Avoiding the big-rip jeopardy in a quintom dark energy model with higher derivatives

In the framework of a single scalar field quintom model with higher derivative, we construct in this Letter a dark energy model of which the equation of state (EOS) w   crosses over the cosmological constant boundary. Interestingly during the evolution of the universe w<−1$w<-1$ happens just for a period of time with a distinguished feature that w   starts with a value above −1, transits into w<−1$w<-1$, then comes back to w>−1$w>-1$. This avoids the big-rip jeopardy induced by w<−1$w<-1$.     

On generalized Leibniz triangles and q-Gaussians

Generalized Leibniz triangles have been used in nonextensive statistical mechanics as theoretical models that yield q  -Gaussians (q<1$q<1$) as attractors. We study such triangles from a probability point of view. Our results show that one can get any distribution on [0,1]$[0,1]$ (or any distribution that has a compact support, after a linear transform) from such triangles, including q  -Gaussians with q<1$q<1$. Next we propose conceptual models that are triangular arrays of row-wise exchangeable random variables and yield q  -Gaussians for q<1$q<1$ and q?1$q?1$ as attractors, via laws of large numbers and central limit theorems, respectively.     

On phantom thermodynamics with negative temperature

We discuss the thermodynamic properties of the Friedmann–Robertson–Walker universe with dark energy fluids labelled by ω=p/ρ<−1/3$\omega =p/\rho <-1/3$. Using the integrability condition, we show that the phantom phase of ω<−1$\omega <-1$ can still be thermodynamically allowed even when the temperature takes on negative values because in that case, there exists at least a condition of keeping physical values for p and ρ.     

Evaluation of charged current neutrino–nucleon interaction differential cross section

The charged current neutrino–nucleon interaction differential cross section are evaluated in the kinematical range 30<Eν<300 GeV$30<E_{\nu }<300\text{GeV}$, 0.1<x<0.8$0.1<x<0.8$ and 0<y<1$0<y<1$ using QCD inspired Thermodynamic Bag Model (TBM). We also discuss the x   and Q²$Q^2$ dependence of nucleon structure functions F₂(x,Q²)$F_2(x,Q^2)$ and xF₃(x,Q²)$x{F}_3(x,Q^2)$ estimated with statistical approach. The contribution of strange quark distribution function to the cross section is explored and the results obtained have been compared with relevant data from NuTeV and CHORUS experiments.     

Atomic parity violation in the economical 3–3–1 model

The deviation δQW$\delta Q_{\mathrm{W}}$ of the weak charge from its standard model prediction due to the mixing of the W boson with the charged bilepton Y as well as of the Z   boson with the neutral Z^′$Z^{\prime }$ and the real part of the non-Hermitian neutral bilepton X   in the economical 3–3–1 model is established. Additional contributions to the usual δQW$\delta Q_{\mathrm{W}}$ expression in the extra U(1)$\mathrm{U}(1)$ models and the left–right models are obtained. Our calculations are quite different from previous analyzes in this kind of the 3–3–1 models and give the limit on mass of the Z^′$Z^{\prime }$ boson, the Z–Z^′$Z\text{–}{Z}^{\prime }$ and W–Y$W\text{–}Y$ mixing angles with the more appropriate values: MZ^′>564 GeV$M_{Z^{\prime }}>564\text{GeV}$, −0.018<sinφ<0$-0.018<\sin \phi <0$ and |sinθ|<0.043$|\sin \theta |<0.043$.     

The Ising spin glass in finite dimensions: A perturbative study of the free energy

Replica field theory is used to study the n  -dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian, independently of the special structure of the order parameter. The free energy difference between the replica symmetric and (infinite level) replica symmetry broken phases is studied in details: the line n(T)$n(T)$ where it is zero coincides with the Almeida–Thouless line for d>8$d>8$. The dimensional domain 6<d<8$6<d<8$ is more complicated, and several scenarios are possible.     

Flame wrinkles from the Zhdanov–Trubnikov equation

The Zhdanov–Trubnikov equation describing wrinkled premixed flames is studied, using pole decompositions as starting points. Its one-parameter (−1?c?+1$-1?c?+1$) nonlinearity generalises the Michelson–Sivashinsky equation (c=0$c=0$) to a stronger Darrieus–Landau instability. The shapes of steady flame crests (or periodic cells) are deduced from Laguerre (or Jacobi) polynomials when c≈−1$c\approx -1$, which numerical resolutions confirm. Large wrinkles are analysed via   a pole density: adapting results of Dunkl relates their shapes to the generating function of Meixner–Pollaczek polynomials, which numerical results confirm for −1<c?0$-1<c?0$ (reduced stabilisation). Although locally ill-behaved if c>0$c>0$ (over-stabilisation) such analytical solutions can yield accurate flame shapes for 0?c?0.6$0?c?0.6$. Open problems are invoked.     

Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity

In this Letter we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, f(^□−1R)$f({\square }^{\mathrm{-1}}R)$. Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, f(^□−1R)∼exp(α^□−1R)$f({\square }^{\mathrm{-1}}R)\sim \exp (\alpha {\square }^{\mathrm{-1}}R)$. The effective EoS parameter is given by, weff=(α−1)/(3α−1)$w_{\mathrm{eff}}=(\alpha -1)/(3\alpha -1)$ and the stability of the solutions is guaranteed provided that 1/3<α<2/3$1/3<\alpha <2/3$. For 1/3<α<1/2$1/3<\alpha <1/2$ and 1/2<α<2/3$1/2<\alpha <2/3$, the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to α=1/2$\alpha =1/2$. For a wide range of initial conditions, the system mimics dust like behavior before reaching the stable fixed point. The late time phantom phase is achieved without involving negative kinetic energy fields. A brief discussion on the entropy of de Sitter space in non-local model is included.     

Conformal two-boundary loop model on the annulus

We study the two-boundary extension of a loop model—corresponding to the dense phase of the O(n)$\mathrm{O}(n)$ model, or to the Q=n²$Q=n^2$ state Potts model—in the critical regime −2<n?2$-2<n?2$. This model is defined on an annulus of aspect ratio τ. Loops touching the left, right, or both rims of the annulus are distinguished by arbitrary (real) weights which moreover depend on whether they wrap the periodic direction. Any value of these weights corresponds to a conformally invariant boundary condition. We obtain the exact seven-parameter partition function in the continuum limit, as a function of τ, by a combination of algebraic and field theoretical arguments. As a specific application we derive some new crossing formulae for percolation clusters.     

Envelope excitations in nonextensive plasmas with warm-ions

In this work we study the modulational instability of plasmas with q-entropy electrons and warm ions, using the hydrodynamic approach. A nonlinear Schrödinger equation (NLSE), governing the dynamics of envelope excitations in the plasma, is obtained by using the conventional multiscales method. Investigation of the modulational instability of the nonextensive plasmas reveals that the criteria for propagation of bright/dark envelope excitations in such plasmas are significantly affected by value of the nonextensivity parameter, q, and the fractional ion-temperature, σ  . In particular, by setting σ≠0$\sigma \ne 0$, a new region of modulational instability appears, indicating that the study of modulation instability in the cold-ion limit (σ=0$\sigma =0$) is completely different from that of warm ions. The study of the growth-rate and rogue-wave amplitudes in terms of different plasma parameters, reveals that their magnitude is of different scales for two ranges of the nonextensivity parameters, q>1$q>1$ and q<1$q<1$.     

Even-dimensional topological gravity from Chern–Simons gravity

It is shown that the topological action for gravity in 2n  -dimensions can be obtained from the (2n+1)$(2n+1)$-dimensional Chern–Simons gravity genuinely invariant under the Poincaré group. The 2n  -dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)$(2n+1)$-dimensional Chern–Simons gravity theory with suitable boundary conditions.     

Wormholes with a barotropic equation of state admitting a one-parameter group of conformal motions

The theoretical construction of a traversable wormhole proposed by Morris and Thorne maintains complete control over the geometry by assigning both the shape and redshift functions, thereby leaving open the determination of the stress–energy tensor. This paper examines the effect of introducing the linear barotropic equation of state p_r=ωρ$p_r=\omega \rho$ on the theoretical construction. If either the energy density or the closely related shape function is known, then the Einstein field equations do not ordinarily yield a finite redshift function. If, however, the wormhole admits a one-parameter group of conformal motions, then both the redshift and shape functions exist provided that −3<ω<−1$-3<\omega <-1$. In a cosmological setting, the equation of state p=ωρ$p=\omega \rho$, ω<−1$\omega <-1$, is associated with phantom dark energy, which is known to support traversable wormholes. The restriction −3<ω<−1$-3<\omega <-1$ that arises in the present wormhole setting can be attributed to the assumption of conformal symmetry.     

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.     

Constraining cosmological parameters with observational data including weak lensing effects

In this Letter, we study the cosmological implications of the 100 square degree Weak Lensing survey (the CFHTLS-Wide, RCS, VIRMOS-DESCART and GaBoDS surveys). We combine these weak lensing data with the cosmic microwave background (CMB) measurements from the WMAP5, BOOMERanG, CBI, VSA, ACBAR, the SDSS LRG matter power spectrum and the Type Ia Supernoave (SNIa) data with the “Union” compilation (307 sample), using the Markov Chain Monte Carlo method to determine the cosmological parameters, such as the equation-of-state (EoS) of dark energy w  , the density fluctuation amplitude σ₈${\sigma }_8$, the total neutrino mass ∑mν$\sum m_{\nu }$ and the parameters associated with the power spectrum of the primordial fluctuations. Our results show that the ΛCDM model remains a good fit to all of these data. In a flat universe, we obtain a tight limit on the constant EoS of dark energy, w=−0.97±0.041$w=-0.97\pm 0.041$ (1σ  ). For the dynamical dark energy model with time evolving EoS parameterized as wde(a)=w₀+wa(1−a)$w_{\mathrm{de}}(a)=w_0+w_a(1-a)$, we find that the best-fit values are w₀=−1.064$w_0=-1.064$ and wa=0.375$w_a=0.375$, implying the mildly preference of Quintom model whose EoS gets across the cosmological constant boundary during evolution. Regarding the total neutrino mass limit, we obtain the upper limit, ∑mν<0.471 eV$\sum m_{\nu }<0.471\text{eV}$ (95% C.L.) within the framework of the flat ΛCDM model. Due to the obvious degeneracies between the neutrino mass and the EoS of dark energy model, this upper limit will be relaxed by a factor of 2 in the framework of dynamical dark energy models. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, within the ΛCDM model, we find that the upper limit on the ratio of the tensor to scalar is r<0.35$r<0.35$ (95% C.L.) and the inflationary models with the slope ns?1$n_s?1$ are excluded at more than 2σ   confidence level. In this Letter we pay particular attention to the contribution from the weak lensing data and find that the current weak lensing data do improve the constraints on matter density Ωm${\Omega }_m$, σ₈${\sigma }_8$, ∑mν$\sum m_{\nu }$, and the EoS of dark energy.     

Critical dynamics in systems controlled by fractional kinetic equations

The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0<α<1$0<\alpha <1$, fractional Laplacian of the order σ$\sigma$, and Gaussian noise correlator. The case of non-linearity φ^m${\phi }^m$ with odd m≥3$m\ge 3$ is considered. It is proved that the model is multiplicatively renormalizable. Propagators were found in the momentum and coordinate representation, expressed in terms of Fox’s H functions.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

Singularities of Berry connections inhibit the accuracy of the adiabatic approximation

Adiabatic approximation for quantum evolution is investigated addressing its dependence on the Berry connections that are functions of a slowly-varying parameter R  . When the Berry connections have singularities of type 1/Rσ$1/R^{\sigma }$ with σ<1$\sigma <1$, the adiabatic fidelity converges to unit according to a power-law; When the singularity index σ becomes larger than one, adiabatic approximation breaks down. Two-level models are used to substantiate our theory.     

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X  . They generate relevant terms proportional to X²$X^2$ in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U=Uc$U=U_c$ and a spin transition at U=Us>Uc$U=U_s>U_c$. For U<Uc$U<U_c$ singlet superconducting correlations dominate, while for U>Us$U>U_s$, the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values Uc<U<Us$U_c<U<U_s$, the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X=0$X=0$. We obtain that the charge transition remains at Uc=0$U_c=0$ for X≠0$X\ne 0$. Solving the RG equations for the spin sector, we provide an analytical expression for Us(X)$U_s(X)$. The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X<t/2$X<t/2$ where t is the hopping.