The environment of an open quantum system is usually modelled as a large many-body quantum system. However, when an isolated quantum system itself is a many-body quantum system, the question of how large and complex it must be to generate internal equilibration is an open key-point in the literature. In this work, by monitoring the degree of equilibration of a single spin through its purity degradation, we are able to sense the chaotic behavior of the generic spin chain to which it is coupled. Quite remarkably, this holds even in the case of extremely short spin chains composed of three spins, where we can also reproduce the whole integrable to chaos transition. Finally, we discuss implications on quantum control experiments and show that quantum chaos reigns over the best degree of control achieved, even in small chains.Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the identification of network communities as well because nodes in the same community should be projected close to each other in the geometric space, where they can be detected via standard data clustering algorithms. In this paper, we test the ability of several graph embedding techniques to detect communities on benchmark graphs. We compare their performance against that of traditional community detection algorithms. We find that the performance is comparable, if the parameters of the embedding techniques are suitably chosen. However, the optimal parameter set varies with the specific features of the benchmark graphs, like their size, whereas popular community detection algorithms do not require any parameter. So, it is not possible to indicate beforehand good parameter sets for the analysis of real networks. This finding, along with the high computational cost of embedding a network and grouping the points, suggests that, for community detection, current embedding techniques do not represent an improvement over network clustering algorithms.The dynamics of an argon plasma in the gap of a thermionic diode is investigated using particle-in-cell (PIC) simulations. The time-averaged diode current, as a function of the relative electrical potential between the electrodes, is studied while the plasma density depletes due to recombination on the electrode surfaces. Simulations were performed in both one and two dimensions, and significant differences were observed in the plasma decay between the two cases. Specifically, in two dimensions it was found that the electrostatic potential gradually changes as the plasma decays, while in one dimension fluctuations in the plasma led to large potential fluctuations which changed the plasma decay characteristics relative to the two-dimensional case. This creates significant differences in the time-averaged diode current. Furthermore, it was found that the maximum time-averaged current is collected when the diode voltage is set to the flat-band condition, where the cathode and anode vacuum biases are equal. This suggests a novel technique of measuring the difference in work functions between the cathode and anode in a thermionic converter.Dynamics of the transition from a linear plasma wave to a nonlinear state characterized by the Bernstein-Greene-Kruskal mode is studied within the framework of the Vlasov-Poisson system. In the linear stage, the plasma distribution function (f) develops finer and finer structures in velocity space through a series of “mixing” processes leading to the Landau damping of the plasma wave. These mixing processes inevitably result in strong phase irregularities in velocity space. Using numerical simulations, it was observed that starting from the wave-particle resonance region, this irregular phase pattern gets “smoothed out” through a process of spreading of phase synchronization, which tends to reduce Landau damping, facilitating the formation of the nonlinear plasma wave as a fully synchronized final state. It is also found that there exists a residual damping for the quasisteady nonlinear wave when the phases of the particles are not fully synchronized.Zipf’s law establishes a scaling behavior for word frequencies in large text corpora. The appearance of Zipfian properties in vocabularies (viewed as an intermediate phase between referentially useless one-word systems and one-to-one word-meaning vocabularies) has been previously explained as an optimization problem for the interests of speakers and hearers. find more Remarkably, humanlike vocabularies can be viewed also as bipartite graphs. Thus, the aim here is double within a bipartite-graph approach to human vocabularies, to propose a decentralized language game model for the formation of Zipfian properties. To do this, we define a language game in which a population of artificial agents is involved in idealized linguistic interactions. Numerical simulations show the appearance of a drastic transition from an initially disordered state towards three kinds of vocabularies. Our results open ways to study Zipfian properties in language, reconciling models seeing communication as a global minima of information entropic energies and models focused on self-organization.We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.