IT technologies, i. e., the limitations and opportunities that determine the form and content of the instruments used. The basic forms of implementation of the IT development strategy in Ukraine are determined. Prospects for further research are to deepen and structure the instrumentarium for managing innovation activities in the IT sphere of Ukraine, which can be applied to specific directions of such activities

Diabetes mellitus type 1 in adults

Public organization “Russian Association of Endocrinologists”. Clinical guidlines

Les droits disciplinaires des fonctions publiques : « unification », « harmonisation » ou « distanciation ». A propos de la loi du 26 avril 2016 relative à la déontologie et aux droits et obligations des fonctionnaires

The production of tt‾ , W+bb‾ and W+cc‾ is studied in the forward region of proton–proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98±0.02 fb−1 . The W bosons are reconstructed in the decays W→ℓν , where ℓ denotes muon or electron, while the b and c quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions.The production of $t\overline{t}$, $W+b\overline{b}$ and $W+c\overline{c}$ is studied in the forward region of proton-proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02 \mbox{fb}^{-1}. The $W$ bosons are reconstructed in the decays $W\rightarrow\ell\nu$, where $\ell$ denotes muon or electron, while the $b$ and $c$ quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions

A study of CP violation in B-+/- -> DK +/- and B-+/- -> D pi(+/-) decays with D -> (KSK +/-)-K-0 pi(-/+) final states

A first study of CP violation in the decay modes $B^\pm\to [K^0_{\rm S} K^\pm \pi^\mp]_D h^\pm$ and $B^\pm\to [K^0_{\rm S} K^\mp \pi^\pm]_D h^\pm$, where $h$ labels a $K$ or $\pi$ meson and $D$ labels a $D^0$ or $\overline{D}^0$ meson, is performed. The analysis uses the LHCb data set collected in $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{-1}$. The analysis is sensitive to the CP-violating CKM phase $\gamma$ through seven observables: one charge asymmetry in each of the four modes and three ratios of the charge-integrated yields. The results are consistent with measurements of $\gamma$ using other decay modes