Coexistence of charge density wave and spin-Peierls orders in quarter-filled quasi-one dimensional correlated electron systems

Charge and spin-Peierls instabilities in quarter-filled (n=1/2) compounds consisting of coupled ladders and/or zig-zag chains are investigated. Hubbard and t-J models including local Holstein and/or Peierls couplings to the lattice are studied by numerical techniques. Next nearest neighbor hopping and magnetic exchange, and short-range Coulomb interactions are also considered. We show that, generically, these systems undergo instabilities towards the formation of Charge Density Waves, Bond Order Waves and (generalized) spin-Peierls modulated structures. Moderate electron-electron and electron-lattice couplings can lead to a coexistence of these three types of orders. In the ladder, a zig-zag pattern is stabilized by the Holstein coupling and the nearest-neighbor Coulomb repulsion. In the case of an isolated chain, bond-centered and site-centered 2k_F and 4k_F modulations are induced by the local Holstein coupling. In addition, we show that, in contrast to the ladders, a small charge ordering in the chains, strongly enhances the spin-Peierls instability. Our results are applied to the NaV_2O_5 compound (trellis lattice) and various phases with coexisting charge disproportionation and spin-Peierls order are proposed and discussed in the context of recent experiments. The role of the long-range Coulomb potential is also outlined.Comment: 10 pages, Revtex, 10 encapsulated figure

CFD-based scale-up of hydrodynamics and mixing in bubble columns

Unsteady and three-dimensional Eulerian–Eulerian CFD simulations of bubble column reactors under operating conditions of industrial interest are discussed in this work. The flow pattern in this equipment depends strongly on the interactions between the gas and liquid phases, mainly via the drag force. In this work, a correlation for the drag force coefficient is tested and improved to consider the so-called swarm effect that modifies the drag force at high gas volume fractions. The improved swarm factor proposed in this work is the adjustment of the swarm factor proposed by Simonnet et al. (2008). This new swarm factor is suitable for very high gas volume fractions without generating stability problems, which were encountered with the original formulation. It delivers an accurate prediction of gas volume fraction and liquid velocity in a wide range of tested operating conditions. Results are validated by comparison with experimental data on bubble column reactors at different scales and for several operating conditions. Hydrodynamics is well predicted for every operating condition at different scales. Several turbulence models are tested. Finally, the contribution of Bubble Induced Turbulence (BIT), as proposed by Alméras et al. (2015), on mixing is evaluated via an analysis of the mixing time

High Energy Hadron-Nucleus Cross Sections and Their Extrapolation to Cosmic Ray Energies

Old models of the scattering of composite systems based on the Glauber model of multiple diffraction are applied to hadron-nucleus scattering. We obtain an excellent fit with only two free parameters to the highest energy hadron-nucleus data available. Because of the quality of the fit and the simplicity of the model it is argued that it should continue to be reliable up to the highest cosmic ray energies. Logarithmic extrapolations of proton-proton and proton-antiproton data are used to calculate the proton-air cross sections at very high energy. Finally, it is observed that if the exponential behavior of the proton-antiproton diffraction peak continues into the few TeV energy range it will violate partial wave unitarity. We propose a simple modification that will guarantee unitarity throughout the cosmic ray energy region.Comment: 8 pages, 9 postscript figures. This manuscript replaces a partial manuscript incorrectly submitte

What do experimental data "say" about growth of hadronic total cross-section?

We reanalyse $\bar p p$ and $pp$ high energy data of the elastic scattering above $\sqrt{s}=5$ GeV on the total cross-section $\sigma_{tot}$ and on the forward $\rho$-ratio for various models of Pomeron, utilizing two methods. The first one is based on analytic amplitudes, the other one relies on assumptions for $\sigma_{tot}$ and on dispersion relation for $\rho$. We argue that it is not possible, from fitting only existing data for forward scattering, to select a definite asymptotic growth with the energy of $\sigma_{tot}$. We find equivalent fits to the data together with a logarithmic Pomeron giving a behavior $\sigma_{tot} \propto \ln ^\gamma s$, $\gamma\in [0.5,2.20]$ and with a supercritical Pomeron giving a behavior $\sigma_{tot} \propto s^\epsilon$, $\epsilon\in [0.01,0.10]$.Comment: LaTeX, 18 pages, 5 eps figures included, to be published in Il Nuovo Ciment

Elastic pp Scattering at LHC Energies

We consider the first LHC data for elastic pp scattering in the framework of Regge theory with multiple Pomeron exchanges. The simplest eikonal approach allows one to describe differential elastic cross sections at LHC, as well as pp and $\bar{p}p$ scattering at lower collider energies, on a reasonable level.Comment: 11 pages, 5 figures, and 1 tabl

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a non-zero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, which the model maps to in the anti-adiabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.Comment: RevTeX, 5 pages, 3 eps figures included using epsf. Improved theories in adiabatic and non-adiabatic regimes give better agreement with DMRG. This version accepted in Physical Review Letter

First Measurement of Proton-Proton Elastic Scattering at RHIC

The first result of the pp2pp experiment at RHIC on elastic scattering of polarized protons at sqrt{s} = 200 GeV is reported here. The exponential slope parameter b of the diffractive peak of the elastic cross section in the t range 0.010 <= |t| <= 0.019 (GeV/c)^2 was measured to be b = 16.3 +- 1.6 (stat.) +- 0.9 (syst.) (GeV/c)^{-2} .Comment: 9 pages 5 figure

Antiferromagnetism in doped anisotropic two-dimensional spin-Peierls systems

We study the formation of antiferromagnetic correlations induced by impurity doping in anisotropic two-dimensional spin-Peierls systems. Using a mean-field approximation to deal with the inter-chain magnetic coupling, the intra-chain correlations are treated exactly by numerical techniques. The magnetic coupling between impurities is computed for both adiabatic and dynamical lattices and is shown to have an alternating sign as a function of the impurity-impurity distance, hence suppressing magnetic frustration. An effective model based on our numerical results supports the coexistence of antiferromagnetism and dimerization in this system.Comment: 5 pages, 4 figures; final version to appear in Phys. Rev.

Excitation Spectra of Structurally Dimerized and Spin-Peierls Chains in a Magnetic Field

The dynamical spin structure factor and the Raman response are calculated for structurally dimerized and spin-Peierls chains in a magnetic field, using exact diagonalization techniques. In both cases there is a spin liquid phase composed of interacting singlet dimers at small fields h < h_c1, an incommensurate regime (h_c1 < h < h_c2) in which the modulation of the triplet excitation spectra adapts to the applied field, and a fully spin polarized phase above an upper critical field h_c2. For structurally dimerized chains, the spin gap closes in the incommensurate phase, whereas spin-Peierls chains remain gapped. In the spin liquid regimes, the dominant feature of the triplet spectra is a one-magnon bound state, separated from a continuum of states at higher energies. There are also indications of a singlet bound state above the one-magnon triplet.Comment: RevTex, 10 pages with 8 eps figure