Dimension of an optimum impurity cluster and multiple-occupancy corrections in the theory of scattering of vibrational excitations in a solid solution

A relationship is derived for the correlation length L determining the size of the region in a solid solution in which excitations are scattered coherently. The correlation length depends on the fraction of impurity atoms x in the solid solution and the lattice dimension d. In the physical analysis of single-particle scattering processes in the solid solution and calculations, it is sufficient to take into account clusters with the number of cells n corresponding to the correlation volume L ^d . A theoretical analysis is illustrated by calculations of the spectral functions of the solid solution at different values of x and n. The multiple-occupancy corrections (polynomials in powers of x) to scattering diagrams are calculated using the method of sequential breaking apart of the interaction lines in the diagrams for the self-energy part. The method used was previously applied to the case of scattering by a single impurity. In this paper, the efficiency of the method is checked for scattering by multi-impurity clusters. It is demonstrated that the method can be useful in analyzing and estimating the contributions of scattering diagrams.     

Relaxation of a 2D MHD flow across a magnetic field (2D hydrodynamic flow) in a bounded region

The problem on magnetohydrodynamic (MHD) flow of a solitary vortex across a magnetic field in a volume confined by rigid walls is solved numerically for large Reynolds numbers (including magnetic Reynolds numbers) and small Alfven-Mach numbers M _A . In this case, the MHD problem is reduced to that of two-dimensional hydrodynamic turbulence. It is shown that sound is not generated by a turbulent medium for small values of M _A ; consequently, this kinetic energy dissipation channel is closed in this case. Calculations show that, in contrast to 3D turbulence, kinetic energy dissipation for 2D turbulence occurs, as expected, over time periods on the order of L²/v(L is the characteristic size of the system and v is the kinematic viscosity). In our calculations with numerical viscosity v～vΔx (Δx is the unit cell size), this corresponds to time values on the order of ～(L/Δx)(L/v). In the kinetic energy spectra for a turbulent flow in a bounded region in the inertial interval (lying between the energy-carrying and viscosity regions), the values of E(k) decrease with increasing wave numbers k at a higher rate than in proportion to k^?3. The volume distribution of vorticity becomes narrower with time (the characteristic values of curlv decrease) and is blurred; for large time periods, the distribution approximately retains its shape as well as asymmetry with respect to positive and negative values, which is associated with the asymmetry of the initial conditions.     

Josephson vortex lattice melting in Bi-2212

The B-T diagram of Josephson vortex lattice melting in Bi-2212 is analyzed (B is magnetic induction parallel to the layers, T is temperature). It is shown that the Josephson vortex lattice melting at B > B* = 0.6–0.7 T is associated with Berezinsky-Kosterlitz-Thouless transition in individual Bi-2212 superconducting layers and is a second-order phase transition.     

Mechanism of decrease in the strength of submicron-sized specimens of FCC metals with a nanocrystalline structure

The effect of decrease in the strength of submicron-sized specimens of face-centered cubic (fcc) metals with a nanocrystalline structure and a cross-sectional size D < 5d, as compared to the strength of the specimens with D ? 5d (where d is the grain size), has been considered theoretically on the basis of the dislocation–kinetic equations and relationships. Previously, it has been found that this decrease is caused by the escape of a part of the dislocations through the surface of the specimen under the action of single-pole dislocation sources in grains adjacent to the surface. In this study, it has been shown that the absorption of lattice dislocations by grain boundaries and its accompanying grain boundary sliding lead to a further decrease in the flow stress of specimens, which is equally related to both thin (D < 5d) and thick (D ? 5d) specimens.     

Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study

Using the renormalization group approximation, specifically the Migdal-Kadanoff technique, we investigate the Blume-Capel model with mixed spins S = 1/2 and S = 5/2 on d-dimensional hypercubic lattice. The flow in the parameter space of the Hamiltonian and the thermodynamic functions are determined. The phase diagram of this model is plotted in the (anisotropy, temperature) plane for both cases d = 2 and d = 3 in which the system exhibits the first and second order phase transitions and critical end-points. The associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. We have also presented a variation of the free energy derivative at the vicinity of the first and second order transitions. Finally, this work is completed by a discussion and comparison with other approximation.     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

Role of critical fluctuations in the formation of a skyrmion lattice in MnSi

The region in the H–T phase diagram near the critical temperature (T _c ) of the cubic helicoidal MnSi magnet is comprehensively studied by small-angle neutron diffraction. Magnetic field H is applied along the [111] axis. The experimental geometry is chosen to simultaneously observe the following three different magnetic states of the system: (a) critical fluctuations of a spin spiral with randomly orientated wavevector k _f , (b) conical structure with k _c ∥ H, and (c) hexagonal skyrmion lattice with k_sk ⊥ H. Both states (conical structure, and skyrmion lattice) are shown to exist above critical temperature T _c = 29 K against the background of the critical fluctuations of a spin spiral. The conical lattice is present up to the temperatures where fluctuation correlation length ξ becomes comparable with pitch of spiral d _s . The skyrmion lattice is localized near T _c and is related to the fluctuations of a spiral with correlation length ξ ≈ 2d _s , and the propagation vector is normal to the field (k_sk ⊥ H). These spiral fluctuations are assumed to be the defects that stabilize the skyrmion lattice and promote its formation.     

Thermally activated flux flow,vortex-glass phase transition and the mixed-state Hall effect in 112-type iron pnictide superconductors

The transport properties in the mixed state of high-quality Ca_(0.8)La_(0.2)Fe_(0.98)Co_(0.02)As_2single crystal,a newly discovered 112-type iron pnictide superconductor,are comprehensively studied by magneto-resistivity measurement.The field-dependent activation energy,U_0,is derived in the framework of thermally activated flux flow(TAFF)theory,yielding a power law dependence U_0～H~αwith a crossover at a magnetic field around 2 T in both H⊥ab and H//ab,which is ascribed to the different pinning mechanisms.Moreover,we have clearly observed the vortex phase transition from vortex-glass to vortex-liquid according to the vortex-glass model,and vortex phase diagrams are constructed for both H⊥ab and H//ab.Finally,the results of mixed-state Hall effect show that no sign reversal of transverse resistivityρ_(xy)(H)is detected,indicating that the Hall component arising from the vortex flow is in theories or experiments previously reported on some high-T_ccuprates.     

Ground State Energy of the Low Density Hubbard Model

We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8π a ? _u ? _d , where ? _u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.     

Classical and quantum regimes of superfluid turbulence

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q^?1 playing the same role as the Reynolds number Re=UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re?1 in classical hydrodynamics, and q?1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re_s=UR/κ, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.     

Gottfried Sum Rule in QCD Nonsinglet Analysis of DIS Fixed-Target Data

Deep-inelastic-scattering data from fixed-target experiments on the structure function F₂ were analyzed in the valence-quark approximation at the next-to-next-to-leading-order accuracy level in the strong-coupling constant. In this analysis, parton distributions were parametrized by employing information from the Gottfried sum rule. The strong-coupling constant was found to be α _s (M²_Z) = 0.1180 ± 0.0020 (total expt. error), which is in perfect agreement with the world-averaged value from an updated Particle Data Group (PDG) report, α^PDG _s (M²_Z) = 0.1181 ± 0.0011. Also, the value of 〈x〉_u?d = 0.187 ± 0.021 found for the second moment of the difference in the u- and d-quark distributions complies very well with the most recent lattice result 〈x〉^LATTICE_u?d = 0.208 ± 0.024.     

A New Family of Solvable Pearson-Dirichlet Random Walks

An n-step Pearson-Gamma random walk in ? ^d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ? ^d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥d ₀ and any n≥2 when q is either \(q = \frac{d}{2} - 1 \) (d ₀=3) or q=d?1 (d ₀=2) (Le Caër in J. Stat. Phys. 140:728–751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type (n≥2), with q=d=2, was shown recently to be a weighted mixture of 1+floor(n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201–229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q=d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q=d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+floor(n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.     

High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice

The low-energy constants, namely the staggered magnetization density M? _s per spin, the spin stiffness ρ _s , and the spinwave velocity c of the two-dimensional (2-d) spin-1/2 Heisenberg model on the honeycomb lattice are calculated using first principles Monte Carlo method. The spinwave velocity c is determined first through the winding numbers squared. M? _s and ρ _s are then obtained by employing the relevant volume- and temperature-dependence predictions from magnon chiral perturbation theory. The periodic boundary conditions (PBCs) implemented in our simulations lead to a honeycomb lattice covering both a rectangular and a parallelogram-shaped region. Remarkably, by appropriately utilizing the predictions of magnon chiral perturbation theory, the numerical values of M? _s , ρ _s , and c we obtain for both the considered periodic honeycomb lattice of different geometries are consistent with each other quantitatively. The numerical accuracy reached here is greatly improved. Specifically, by simulating the 2-d quantum Heisenberg model on the periodic honeycomb lattice overlaying a rectangular area, we arrive at M? _s = 0.26882(3), ρ _s  = 0.1012(2)J, and c = 1.2905(8)Ja. The results we obtain provide a useful lesson for some studies such as simulating fermion actions on hyperdiamond lattice and investigating second order phase transitions with twisted boundary conditions.     

Semiclassical dynamics of vortices in 2D easy-plane ferromagnets

Semiclassical dynamics of magnetic vortices in 2D lattice models of easy-plane ferromagnets is investigated. It is shown that the low-energy part of the spectrum of vortices treated as quantum excitations of the system exhibits a nontrivial structure. The simplest spectrum is observed for standard magnetic vortices, in which magnetization at long distances from the center of a vortex is parallel to the basal plane. In this case, the spectrum has a band structure consisting of several nonintersecting bands, whose number is determined only by the value of atomic spin S and lattice symmetry. For purely 2D magnets with a single spin per unit cell, the number of bands is S or 2S for integral and half-integral values of spin S, respectively. For a lattice with the basis with an even number 2n of spins per unit cell, the number of bands is 2nS for any spins. The situation radically changes for vortices in the cone state as compared to standard vortices, for which the magnetization at a long distance from the center of a vortex rotates in the easy plane of the magnet. Vortices in the cone state are formed under the action of a constant external field perpendicular to the easy plane of the magnet. As a rule, the spectrum for such vortices is not a standard band spectrum and forms a set such that a forbidden energy value can be found in any small neighborhood of an allowed value, and vice versa. The possibility of an oscillatory motion of a vortex under the action of a constant external force is indicated (analog of Bloch oscillations of electrons in crystals). Possible realization of these effects in other ordered media with vortices is considered.     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Influence of thermophoresis on heat and mass transfer under non-Darcy MHD mixed convection along a vertical flat plate embedded in a porous medium in the presence of radiation

The paper presents an investigation of the influence of thermophoresis on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid along a vertical flat plate with radiation effects. The plate is permeable and embedded in a porous medium. To describe the deviation from the Darcy model the Forchheimer flow model is used. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The nonlinear ordinary differential equations are linearized by using quasilinearization technique and then solved numerically by using implicit finite difference scheme. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, mixed convection parameter Ra _d /Pe _d , Reynolds number Red, radiation parameter R, thermophoretic parameter τ, Prandtl number Pr, and Schmidt number Sc. The heat transfer coefficient is also tabulated for different values of physical parameters.     

New omega vortex identification method

A new vortex identification criterion called W-method is proposed based on the ideas that vorticity overtakes deformation in vortex.The comparison with other vortex identification methods like Q-criterion and λ_2-method is conducted and the advantages of the new method can be summarized as follows:(1) the method is able to capture vortex well and very easy to perform;(2) the physical meaning of W is clear while the interpretations of iso-surface values of Q and λ_2 chosen to visualize vortices are obscure;(3)being different from Q and λ_2 iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, W is pretty universal and does not need much adjustment in different cases and the iso-surfaces of W=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated;(4) both strong and weak vortices can be captured well simultaneously while improper Q and λ_2 threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared;(5) W=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate W, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow,the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity.     

The proximity effect in an Fe-Cr-V-Cr-Fe system

The proximity effect was studied in a thin-film Fe-Cr-V-Cr-Fe layered system. As the chromium layer thickness (d_Cr) increases at a fixed thickness of iron layers (d_Fe), the dependence of the superconducting transition temperature (T_c) on d_Cr exhibits a maximum at d_Cr ? 40 Å followed by a sharp decrease. Investigation of the dependence of T_c on d_Fe at a fixed d_Cr showed that the depth of penetration of the Cooper pairs into a chromium layer does not exceed 40 Å. Analysis of the results obtained suggests that, at d_Cr ? 40 Å, chromium layers exhibit the transition from a nonmagnetic state to an incommensurate spin density wave state.