If Gauss–Bonnet interaction plays the role of dark energy

A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞$q\to \infty$ and infinite equation of state parameter, w→∞$w\to \infty$. During evolution it subsequently passes through the stiff fluid era, q=2$q=2$, w=1$w=1$, the radiation dominated era, q=1$q=1$, w=1/3$w=1/3$ and the matter dominated era, q=1/2$q=1/2$, w=0$w=0$. Finally, deceleration halts, q=0$q=0$, w=−1/3$w=-1/3$, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1$q\to -1$, w→−1$w\to -1$. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1)$(w<-1)$ the model.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

Transition to chaos in discrete nonlinear Schrödinger equation with long-range interaction

Discrete nonlinear Schrödinger (DNLS) equation describes a chain of oscillators with nearest-neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to 1/l^1+α$1/l^{1+\alpha }$ with fractional α<2$\alpha <2$ and l   as a distance between oscillators. This model is called α$\alpha$DNLS. It exhibits competition between the nonlinearity and a level of correlation between interacting far-distanced oscillators, that is defined by the value of α$\alpha$. We consider transition to chaos in this system as a function of α$\alpha$ and nonlinearity. It is shown that decreasing of α$\alpha$ with respect to nonlinearity stabilize the system. Connection of the model to the fractional generalization of the NLS (called FNLS) in the long-wave approximation is also discussed and some of the results obtained for α$\alpha$DNLS can be correspondingly extended to the FNLS.     

Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation

Tsallis maximum entropy distributions provide useful tools for the study of a wide range of scenarios in mathematics, physics, and other fields. Here we apply a Tsallis maximum entropy ansatz, the q$q$-Gaussian, to obtain time dependent wave-packet solutions to a nonlinear Schrödinger equation recently advanced by Nobre, Rego-Monteiro and Tsallis (NRT) [F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106 (2011) 140601]. The NRT nonlinear equation admits plane wave-like solutions (q$q$-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the q$q$-generalized thermostatistical formalism, is characterized by a parameter q$q$ and in the limit q→1$q\to 1$ reduces to the standard, linear Schrödinger equation. The q$q$-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known q$q$-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the q→1$q\to 1$ limit the q$q$-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrödinger equation. In the present work we also show that there are other families of nonlinear Schrödinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations.     

Higher dimensional Yang–Mills black holes in third order Lovelock gravity

By employing the higher (N>5$N>5$)-dimensional version of the Wu–Yang ansatz we obtain magnetically charged new black hole solutions in the Einstein–Yang–Mills–Lovelock (EYML) theory with second (α₂${\alpha }_2$) and third (α₃${\alpha }_3$) order parameters. These parameters, where α₂${\alpha }_2$ is also known as the Gauss–Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically (r→∞$r\to \infty$), these parameters contribute to an effective cosmological constant—without cosmological constant—so that the solution behaves de-Sitter (anti de-Sitter) like.     

Vortices and Jacobian varieties

We investigate the geometry of the moduli space of N$N$ vortices on line bundles over a closed Riemann surface Σ$\Sigma$ of genus g>1$g>1$, in the little explored situation where 1≤N<g$1\le N<g$. In the regime where the area of the surface is just large enough to accommodate N$N$ vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ$\Sigma$. For N=1$N=1$, we show that the metric on the moduli space converges to a natural Bergman metric on Σ$\Sigma$. When N>1$N>1$, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ$\Sigma$ at degree N$N$. We describe consequences of this phenomenon from the point of view of multivortex dynamics.     

Intertwining operators for Sklyanin algebra and elliptic hypergeometric series

Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ?$?$ and −?−1$-?-1$ are constructed using the technique of intertwining vectors for elliptic L$L$-operator. They are expressed in terms of elliptic hypergeometric series with operator argument. The intertwining operators obtained (W$W$-operators) serve as building blocks for the elliptic R$R$-matrix which intertwines tensor product of two L$L$-operators taken in infinite-dimensional representations of the Sklyanin algebra with arbitrary spin. The Yang–Baxter equation for this R$R$-matrix follows from simpler equations of the star–triangle type for the W$W$-operators. A natural graphic representation of the objects and equations involved in the construction is used.     

Bertrand curves in the three-dimensional sphere

A curve α$\alpha$ immersed in the three-dimensional sphere S³${\mathbb{S}}^3$ is said to be a Bertrand curve if there exists another curve β$\beta$ and a one-to-one correspondence between α$\alpha$ and β$\beta$ such that both curves have common principal normal geodesics at corresponding points. The curves α$\alpha$ and β$\beta$ are said to be a pair of Bertrand curves in S³${\mathbb{S}}^3$. One of our main results is a sort of theorem for Bertrand curves in S³${\mathbb{S}}^3$ which formally agrees with the classical one: “Bertrand curves in S³${\mathbb{S}}^3$ correspond to curves for which there exist two constants λ≠0$\lambda \ne 0$ and μ$\mu$ such that λκ+μτ=1$\lambda \kappa +\mu \tau =1$”, where κ$\kappa$ and τ$\tau$ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S³${\mathbb{S}}^3$ as the only twisted curves in S³${\mathbb{S}}^3$ having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S³${\mathbb{S}}^3$ and (1,3)-Bertrand curves in R⁴${\mathbb{R}}^4$.     

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0$T>0$ transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0$T=0$ 1D insulator the charge stiffness D(T)$D\left(T\right)$ vanishes for T>0$T>0$ and finite values of the on-site repulsion U$U$ in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T$T$ and U>0$U>0$ it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0$U=0$ and vanishes for U>0$U>0$ is found to result from a general transition from a conductor to an insulator or resistor occurring at U=U_c=0$U=U_c=0$ for all finite temperatures T>0$T>0$. (At T=0$T=0$ such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η$\eta$-spin SU(2)$SU\left(2\right)$ symmetry with the hidden U(1)$U\left(1\right)$ symmetry beyond SO(4)$SO\left(4\right)$ is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.     

On the length of stabilograms: A study performed with detrended fluctuation analysis

The effects associated to the length of stabilograms, a measure of the time dependence of the center of pressure of an individual standing up, are analyzed. The fractal characteristics of 27 signals with a length of 2¹⁴$2^{14}$ points, each one corresponding to a different individual, are studied by using the Detrended Fluctuation Analysis technique. The properties of the complete signals are compared to those of various subsignals extracted from them. No differences have been found between the characteristic exponents found for x$x$ and y$y$ signals. The relation between the exponents of the position and velocity signals is accomplished by the 2¹⁴$2^{14}$ point signals, while subsignals with up to 2¹²$2^{12}$ points do not verify it. Using artificial signals with 2¹⁴$2^{14}$ points, generated for α$\alpha$ values given, it has been demonstrated that the exponents obtained from these signals take values larger than expected for α<0.3$\alpha <0.3$, while the exponents of the accumulated series are smaller than expected for 0.7<α$0.7<\alpha$. For CoP trajectories this indicates that DFA-1 provides feasible exponents for the short τ$\tau$-end region of the velocity signal and the large τ$\tau$-end region of the accumulated (position) one. It has been found that the characteristic exponents vary along the series. A slightly larger persistence is found in the last part of the signal for large frequencies in the x$x$ direction.     

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.     

Suppression of flavor symmetry breaking in B decay sum rules

While flavor symmetries are useful for studying hadronic B   decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B→Kπ$B\to K\pi$ decays, where isospin breaking is shown to be negligible. (2) An SU(3)$\mathrm{SU}(3)$ sum rule for pairs of B→Kπ$B\to K\pi$ and B→Kη₈$B\to K{\eta }_8$, generalized to pairs of B→Kπ$B\to K\pi$, B→Kη$B\to K\eta$ and B→Kη^′$B\to K{\eta }^{\prime }$.     

Complex dynamics in the distribution of players’ scoring performance in Rugby Union world cups

The evolution of the scoring performance of Rugby Union players is investigated over the seven rugby world cups (RWC) that took place from 1987 to 2011, and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995. The distribution of the points scored by individual players, _Ps$P_s$, ranked in order of performance were well described by the simplified canonical law _Ps∝(r+?)^−α$P_s\propto {(r+?)}^{-\alpha }$, where r$r$ is the rank, and ?$?$ and α$\alpha$ are the parameters of the distribution. The parameter α$\alpha$ did not significantly change from 1987 to 2007 (α=0.92±0.03)$(\alpha =0.92\pm 0.03)$, indicating a negligible effect of professionalism on players’ scoring performance. In contrast, the parameter ?$?$ significantly increased from ?=1.32$?=1.32$ for 1987 RWC, ?=2.30$?=2.30$ for 1999 to 2003 RWC and ?=5.60$?=5.60$ for 2007 RWC, suggesting a progressive decrease in the relative performance of the best players. Finally, the sharp decreases observed in both α(α=0.38)$\alpha (\alpha =0.38)$ and ?(?=0.70)$?(?=0.70)$ in the 2011 RWC indicate a more even distribution of the performance of individuals among scorers, compared to the more heterogeneous distributions observed from 1987 to 2007, and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players. Note that neither α$\alpha$ nor ?$?$ significantly correlate with traditional performance indicators such as the number of points scored by the best players, the number of games played by the best players, the number of points scored by the team of the best players or the total number of points scored over each RWC. This indicates that the dynamics of the scoring performance of Rugby Union players is influenced by hidden processes hitherto inaccessible through standard performance metrics; this suggests that players’ scoring performance is connected to ubiquitous phenomena such as anomalous diffusion.     

Pion radiative weak decays in nonlocal chiral quark models

We analyze the radiative pion decay π⁺→e⁺νeγ${\pi }^{+}\to e^{+}{\nu }_e\gamma$ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV$F_V$ and FA$F_A$ at q²=0$q^2=0$ — where q²$q^2$ is the e⁺νe$e^{+}{\nu }_e$ squared invariant mass — and the slope a   of FV(q²)$F_V(q^2)$ at q²→0$q^2\to 0$. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV$F_V$ and a   with the form factor in π⁰→γ^?γ${\pi }^0\to {\gamma }^{?}\gamma$ decays are discussed.     

Relativistic kinetic theory and non-gaussian statistical

The nonextensive statistical mechanics is extended in the special relativity context through a generalization of H$H$-theorem. We show that the Tsallis framework is compatible with the second law of the thermodynamics when the nonadditive effects are consistently introduced on the collisional term of the Boltzmann equation. The proof of the H$H$-theorem follows from using of q$q$-algebra in the generalization of the molecular chaos hypothesis (Stosszahlansatz). A thermodynamic consistency is possible whether the entropic parameter belongs to interval q∈[0,2]$q\in [0,2]$.     

Properties of CFTs dual to charged BTZ black hole

We study properties of strongly coupled CFT's with non-zero background electric charge in 1+1$1+1$ dimensions by studying the dual gravity theory—which is a charged BTZ black hole. Correlators of operators dual to scalars, gauge fields and fermions are studied at both T=0$T=0$ and T≠0$T\ne 0$. In the T=0$T=0$ case we are also able to compare with analytical results based on AdS₂${\mathit{AdS}}_2$ and find reasonable agreement. In particular the correlation between log periodicity and the presence of finite spectral density of gapless modes is seen. The real part of the conductivity (given by the current–current correlator) also vanishes as ω→0$\omega \to 0$ as expected. The fermion Green's function shows quasiparticle peaks with approximately linear dispersion but the detailed structure is neither Fermi liquid nor Luttinger liquid and bears some similarity to a “Fermi–Luttinger” liquid. This is expected since there is a background charge and the theory is not Lorentz or scale invariant. A boundary action that produces the observed non-Luttinger liquid like behavior (k  -independent non-analyticity at ω=0$\omega =0$) in the Green's function is discussed.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Electronic and magnetic properties of hydrogenated graphene nanoflakes

We investigated the energetic stability, electronic, and magnetic properties of hydrogenated graphene nanoflakes (GNFs) by using density-functional theory (DFT). Hydrogenated GNFs were found to be the stable heterojunction structures. As the increase of H coverage, a transition of a small-gap semiconductor to wide-gap semiconductor occurs, accompanied with a nonmagnetic (with the coverage χ=0$\chi =0$) → magnetic (with the coverage 0<χ<1$0<\chi <1$) → nonmagnetic (with the coverage χ=1$\chi =1$) transfer for hexagonal nanoflakes and magnetic (with the coverage 0?χ<1$0?\chi <1$) → nonmagnetic (with the coverage χ=1$\chi =1$) transfer for triangular nanoflakes. The efficacious tune of band gaps and the magnetic moments on these nanoflakes by hydrogenation offers an effectual avenue for the applications of C-based nanomagnets.     

Generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy

We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order q$q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for q=2$q=2$ or 3$3$. This generalization encapsulates the multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-q$q$ entropy for 1≤q≤2$1\le q\le 2$ or 3≤q≤4$3\le q\le 4$, which also contains the multi-qubit polygamy inequality as a special case.