Empirically derived Hund's rules of the pre-quantum-mechanics era predict the ordering of the energy levels possessing different spin and orbital angular momentum quantum numbers. They have proved to be almost universally valid for atoms, molecules, and quantum dots. Yet, despite of a long-standing debate, the search for their origin persists primarily due to the lack of the precise knowledge of the electronic structure in different spin states. We explore the origin of the first Hund rule for a two-dimensional model of He-like systems and that of two-electron quantum dots. They represent ideal systems providing a direct fundamental insight into the structure of the internal part of the fully correlated wave functions, allowing an unambiguous argument.

An examination of their probability density distributions reveals indeed the existence of a region in the internal space, which we refer to as a conjugate Fermi hole. In this region the singlet wave function has a smaller probability density than the corresponding triplet one, in contrast to the genuine Fermi hole where the triplet has a smaller density than the singlet. Due to the presence of this conjugate Fermi hole the singlet probability density has to migrate far away from the centre of the one-electron potential. This rationalizes the well-known broader electron density distribution of the singlet state relative to the corresponding triplet. This key observation explains the singlet-triplet energy gap.

Quantum-control methods are employed to manipulate physical and chemical processes using time-dependent fields. In particular they can be used to develop quantum logic gates thus helping us achieve a major goal of modern physics, the realization of scalable quantum computation.

A large body of work in quantum control has been devoted to the study of interacting spin-1/2 chains since these are effective models of qubit arrays. While interactions between qubits are necessary for realizing entangling two-qubit gates, standard approaches for controlling such arrays by acting on each qubit do not make an explicit use of these interactions. However for some particular types of interaction it suffices to control only a small subsystem of a given system, the idea underpinning the local-control approach.

In this paper we have explored anisotropic Heisenberg interactions, relevant for the use of Josephson junction based superconducting charge-qubit arrays. This example is particularly interesting as the concept of local control can be taken to the extreme -- controlling just one end qubit in an  array. We investigated how time-dependent control fields acting on the first qubit in an array can be selected in order to realize relevant quantum logic operations (e.g. controlled-NOT, square-root-of-SWAP) in the shortest possible times.

Further extending the idea of local control, we showed that in building some quantum gates the degree of control over the chosen end qubit can be further reduced by acting with a control field in only one direction (say, x direction). Most remarkably, we demonstrated that in the parameter regime of interest for superconducting charge qubits this reduced  control can lead to a more time-efficient realization of relevant   gates than the approach involving alternate x and y control fields. We anticipate that our findings will facilitate implementations of quantum  computation in superconducting qubit arrays.

This work shows that a successful interpretation of quantum mechanics can be seen to emerge by taking the actual, or internal, states of a sub-system to correspond to one the eigenvectors of its reduced density matrix. Previous work has highlighted serious objections to such a modal type interpretation because it apparently leads to macroscopic superpositions and physically unacceptable instabilities near degeneracies. We show that both these problems are solved if the sub-system consists of a large number of coarse-grained degrees of freedom which is natural as real measuring devices have both finite spatial and temporal resolution. What results is an interpretation in which both decoherence and coarse graining play key roles and from which the rules of the Copenhagen Interpretation are seen to emerge in realistic situations. In this interpretation a measurement process is smooth but results in internal states that corresponds to the distinct outcomes ones expects. Previous work has suggested that the internal states of a device measuring the position of a particle would be spread out macroscopically.

It took eventually from the turn of the century until 1926 before the extraterrestrial nature of the penetrating radiation was generally accepted.

In the work that culminated with high altitude balloon flights, many important contributions have been forgotten and in particular those of Domenico Pacini, who, in June 1911, demonstrated by studying the decrease of radioactivity with an electroscope immersed in water that the radiation today called "cosmic rays" could not come from the crust of the Earth. This was the first time in which the technique of comparison of undersea measurements with measurements at sea level has been used to obtain a result in fundamental physics; this technique will be used in neutrino experiments of the near future. This article carefully retraces the history of the discovery of cosmic rays and puts the unfolding story in both the political and scientific contexts. With the help of material previously unknown to the history of science, for example the nominations for the Nobel prizes related to cosmic ray research and the relevant internal reports of the Swedish Royal Academy of Science, and letters exchanged between Victor Hess and Pacini, a more complete view of this fascinating discovery is possible.

Methods to study the formation of our universe are used to understand long-range interactions between particles at the micrometric scale. In the article summarised here, it it is shown that micron-size particles trapped at fluid interfaces exhibit a collective dynamic that is subject to seemingly unrelated governing laws smoothly transitioning from long-ranged cosmological-style gravitational attraction down to short-range attractive and repulsive forces.

The authors used so-called colloidal particles that are larger than molecules but too small to be observed with the naked eye, which are adsorbed at the interface between two fluids and assembled into a monolayer. This constitutes a 2D model in which particles larger than a micron deform the interface through their own weight and generate an effective long-range attraction which looks like gravitation in 2D, and thus assemble in clusters.

To model long-range forces between particles, numerical simulations based on random movement of particles, known as Brownian dynamics, have been used. It takes advantage of the formal analogy between so-called capillary attraction - the long-ranged interaction through interface deformation - and gravitational attraction.

It is also found that this long-range interaction no longer matters beyond a certain length determined by the properties of both the particles and the interface, and short-range forces come into play. This means that for systems exceeding this length, particles first tend to self-assemble into several clusters which eventually merge into a single, large cluster.

The study of monolayer aggregates of micron-size colloids are used in nanotechnology applications.

The first model demonstrating that it is possible for two particles to cross an energy barrier together, where a single particle could not, is shown here.

A new kind of so-called Klein tunnelling - representing the quantum equivalent of crossing an energy wall - is presented in a model of two interacting particles. The authors relied on an analytical and numerical study of a landmark model of interacting particles, called the Hubbard model. They predict a new type of Klein tunnelling for a couple of interacting particles confronted by an energy barrier. Even though the barrier is impenetrable for single particles, it becomes transparent when the two particles cross the energy barrier together. They expect these predictions to be confirmed experimentally in ultra-cold atoms trapped in optical lattices. If this is the case, similar quantum simulation could be a tool for emulating multiple-particle systems.

A nucleation site initiates the birth of a crystal. In most cases, take for example the dust particle in a snowflake, nucleation starts from a heterogenous defect. Homogenous nucleation is more elusive because of the prevalence of defects in any bulk sample. Crystallisation in tiny droplets alleviates this difficulty in a manner that is conceptually simple: subdivide the system into more domains than the number of defects. If the domains greatly outnumber the defects then only the homogenous mechanism can induce nucleation in a defect free compartment.

Such an approach has been used here to investigate nucleation in polyethylene (PE) droplets. At high temperatures, a thin PE film dewets from an unfavourable surface forming tiny droplets, much like water beading up on a waxy leaf (Fig. (b)). The resulting sample geometry is ideal: thousands of droplets ranging in size can be monitored simultaneously with optical microscopy, with a nucleation event easily distinguishable by the rapid growth of the crystal (Fig. (c)). Each droplet becomes an isolated independent nucleation experiment. By investigating thousands of droplets supercooled well below the melting temperature, studies of homogenous nucleation become straightforward. Relating the probability of homogenous nucleation to the size of the droplet, the authors show that nucleation is surface activated. Stated most simply, a droplet with twice the surface area is twice as likely to nucleate, indicating that the perturbation induced by the interface reduces the intrinsic activation barrier to crystal nucleation.

The problem of the accurate identification of a contour arises in many fields of physics. This contour can be an image of an elongated object, for example a fibre, a filament or a structure of larger dimension such as the cable of a bridge. It can also be a front of a physical event, such as a thermal or chemical front revealed by a convenient marker.

Current methods are optimized in the sense of the capacity of detection of a contour hidden in a noisy image, mainly for medicinal applications. The given information consists in a discrete set of locations (generally a set of pixels). Due to this discontinuous nature, the derivatives (slopes and curvatures) require a filtering and the result depends on its choice. However this knowledge is crucial for many applications. For example fluxes computations depend upon slopes; momentums on beams (in mechanics) depend upon curvatures.

The proposed method, issued from the Digital Image Correlation methods used in solid mechanics, is more focused on the precision of the identification, in the sense of metrology. It consists in the research of the best fit between the image of the physical contour and a virtual image, a curve roughly of the same thickness as the contour. This curve (the virtual beam) is defined analytically thus the obtained shape and its derivatives are smooth, given with confidence and defined at any scale of refinement.

The method can be easily extended to edge detection. It will also be possible to use an analytical expression of the considered problem thus the method will give its best coefficients, leading to a straightforward identification of the phenomenon from an unfiltered image.

In recent years, evidence has been accumulating that seismic waves generated by a large earthquake can produce additional quakes far away of the main shock. This may not be surprising when the secondary quakes occur right at the occurrence of the seismic waves. However, in general these dynamically triggered earthquakes occur hours or days after the main shock, namely when the seismic waves have elapsed.

In order to understand the origin of this phenomenon, we have adapted a recently proposed statistical model of seismicity that takes into account the existence of plastic relaxation processes within the faults. This kind of model has been used before to obtain realistic sequences of earthquakes, including in particular aftershocks. By appropriately defining a perturbation (assumed to be the occurrence of seismic waves), it is observed that the seismic activity in the system has a sharp increase following the perturbation, well after it has vanished.

The origin of a temporarily delayed effect in the model is tightly related to the existence of relaxation processes, as the effect does not exist in the case in which relaxation is absent. In this respect delayed dynamically triggered earthquakes are in some sense similar to aftershocks: the latter are delayed events triggered by a permanent perturbation (the change in the stress field caused by the main shock) while the former are delayed events triggered by a transient perturbation (the passage of seismic waves), once the perturbation has vanished.

The present investigation suggests that both aftershocks and delayed dynamically triggered quakes originate in the same kind of physical mechanism, namely internal relaxation mechanisms within the faults, that the present model appropriately captures.