Cusp-scaling behavior in fractal dimension of chaotic scattering

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a striking feature associated with these subtle bifurcations: the dimension typically exhibits a sharp, cusplike local minimum at the bifurcation.Comment: 4 pages, 4 figures, Revte

Possible nodal superconducting gap emerging at the Lifshitz transition in heavily hole-doped Ba0.1K0.9Fe2As2

We performed a high energy resolution ARPES investigation of over-doped Ba0.1K0.9Fe2As2 with T_c= 9 K. The Fermi surface topology of this material is similar to that of KFe2As2 and differs from that of slightly less doped Ba0.3K0.7Fe2As2, implying that a Lifshitz transition occurred between x=0.7 and x=0.9. Albeit for a vertical node found at the tip of the emerging off-M-centered Fermi surface pocket lobes, the superconducting gap structure is similar to that of Ba0.3K0.7Fe2As2, suggesting that the paring interaction is not driven by the Fermi surface topology.Comment: 5 pages, 4 figure

Tableaux for Policy Synthesis for MDPs with PCTL* Constraints

Markov decision processes (MDPs) are the standard formalism for modelling sequential decision making in stochastic environments. Policy synthesis addresses the problem of how to control or limit the decisions an agent makes so that a given specification is met. In this paper we consider PCTL*, the probabilistic counterpart of CTL*, as the specification language. Because in general the policy synthesis problem for PCTL* is undecidable, we restrict to policies whose execution history memory is finitely bounded a priori. Surprisingly, no algorithm for policy synthesis for this natural and expressive framework has been developed so far. We close this gap and describe a tableau-based algorithm that, given an MDP and a PCTL* specification, derives in a non-deterministic way a system of (possibly nonlinear) equalities and inequalities. The solutions of this system, if any, describe the desired (stochastic) policies. Our main result in this paper is the correctness of our method, i.e., soundness, completeness and termination.Comment: This is a long version of a conference paper published at TABLEAUX 2017. It contains proofs of the main results and fixes a bug. See the footnote on page 1 for detail

Signatures of charmonium modification in spatial correlation functions

We study spatial correlation functions of charmonium in 2+1 flavor QCD using an improved staggered formulation. Contrary to the temporal correlation functions the spatial correlation functions exhibit a strong temperature dependence above the QCD transition temperature. Above this temperature they are sensitive to temporal boundary conditions. Both features become significant at a temperature close to 1.5 Tc and suggest corresponding modifications of charmonium spectral functions.Comment: 12 pages, LaTeX, 3 figure

Fine Details of the Nodal Electronic Excitations in Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

Very high energy resolution photoemission experiments on high quality samples of optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ show new features in the low-energy electronic excitations. A marked change in the binding energy and temperature dependence of the near-nodal scattering rates is observed near the superconducting transition temperature, $T_C$. The temperature slope of the scattering rate measured at low energy shows a discontinuity at ~$T_C$. In the superconducting state, coherent excitations are found with the scattering rates showing a cubic dependence on frequency and temperature. The superconducting gap has a d-wave magnitude with negligible contribution from higher harmonics. Further, the bi-layer splitting has been found to be finite at the nodal point.Comment: 5 pages, 4 figure

ARPES observation of isotropic superconducting gaps in isovalent Ru-substituted Ba(Fe0.75_{0.75}Ru0.25_{0.25})2_2As2_2

We used high-energy resolution angle-resolved photoemission spectroscopy to extract the momentum dependence of the superconducting gap of Ru-substituted Ba(Fe$_{0.75}$Ru$_{0.25}$)$_2$As$_2$ ($T_c = 15$ K). Despite a strong out-of-plane warping of the Fermi surface, the magnitude of the superconducting gap observed experimentally is nearly isotropic and independent of the out-of-plane momentum. More precisely, we respectively observed 5.7 meV and 4.5 meV superconducting gaps on the inner and outer $\Gamma$-centered hole Fermi surface pockets, whereas a 4.8 meV gap is recorded on the M-centered electron Fermi surface pockets. Our results are consistent with the $J_1-J_2$ model with a dominant antiferromagnetic exchange interaction between the next-nearest Fe neighbors.Comment: 5 pages, 4 figure

An efficient and principled method for detecting communities in networks

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based on a principled statistical approach using generative network models. We show how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times. We test the method both on real-world networks and on synthetic benchmarks and find that it gives results competitive with previous methods. We also show that the same approach can be used to extract nonoverlapping community divisions via a relaxation method, and demonstrate that the algorithm is competitively fast and accurate for the nonoverlapping problem.Comment: 14 pages, 5 figures, 1 tabl

Viewing the efficiency of chaos control

This paper aims to cast some new light on controlling chaos using the OGY- and the Zero-Spectral-Radius methods. In deriving those methods we use a generalized procedure differing from the usual ones. This procedure allows us to conveniently treat maps to be controlled bringing the orbit to both various saddles and to sources with both real and complex eigenvalues. We demonstrate the procedure and the subsequent control on a variety of maps. We evaluate the control by examining the basins of attraction of the relevant controlled systems graphically and in some cases analytically

Universal Magnetic Properties of La2−δSrδCuO4La_{2-\delta} Sr_{\delta} Cu O_4 at Intermediate Temperatures

We present the theory of two-dimensional, clean quantum antiferromagnets with a small, positive, zero temperature ($T$) stiffness $\rho_s$, but with the ratio $k_B T / \rho_s$ arbitrary. Universal scaling forms for the uniform susceptibility ($\chi_u$), correlation length($\xi$), and NMR relaxation rate ($1/T_1$) are proposed and computed in a $1/N$ expansion and by Mont\'{e}-Carlo simulations. For large $k_B T/\rho_s$, $\chi_u (T)/T$ and $T\xi(T)$ asymptote to universal values, while $1/T_{1}(T)$ is nearly $T$-independent. We find good quantitative agreement with experiments and some numerical studies on $La_{2-\delta} Sr_{\delta} Cu O_4$.Comment: 14 pages, REVTEX, 1 postscript figure appende

Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit

We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system constructed using a negative conductance series LCR circuit with a diode both numerically and experimentally. The birth of SNAs by these three routes is verified from both experimental and their corresponding numerical data by maximal Lyapunov exponents, and their variance, Poincar\'e maps, Fourier amplitude spectrum, spectral distribution function and finite-time Lyapunov exponents. Although these three routes have been identified numerically in different dynamical systems, the experimental observation of all these mechanisms is reported for the first time to our knowledge and that too in a single second order electronic circuit.Comment: 21 figure