Commuting conformal and dual conformal symmetries in the Regge limit

In this paper we continue our study of the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry of the BFKL equation, analogous to the dual conformal symmetry of N=4$N=4$ super-Yang–Mills. We find that the ordinary and dual SL(2,C)$\mathit{SL}(2,C)$ symmetries do not generate a Yangian, in contrast to the ordinary and dual conformal symmetries in the four-dimensional gauge theory. The algebraic structure is still reminiscent of that of N=4$N=4$ SYM, however, and one can extract a generator from the dual SL(2,C)$\mathit{SL}(2,C)$ close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry, which in its original form is broken by IR effects, is broken in a controlled way, similar to the way the dual conformal symmetry of N=4$N=4$ satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual SL(2,C)$\mathit{SL}(2,C)$ by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to N=4$N=4$ scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.     

Understanding the radiative decays of vector charmonia to light pseudoscalar mesons

We show that the newly measured branching ratios of vector charmonia (J/ψ$J/\psi$, ψ^′${\psi }^{\prime }$ and ψ(3770)$\psi (3770)$) into γP, where P   stands for light pseudoscalar mesons π⁰${\pi }^0$, η  , and η^′${\eta }^{\prime }$, can be well understood in the framework of vector meson dominance (VMD) in association with the ηc–η(η^′)${\eta }_c\text{–}\eta ({\eta }^{\prime })$ mixings due to the axial gluonic anomaly. These two mechanisms behave differently in J/ψ$J/\psi$ and ψ^′→γP${\psi }^{\prime }\to \gamma P$. A coherent understanding of the branching ratio patterns observed in J/ψ(ψ^′)→γP$J/\psi ({\psi }^{\prime })\to \gamma P$ can be achieved by self-consistently including those transition mechanisms at hadronic level. The branching ratios for ψ(3770)→γP$\psi (3770)\to \gamma P$ are predicted to be rather small.     

Hadro-charmonium

We argue that relatively compact charmonium states, J/ψ$J/\psi$, ψ(2S)$\psi (2S)$, χc${\chi }_c$, can very likely be bound inside light hadronic matter, in particular inside higher resonances made from light quarks and/or gluons. The charmonium state in such binding essentially retains its properties, so that the bound system decays into light mesons and the particular charmonium resonance. Thus such bound states of a new type, which we call hadro-charmonium, may explain the properties of some of the recently observed resonant peaks, in particular of Y(4.26)$Y(4.26)$, Y(4.32–4.36)$Y(4.32\text{–}4.36)$, Y(4.66)$Y(4.66)$, and Z(4.43)$Z(4.43)$. We discuss further possible implications of the suggested picture for the observed states and existence of other states of hadro-charmonium and hadro-bottomonium.     

Cross sections for (d–t) neutron interaction with germanium isotopes

The cross sections for (n,x)$(n,x)$ reactions with Ge isotopes were measured at (d–t) neutron energies around 14 MeV with the activation technique using metal discs of natural composition. Calculations of detector efficiency, incident neutron spectrum and correction factors were performed with the Monte Carlo technique (MCNP4C code). Cross sections data are presented for ⁷⁰Ge(n,2n$n,2n$)⁶⁹Ge, ⁷⁴Ge(n,α$n,\alpha$)^71mZn, ⁷⁶Ge(n,2n$n,2n$)^75(m + g)Ge, ⁷⁰Ge(n,p$n,p$)⁷⁰Ga and ⁷²Ge(n,2n$n,2n$)^71gGe reactions. The cross section results for ⁷²Ge(n,2n$n,2n$)^71gGe reaction were reported for the first time. Some other cross sections were obtained with higher precision, including the ⁷⁰Ge(n,p$n,p$)⁷⁰Ga reaction. Theoretical calculations of excitation functions were performed with the TALYS-1.0 code and compared with the experimental cross section values. Data were included in the EXFOR database.     

Effects of oxygen-containing defect complex on the electronic structures and transport properties of single-walled carbon nanotubes

The electronic structures and transport properties of (10,0)$(10,0)$ single-walled carbon nanotube ((10,0)$(10,0)$ (SWNT)) with oxygen-containing defect complex are investigated using density functional theory in combination with nonequilibrium Green?s function method. The complex delocalizes the local states of (10,0)$(10,0)$ SWNT induced by mono- and di-vacancy but strengthens the localization of the states induced by the Stone–Wales defect. As a result, the complex partially restores the transport properties of (10,0)$(10,0)$ SWNT with vacancies, but reduces the transmission of (10,0)$(10,0)$ SWNT with Stone–Wales defect. However, the oxygen-containing defect complex only slightly influences the transmission gap and threshold voltage of the system.     

Spin dynamics of layered triangular antiferromagnets with uniaxial anisotropy

The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both in the ordered phase and in the paramagnetic phase, using the Monte Carlo-molecular dynamics technique. The important quantities calculated are the full dynamic structure function S(q,ω)$S(\mathbf{q},\omega )$, the chiral dynamic structure function _Schi(ω)$S_{\mathrm{chi}}(\omega )$, the static order parameter and some thermodynamic quantities. Our results show the existence of propagating modes corresponding to both S(q,ω)$S(\mathbf{q},\omega )$ and _Schi(ω)$S_{\mathrm{chi}}(\omega )$ in the ordered phase, supporting the recent conjectures. Our results for the static properties show the magnetic ordering in each layer to be of coplanar 3-sublattice type deviating from 120^°${120}^{°}$ structure. In the presence of magnetic trimerization, however, we find the 3-sublattice structure to be weakened along with the tendency towards non-coplanarity of the spins, supporting the experimental conjecture. Our results for the spin dynamics are in qualitative agreement with those from the inelastic neutron scattering experiments performed recently.     

Rational r-matrices,higher rank Lie algebras and integrable proton–neutron BCS models

We study integrable cases of pairing BCS hamiltonians containing several types of fermions. We prove that there exist three classes of such integrable models associated with classical rational r  -matrices and Lie algebras gl(2m)$\mathit{gl}(2m)$, sp(2m)$\mathit{sp}(2m)$ and so(2m)$\mathit{so}(2m)$ correspondingly. We diagonalize the constructed hamiltonians by means of the algebraic Bethe ansatz. In the partial case of two types of fermions (m=2$m=2$) the obtained models may be interpreted as N=Z$N=Z$ proton–neutron integrable models. In particular, in the case of sp(4)$\mathit{sp}(4)$ we recover the famous integrable proton–neutron model of Richardson.     

Exact solution of the alternating XXZ spin chain with generic non-diagonal boundaries

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K$K$-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused R$R$-matrices and K$K$-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T−Q$T-Q$ relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix.     

Multicritical behaviors of the antiferromagnetic Blume–Emery–Griffiths model with the external magnetic field on the Bethe lattice

The antiferromagnetic Blume–Emery–Griffiths model in an external magnetic field is studied by using the exact recursion relations on the Bethe lattice for arbitrary values of biquadratic and for negative values of bilinear interactions. We have studied the thermal variations of two-sublattice magnetizations belonging to spin-1 BEG model to obtain the phase diagrams on the (H/|J|,kT/|J|)$(H/|J|,\mathit{kT}/|J|)$ plane. As a result, we have found that the system presents second- and first-order phase transitions, therefore, tricritical points for appropriate values of K/|J|$K/\left|J\right|$, D/|J|$D/\left|J\right|$ and q  . We have also found that the second-order phase transition lines exhibit reentrant phenomena in temperature, besides it also shows reentrant phenomena for the first-order phase lines in external magnetic field for q=4$q=4$ and 6.     

Schizophrenic active neutrinos and exotic sterile neutrinos

We implement a schizophrenic scenario for the active neutrinos in a model in which there are also exotic right-handed neutrinos making a model with a local U_(1)B−L$U{(1)}_{B-L}$ anomaly free. Two of right-handed neutrinos carry B−L=−4$B-L=-4$ while the third one carries B−L=5$B-L=5$. Unlike the non-exotic version of the model, in which all right-handed neutrinos carry the same B−L=−1$B-L=-1$ charge, in this case the neutrinos have their own scalar sector and no hierarchy in the Yukawa coupling in the Dirac mass term is necessary.     

Magnetic properties of the bond and crystal field dilution spin-3/2 Blume–Capel model in an external magnetic field

Magnetic properties of the bond and crystal field dilution spin-3/2 Blume–Capel model in an external magnetic field (h)$(h)$ on simple cubic lattice are studied by using the effective field theory. In the m−T$m-T$ plane, the degeneracy of the magnetization (m)$(m)$ is affected by the concentration of bond or crystal field dilution at low temperature (T)$(T)$. The magnetization curves can appear to fluctuate in certain regions of negative crystal field. In the m−h$m-h$ plane, the initial magnetization curve has an irregular behavior due to the introduction of bond dilution. The crystal field dilution has the influence on the process of magnetic domain displacement. In the χ−h$\chi -h$ plane, there exists one susceptibility (χ)$(\chi )$ shoulder and one step for different negative crystal field. The susceptibility curve takes on the feature of multi-peaks distribution under bond and crystal field dilution conditions.     

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

Some properties of generalized Fisher information in the context of nonextensive thermostatistics

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q$q$-Gaussian distributions and the q$q$-entropies. The minimum of the generalized Fisher information among distributions with a fixed moment, or with a fixed q$q$-entropy is attained, in both cases, by a generalized q$q$-Gaussian distribution. This complements the fact that the q$q$-Gaussians maximize the q$q$-entropies subject to a moment constraint, and yields new variational characterizations of the generalizedq$q$-Gaussians. We show that the generalized Fisher information naturally pop up in the expression of the time derivative of the q$q$-entropies, for distributions satisfying a certain nonlinear heat equation. This result includes as a particular case the classical de Bruijn identity. Then we study further properties of the generalized Fisher information and of their minimization. We show that, though non additive, the generalized Fisher information of a combined system is upper bounded. In the case of mixing, we show that the generalized Fisher information is convex for q≥1$q\ge 1$. Finally, we show that the minimization of the generalized Fisher information subject to moment constraints satisfies a Legendre structure analog to the Legendre structure of thermodynamics.