PACS 74.20.-z -Theories and models of superconducting state PACS 75.30.Fv -Spin-density waves PACS 71.45.Lr -Charge-density-wave systems Abstract. -Recent discovery of high Tc superconductivity in Fe-based compounds may have opened a new pathway to the room temperature superconductivity. The new materials feature FeAs layers instead of the signature CuO2 planes of much-studied cuprates. A model Hamiltonian describing FeAs layers is introduced, highlighting the crucial role of puckering of As atoms in promoting d-electron itinerancy and warding off large local-moment magnetism of Fe ions, the main enemy of superconductivity. Quantum many-particle effects in charge, spin and multiband channels are explored and a nesting-induced spin density-wave order is found in the parent compund. We argue that this largely itinerant antiferromagnetism and high Tc itself are essentially tied to the multiband nature of the Fermi surface.Recently, a surprising new path to room-temperature superconductivity might have been discovered. The quaternary compound LaOFeP was already known to become superconducting below 7K [1], when its doped sibling LaO 1−x F x FeAs (x > 0.1) turned out to have unexpectedly high T c of 26K [2]. Even higher T c 's were found by replacing La with other rare-earths (RE), reaching the current record of T c = 55K [3]. These are the first non-cuprate superconductors exhibiting such high T c 's.The surprise here is that the most prominent characteristic of iron is its natural magnetism. By conventional wisdom, the high T c superconductivity in RE-OFeAs compounds is unexpected, all the more so since the superconductivity apparently resides in FeAs layers. Following standard ionic accounting, rare-earths are 3 + , giving away three electrons, while As and O are 3 − and 2 − , respectively. One then expects Fe to be in its 2 + configuration, two of its 4s electrons given away to fill As and O p-orbitals, with assistance from a single rare-earth atom. The remaining six d-electrons fill atomic orbitals of Fe in the overall tetragonal As/O environment of Fig. 1; the lower three t 2g orbitals should be filled while the upper two e g orbitals should be empty. However, the Coulomb interactions intervene via the Hund's rule: the total energy can be reduced by making the spin part of the atomic wavefunction most symmetric and consequently the orbital part of it as antisymmetric as possible, reducing thereby the cost of Coulomb repulsion. The simplest realization of this is to occupy a low t 2g orbital with one spin-up and one spin-down electron while storing the remaining four electrons into the spin-up states. The result is a total spin S = 2 of Fe ++ , with the associated local magnetic moment and likely magnetism in the parent compounds. This is the situation similar to manganese, the Fe's nearest relative, whose five d-electrons feel the full brunt of the Hund's rule and typically line up into a large spin state, and very different from copper, where dorbitals are either fully occupied or contain only a single d-hole,...

We construct the symmetry adapted low energy effective Hamiltonian for the electronic states in the vicinity of the Fermi level in iron based superconductors. We use Luttinger's method of invariants, expanding about Γ and M points in the Brillouin zone corresponding to two iron unit cell, and then matching the coefficients of the expansion to the 5-and 8-band models. We then use the method of invariants to study the effects of the spin-density wave order parameters on the electronic spectrum, with and without spin-orbit coupling included. Among the results of this analysis is the finding that the nodal spin-density wave is unstable once spin-orbit coupling is included. Similar analysis is performed for the A1g spin singlet superconducting state. Without spin-orbit coupling there is one pairing invariant near the Γ point, but two near the M point. This leads to an isotropic spectral gap at the hole Fermi surface near Γ, but anisotropic near M. The relative values of these three parameters determine whether the superconducting state is s++, s+−, or nodal. Inclusion of spin-orbit coupling leads to additional mixing of spin triplet pairing, with one additional pairing parameter near Γ and one near M. This leads to an anisotropic spectral gap near both hole and electron Fermi surfaces, the latter no longer cross, but rather split.

A Lagrangian framework is used for analysing reactive solute transport by a steady random velocity field, which is associated with flow through a heterogeneous porous formation. The reaction considered is kinetically controlled sorption–desorption. Transport is quantified by the expected values of spatial and temporal moments that are derived as functions of the non-reactive moments and a distribution function which characterizes sorption kinetics. Thus the results of this study generalize the previously obtained results for transport of non-reactive solutes in heterogeneous formations (Dagan 1984; Dagan et al. 1992). The results are illustrated for first-order linear sorption reactions. The general effect of sorption is to retard the solute movement. For short time, the transport process coincides with a non-reactive case, whereas for large time sorption is in equilibrium and solute is simply retarded by a factor R = 1+Kd, where Kd is the partitioning coefficient. Within these limits, the interaction between the heterogeniety and kinetics yields characteristic nonlinearities in the first three spatial moments. Asymmetry in the spatial solute distribution is a typical kinetic effect. Critical parameters that control sorptive transport asymptotically are the ratio εr between a typical reaction length and the longitudinal effective (non-reactive) dispersivity, and Kd. The asymptotic effective dispersivity for equilibrium conditions is derived as a function of parameters εr and Kd. A qualitative agreement with field data is illustrated for the zero- and first-order spatial moments.

We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons ("stress photons"), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson-Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. After providing the necessary background knowledge, including the order parameter theory of two-dimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed step-by-step via the disorder theory of dislocation-mediated melting. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this 'deconfined' mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a non-trivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.

We map out the possible ordered states in bilayer graphene at the neutrality point by extending the previous renormalization group treatment of many-body instabilities to finite temperature, trigonal warping and externally applied perpendicular electric field. We were able to analytically determine all outcomes of the RG flow equations for the nine four-fermion coupling constants. While the full phase diagram exhibits a rich structure, we confirm that when forward scattering dominates, the only ordering tendency with divergent susceptibility at finite temperature is the nematic. At finite temperature, this result is stable with respect to small back and layer imbalance scattering; further increasing their strength leads to the layer antiferromagnet. We also determine conditions for other ordered states to appear and compare our results to the special cases of attractive and repulsive Hubbard models where exact results are available.

It is common to represent solute tranport in heterogeneous formations in terms of the resident concentration C(x, t), regarded as a random space function. The present study investigates the alternative representation by q, the solute mass flux at a point of a control plane normal to the mean flow. This representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface. A general framework to compute the statistical moments of q and of the associated total solute discharge Q and mass M is established. With x the direction of the mean flow, a solute particle is crossing the control plane at y = η, z = ζ and at the travel (arrival) time τ. The associated expected solute flux value is proportional to the joint probability density function (pdf) g1 of η, ζ and τ, whereas the variance of q is shown to depend on the joint pdf g2 of the same variables for two particles. In turn, the statistical moments of η, ζ and τ depend on those of the velocity components through a system of stochastic ordinary differential equations. For a steady velocity field and neglecting the effect of pore‐scale dispersion, a major simplification of the problem results in the independence of the random variables η, ζ and τ. As a consequence, the pdf of η and ζ can be derived independently of τ. A few approximate approaches to derive the statistical moments of η, ζ and τ are outlined. These methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass, while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of η, ζ and τ

Longitudinal advective solute movement in heterogeneous porous media is investigated by considering the solute arrival time at a plane perpendicular to the mean fluid velocity. The moments of the solute arrival time are defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field. The flux-averaged concentration is specified by introducing the moments of the arrival time into a probability density function for the arrival time. The quadratic dependence of the arrival time variance on position in the vicinity of an injection point is indicative of a nondiffusive process. For the assumed spatial correlation of the hydraulic conductivity, the variance of the arrival time asymptotically approaches a linear dependence on the position from the injection point similar to a diffusion process. The impact of assuming solute movement to be a diffusive process from the onset of the solute injection causes erroneous estimates of flux-averaged concentrations at distances from the injection point that are of the order of the correlation length of the hydraulic conductivity. The arrival time analysis and the particle position analysis given in Dagan (1982, 1984) are complementary interpretations of advective solute movement that yield different definitions of the solute concentration; the position analysis intrinsically defines the resident or volume-averaged concentration, while the flux-averaged concentration is defined from the arrival time analysis. The temporal variation of the resident and flux-averaged concentration are similar at a given position for small values of the variance of the hydraulic conductivity, or at distances from the solute injection point that are large relative to correlation length of the hydraulic conductivity. 18, 1193-1214, 1982. Todorovic, P., A stochastic model of longitudinal diffusion in porous media, Water Resour. Res., 6, 211-222, 1970.

Transport of tracers subject to mass transfer reactions in single rock fractures is investigated. A Lagrangian probabilistic model is developed where the mass transfer reactions are diffusion into the rock matrix and subsequent sorption in the matrix, and sorption on the fracture surface as well as on gauge (infill) material in the fracture. Sorption reactions are assumed to be linear, and in the general case kinetically controlled. The two main simplifying assumptions are that diffusion in the rock matrix is one-dimensional, perpendicular to the fracture plane, and the tracer is displaced within the fracture plane by advection only. The key feature of the proposed model is that advective transport and diffusive mass transfer are related in a dynamic manner through the flow equation. We have identified two Lagrangian random variables τ and β as key parameters which control advection and diffusive mass transfer, and are determined by the flow field. The probabilistic solution of the transport problem is based on the statistics of (τ, β), which we evaluated analytically using first-order expansions, and numerically using Monte Carlo simulations. To study (τ, β)-statistics, we assumed the ‘cubic law’ to be applicable locally, whereby the pressure field is described with the Reynolds lubrication equation. We found a strong correlation between τ and β which suggests a deterministic relationship β∼τ3/2; the exponent 3/2 is an artifact of the ‘cubic law’. It is shown that flow dynamics in fractures has a strong influence on the variability of τ and β, but a comparatively small impact on the relationship between τ and β. The probability distribution for the (decaying) tracer mass recovery is dispersed in the parameter space due to fracture aperture variability.