Abstract:
Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free behavior of the distribution of returns of different financial assets have been confirmed in a series of works. The existence of a Pareto-like distribution of the wealth of market participants has been connected with the scale-free distribution of trading volumes and price-returns. The origin of the Pareto-like wealth distribution, however, remained obscure. Here we show that it is the process of trading itself that under two mild assumptions spontaneously leads to a self-organization of the market with a Pareto-like wealth distribution for the market participants and at the same time to a scale-free behavior of return fluctuations. These assumptions are (i) everybody trades proportional to his current capacity and (ii) supply and demand determine the relative value of the goods.

Abstract:
Using recent data for the decays $f_0 \to \gamma\gamma$, $f_0 \to \pi \pi$, we determine the mixing angle of scalar mesons in a chiral quark $\sigma$-model. This value is employed to analyze of the kaon polarizability. It is shown that pole diagrams from intermediate scalar mesons and their mixing angle significantly affect the electromagnetic polarizability of charged and neutral kaons. Our results are compared with other models and the results of the chiral symmetry limit. The temperature dependence of the kaon polarizabilities is investigated.

Abstract:
In this article, the gap equation for the constituent quark mass in the U(2)*U(2) Nambu-Jona-Lasinio model for the 1/Nc approximation is investigated. It is shown that taking into account scalar isovector mesons plays an important role for the correct description of quark masses in this approximation. The role of the Ward identity in calculations of 1/Nc corrections to the meson vertex functions is shortly discussed.

Abstract:
A chiral SU(2) x SU(2) Lagrangian containing, besides the usual meson fields, their first radial excitations is considered. The Lagrangian is derived by bosonization of the Nambu-Jona-Lasinio quark model with separable non-local interactions, with form factors corresponding to 3-dimensional ground and excited state wave functions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the pions, rho-and omega-mesons are described with the help of two form factors. The weak decay constant F_pi' is calculated. The values for the decay widths of the processes rho -> 2 pi, pi' -> rho pi, rho' -> 2 pi, rho' -> omega pi and omega' -> rho pi are obtained in agreement with the experimental data.

Abstract:
We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non-interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occurs we find that the interaction can significantly reduce the rate of energy increase. The implications for applications of our findings to cool or heat the system are also dicussed.

Abstract:
In \cite{Boed}, C.-F. B\"odigheimer constructed a finite cell-complex $\mf{Par}_{g,n,m}$ and a bijective map $\cH: \mf{Dip}_{g,n,m} \to \mf{Par}_{g,n,m}$ (the Hilbert-uniformization) from the moduli space of dipole functions on Riemann surfaces with $n$ directions and $m$ punctures to $\mf{Par}_{g,n,m}$. In \cite{Boed} and \cite{Eb}, it is proven that $\cH$ is a homeomorphism. The first result of this note is that the space $\mf{Dip}_{g,n,m}$ carries a natural structure of a real-analytic manifold. Our second result is that $\cH$ is real-analytic, at least on the preimage of the top-dimensional open cells of $\mf{Par}_{g,n,m}$.

Abstract:
We demonstrate $|W\rangle$ state encoding of multi-atom ensemble qubits. Using optically trapped Rb atoms the $T_2$ coherence time is 2.6(3) ms for $\bar N=7.6$ atoms and scales approximately inversely with the number of atoms. Strong Rydberg blockade between two ensemble qubits is demonstrated with a fidelity of $0.89(1)$ and a fidelity of $\sim \hspace{-.05cm}1.0$ when postselected on control ensemble excitation. These results are a significant step towards deterministic entanglement of atomic ensembles.

Abstract:
Positive streamers in ambient air at pressures from 0.013 to 1 bar are investigated experimentally. The voltage applied to the anode needle ranges from 5 to 45 kV, the discharge gap from 1 to 16 cm. Using a "slow" voltage rise time of 100 to 180 ns, the streamers are intentionally kept thin. For each pressure p, we find a minimal diameter d_{min}. To test whether streamers at different pressures are similar, the minimal streamer diameter d_{min} is multiplied by its pressure p; we find this product to be well approximated by p*d_{min}=0.20 \pm 0.02 mm*bar over two decades of air pressure at room temperature. The value also fits diameters of sprite discharges above thunderclouds at an altitude of 80 km when extrapolated to room temperature (as air density rather than pressure determines the physical behavior). The minimal velocity of streamers in our measurements is approximately 0.1 mm/ns = 10^5 m/s. The same minimal velocity has been reported for tendrils in sprites. We also investigate the size of the initial ionization cloud at the electrode tip from which the streamers emerge, and the streamer length between branching events. The same quantities are also measured in nitrogen with a purity of approximately 99.9 %. We characterize the essential differences with streamers in air and find a minimal diameter of p*d_{min}=0.12 \pm 0.02 mm*bar in our nitrogen.

Abstract:
Photographs show distinct differences between positive streamers in air or in a nitrogen-oxygen mixture (0.2% O2). The streamers in the mixture branch more frequently, but the branches also extinguish more easily. Probably related to that, the streamers in the mixture propagate more in a zigzag manner while they are straighter in air. Furthermore, streamers in the mixture can become longer; they are thinner and more intense.

Abstract:
This proceedings paper from 2004 contains figures of discharges in different gap lengths at the same potential that are not available elsewhere. The 2004 abstract: The evolution of streamers is known to depend on gas composition and electrode geometry, on polarity and size of the voltage and also on the electric circuit that produces the high voltage pulse. To characterize the phenomena better and to compare with theory, a new larger experimental setup with vacuum enclosure has been built. We here present first results in this setup on positive streamers in air at fixed voltage and varying electrode distance. While next to the emitting anode tip, a similar number of streamers seems to emerge due to multiple branching, more streamers seem to survive over a fixed distance, when the gap is shorter. When lowering the voltage, streamers branch less at all distances from the anode tip or do not branch at all beyond a certain distance.