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In this work we introduce the concept of quasi – injective gamma acts as a generalization of both injective and weakly injective gamma acts. In general we study the endomorphism set of gamma acts and certain types of gamma subacts which are used later. In the main part, we study basic properties of quasi – injective gamma acts and the effect of their endomorphism set to quasi – injective. We show that for any gamma act there is quasi – injective extension.

Two fundamental (meta)physical principles - NS (Non-Signalling condition which states the impossibility to communicate by means of physical correlations) and LC (the principle of Local Causality which isolates classical correlations from those responsible for non-locality) are considered in the framework of category theory. The original form of these principles operates with properties of common probability distributions for outcomes of measurements implemented in two space-time regions. The suggested category form consists of some assertions about special commutative diagrams. To any common probability distribution in the matter of discourse, an arrow (morphism) in these diagrams is associated. In fact, LC turns into the condition of the arrow being able to factor through a definite standard arrow. NS looks like uniqueness of an arrow which makes commutative a special diagram incorporating the considered arrow associated to the distribution. By means of these diagrams dual forms of NS and LC are suggested.

First antihydrogen atoms in captivity Antihydrogen, the bound state of an antiproton and a positron, has been produced at low energies since 2002 at CERN, Europe's particle-physics lab near Geneva, Switzerland. Antihydrogen is of fundamental interest for testing the standard model of elementary particles and interactions. However, experiments to date have produced antihydrogen that is not confined, precluding detailed study of its structure. Now the trapping and controlled release of atoms of antihydrogen has been achieved, paving the way for precision measurements on anti-atoms. In this historic experiment, an interaction between about 10 7 antiprotons and 7 × 10 8 positrons generated an observed 38 annihilation events corresponding to 38 atoms of antihydrogen briefly confined in ultra-cold superconducting traps. Antihydrogen, the bound state of an antiproton and a positron, has been produced at low energies at CERN since 2002. It is of fundamental interest for testing the standard model of elementary particles and interactions. However, experiments so far have produced antihydrogen that is not confined, precluding detailed study of its structure. Here, trapping of antihydrogen atoms is demonstrated, opening the door to precision measurements on anti atoms. Antimatter was first predicted 1 in 1931, by Dirac. Work with high-energy antiparticles is now commonplace, and anti-electrons are used regularly in the medical technique of positron emission tomography scanning. Antihydrogen, the bound state of an antiproton and a positron, has been produced 2 , 3 at low energies at CERN (the European Organization for Nuclear Research) since 2002. Antihydrogen is of interest for use in a precision test of nature’s fundamental symmetries. The charge conjugation/parity/time reversal (CPT) theorem, a crucial part of the foundation of the standard model of elementary particles and interactions, demands that hydrogen and antihydrogen have the same spectrum. Given the current experimental precision of measurements on the hydrogen atom (about two parts in 10 14 for the frequency of the 1 s -to-2s transition 4 ), subjecting antihydrogen to rigorous spectroscopic examination would constitute a compelling, model-independent test of CPT. Antihydrogen could also be used to study the gravitational behaviour of antimatter 5 . However, so far experiments have produced antihydrogen that is not confined, precluding detailed study of its structure. Here we demonstrate trapping of antihydrogen atoms. From the interaction of about 10 7 antiprotons and 7 × 10 8 positrons, we observed 38 annihilation events consistent with the controlled release of trapped antihydrogen from our magnetic trap; the measured background is 1.4 ± 1.4 events. This result opens the door to precision measurements on anti-atoms, which can soon be subjected to the same techniques as developed for hydrogen.

One of the earliest and most intensively studied problems in quantum optics is the interaction of a two-level system (an atom) with a single photon. This simple system provides a rich platform for exploring exotic light-matter interactions and the emergence of more complex phenomena such as superradiance, which is a cooperative effect that emerges when the density of atoms is increased and coupling between them is enhanced. Going beyond the light-matter system, Li et al. observed analogous cooperative effects for coupled magnetic systems. The results suggest that ideas in quantum optics could be carried over and used to control and predict exotic phases in condensed matter systems. Science , this issue p. 794 Cooperatively enhanced coupling, similar to that of light-matter interactions, is generalized to a coupled spin system. The interaction of N two-level atoms with a single-mode light field is an extensively studied many-body problem in quantum optics, first analyzed by Dicke in the context of superradiance. A characteristic of such systems is the cooperative enhancement of the coupling strength by a factor of N . In this study, we extended this cooperatively enhanced coupling to a solid-state system, demonstrating that it also occurs in a magnetic solid in the form of matter-matter interaction. Specifically, the exchange interaction of N paramagnetic erbium(III) (Er 3+ ) spins with an iron(III) (Fe 3+ ) magnon field in erbium orthoferrite (ErFeO 3 ) exhibits a vacuum Rabi splitting whose magnitude is proportional to N . Our results provide a route for understanding, controlling, and predicting novel phases of condensed matter using concepts and tools available in quantum optics.

Our knowledge of the fundamental particles of nature and their interactions is summarized by the standard model of particle physics. Advancing our understanding in this field has required experiments that operate at ever higher energies and intensities, which produce extremely large and information-rich data samples. The use of machine-learning techniques is revolutionizing how we interpret these data samples, greatly increasing the discovery potential of present and future experiments. Here we summarize the challenges and opportunities that come with the use of machine learning at the frontiers of particle physics. The application and development of machine-learning methods used in experiments at the frontiers of particle physics (such as the Large Hadron Collider) are reviewed, including recent advances based on deep learning.

The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically different universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of 300 kilo–electron volts, which is greater than 0 by 5 standard deviations. We also determine the splittings in the Σ, Ξ, D, and Ξcc isospin multiplets, exceeding in some cases the precision of experimental measurements.

Density functional theory (DFT) is now routinely used for simulating material properties. Many software packages are available, which makes it challenging to know which are the best to use for a specific calculation. Lejaeghere et al. compared the calculated values for the equation of states for 71 elemental crystals from 15 different widely used DFT codes employing 40 different potentials (see the Perspective by Skylaris). Although there were variations in the calculated values, most recent codes and methods converged toward a single value, with errors comparable to those of experiment. Science , this issue p. 10.1126/science.aad3000 ; see also p. 1394 A survey of recent density functional theory methods shows a convergence to more accurate property calculations. [Also see Perspective by Skylaris ] The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.