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We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization.
We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency set up for a density at the onset of cooperative effects. To this end, we include mean-field models for the influence of local-field corrections and radiation trapping into our calculation. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local-field-induced phase modulation and demonstrate that it distinctively differs from the nonlinear self-phase-modulation that a strong pulse experiences in a Kerr medium.
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.
Electron beam plasma measurement was realised by means of DIABEAM system invented by ISF RWTH Aachen. The Langmuir probe method is used for measurement. The relative simplicity of the method and the possibility of dispersion of high power on the probe allow its application for the investigation of high-power electron beams. The key element of the method is a rotating thin tungsten wire, which intersects the beam transversely on its axis and collects part of the current by itself. The signals, which are registered in the DIABEAM as a voltage, were taken in the form of amplitude. The conversion of the probe current into the distribution along the beam radius was realised using the Abel’s method. A voltage-current characteristic was built for the beam current. The local electron density as well as the electron temperature, the floating potential and the plasma potential were measured and calculated by means of this characteristic.