Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N _eff of states. A plot of ln(F) versus N ∝ ln(N _eff ) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(N _eff ) plot for the Kondo impurity diverges for large N _eff . On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N _eff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.     

On The Contribution of the P and D Partial-Wave States to the Binding Energy of the Triton in the Bethe-Salpeter-Faddeev Approach

The influence of the partial-wave states with nonzero orbital moment of the nucleon pair on the binding energy of the triton T(nnp) in the relativistic case is considered. The relativistic generalization of the Faddeev equation in the Bethe-Salpeter formalism is applied. Two-nucleon t matrix is obtained from the Bethe-Salpeter equation with separable kernel of nucleon-nucleon interaction of the rank one. The kernel form factors are the relativistic type of the Yamaguchi functions. The following two-nucleon partial-wave states are considered: ¹S₀, ³S₁, ³D₁, ³P₀, ¹P₁, ³P₁. The system of the integral equations are solved by using the iteration method. The binding energy of the triton and three-nucleon amplitudes are found. The contribution of the P and D states to the binding energy of triton is given.

     

Molecular and atomic ions of the elements of the sub-groupsA of the periodic system

The production of positive and negative ions of all elements of the sub-groupsA and some of the sub-groupsB has been investigated as an extension of previous work on Penning sources. Molecular ions of the typeX _n ^± ,n>1 and ions of hydride moleculesX _nH _m ^± ,n,m>1 have been found. The maximum numberm _max of the H atoms bound in the cluster is determined by the position of the element in the periodic system. The yield of the atomic and molecular beams has been measured as a function of the electric source parameters and the different gases maintaining the discharge to establish the production mechanism. The data on ion beam intensities and the state of clustering of molecules are listed in tables.     

Prospects for observing the Kaluza-Klein excitations of the W boson in the ATLAS detector at the LHC

The European Physical Journal C - Kaluza-Klein excitations of the gauge bosons are a notable feature of theories with “small” (~ 1 TeV) extra dimensions. The leptonic decays of...     

Factorization and the couplings of the vacuum trajectory

The decoupling theorems associated with an isolated factorizable pomeron pole of unit intercept are re-examined. It is found that the coupling of three such poles, Γ(t, t, 0), need not vanish, precisely at the point t = 0. This is demonstrated by summing only over states in the appropriate unitarity sum, and sum rule, which are consistent with the M², s/M² → ∞ limit. The triple-Regge region then makes a constant contribution to σ_total, insteadsb of the ln lns result obtained if the isolated pole is assumed to couple also to states such that s/M² = constant. The physical implications regarding factorization and the pole-cut relationship are discussed. The relationship between higher order optical theorems (Mueller discontinuities) and particular terms in the unitarity sum for the two → two absorptive part A₂₂ is exploited. Consistent contributions to the triple-Regge region contribute constant vertex corrections to pure pole behaviour in A₂₂. There is no cut contribution and the magnitude of the vertex corrections reflects the relative amount of diffractive production. The analysis is extended to multiple fireball production where pure multipole structures emerge. The series naturally terminates if the diffractive component is sufficiently small. The implications for the behaviour of the total cross section at machine energies are discussed.     

Study of the total reactive dynamics of the H + DCl reaction within the framework of the quantum approach

The reactive dynamics of the H + DCl reaction was studied by the wave-packet method at an arbitrary total angular momentum. Two reaction channels (exchange and abstraction) are considered. The reaction cross sections calculated depending on collision energies up to 2.5 eV and initial states of the DCl molecule remain unchanged for the rotational levels j ₀ = 0, 1, 4 at a vibrational level v ₀ = 0. The reaction threshold and cross section agree with the known experimental data.     

On the broadening of the annihilation line

The broadening of annihilation line was studied with a Ge detector. The annihilation line was deconvoluted taking into account the instrumental resolution of 1.08 keV. The P_f in several metals are found. The contribution of core electrons to annihilation is deduced.     

Constraining the size of the carrier of the λ5797.1 diffuse interstellar band

The diffuse interstellar band (DIB) at 5797.1 Å is simulated based on three premises: (1) The carrier of the DIB is polar as concluded by T. Oka et al. from the anomalous spectrum toward Herschel 36 (Her 36). (2) The sharp central feature observed by P.J. Sarre's group is the Q-branch of a parallel band of a prolate top. (3) The radiative temperature of the environment is T_r = 2.73 K. A ²Π ← ²Π transition of a linear radical is simulated. Results depend on 10 parameters, with the rotational constant B being the most critical. Comparisons of calculated spectra with observed data constrain B, which in turn constrains the number of heavy atoms to 5 ≤ n ≤ 7. Upper limits based on the Her 36 spectrum and lower limits based on stability against photodissociation are also discussed. The latter is based on the assumption that the DIB molecules are produced top-down from the breakdown of dust rather than bottom-up by chemical reactions. A difficulty with this limit is that J.P. Maier's laboratory has observed many molecules within this size range, some of which have been tested astronomically. Candidates are discussed in light of many prolate tops observed by the P. Thaddeus and M.C. McCarthy microwave group.     

On the determination of the volume fraction of the crystalline phase in amorphous-crystalline alloys

The possibility of determining volume fractions of crystalline and amorphous phases of partially crystalline alloys from X-ray diffraction data has been discussed. The crystallization of an amorphous microwire of the Fe_73.9B_13.2Si_10.9C₂ composition has been investigated. The crystallization leads to the formation of α-Fe and Fe(Si). An analysis has been made of the X-ray diffraction patterns recorded for a series of samples with different contents of the crystalline and amorphous phases. The angular range has been determined and the calibration graph has been constructed, which can be used to determine the volume fractions of the amorphous and crystalline components in amorphous-crystalline samples.     

On the connectedness structure of the CoulombS-matrix

The forward direction singularity of the non-relativistic CoulombS-matrix is examined and discussed. The relativistic CoulombS-matrix to order α is shown to have a similar singularity.     

On the scale variation of the total cross section for Higgs production at the LHC and at the Tevatron

We present a detailed study of the total pp cross section for scalar Higgs production to next-to-next-to-leading order in α_s at LHC energies, and of the pp̄ cross section at the Tevatron, combining an implementation of the solutions of the parton evolution equations at the three-loop order with the corresponding hard scatterings, evaluated at the same perturbative order. Our solutions of the DGLAP equations are implemented directly in x-space and allow for the study of the dependence of the results on the factorization (μ_F) and renormalization scales (μ_R) typical of a given process, together with the stability of the perturbative expansion. The input sets for the parton evolutions are those given by Martin, Roberts, Stirling and Thorne and by Alekhin. Results for K-factors are also presented. The NNLO corrections can be quite sizeable at typical collider energies. The stability region of the perturbative expansion is found when μ_R>m_H∼μ_F.     

Investigation of the electronic structure of the SbSeBr cluster

The energy levels of valence bands (VB) in SbSeBr crystals were calculated for investigation of the photoelectron emission spectra of A⁵B⁶C⁷ — type crystals. The molecular model of this crystal was used for calculation of VB by the Density Functional Theory (DFT) and Unrestricted Hartree — Fock (UHF) methods. The molecular cluster consisting of 20 molecules of SbSeBr was used for calculations of averaged total density of states including atom vibrations. The spectra of averaged total density of states from VB in the SbSeBr cluster were compared with experimental photoelectron emission spectra from VB of A⁵B⁶C⁷ — type crystals. The results of comparison clarify that the atomic vibrations are one of possible reasons for the smoother appearance of the experimental X-ray photoelectron spectrum (XPS).      

Precision measurement of the rate of nuclear muon capture in the muonic hydrogen atom and the determination of the pseudoscalar form factor of the nucleon

The rate Λ _S of nuclear muon capture by a proton from the hyperfine singlet ground state of the µp atom has been measured using a new experimental method based on a time-projection chamber operating in an ultrapure hydrogen gas at a pressure of 10 atm. The capture rate has been determined from the difference between the measured lifetime of the negative muon in hydrogen and the world average lifetime of the positive muon. The analysis of 10% of the collected statistics (2 × 10¹⁰) of µe decays yields the muon capture rate Λ _S = 725.0 ± 17.4 s^?1, from which the pseudoscalar form factor of the nucleon, g _P (q _c ² = ?0.88m _µ ² ) = 7.3 ± 1.1, is determined. The further analysis of the collected experimental data should improve the precision of this measurement by a factor of 3.     

On the lifetime of the kappa meson

The lifetime of a hypotheticalκ meson with low mass, introduced byGlashow andWeinberg in a model for simultaneous breaking ofSU(3) and chiral symmetry, is calculated. The coupling constant of theκ toKπ is obtained by assuming that the divergence of the strangeness changing vector current is dominated by theκ pole.     

On the volume dependence of the total energy and the equation of state for copper

The total energy of metallic copper as a function of the atomic radius is calculated. The model assumes that in copper one has nearly free s-electrons in OPW states and d-electrons localized at the ions in atomic-like orbitals. The coulomb interactions in the energy are calculated by using the model of neutral spheres, while the kinetic and exchange contributions to the S²-energy are approximated by the exchange charge model. Instead of the familiar Born-Mayer repulsion, which was found to lead to controversies in the case of copper, the d-type interaction energy shows a more complex behaviour having a minimum near the equilibrium atomic radius. The prediction for the cohesive energy and the equation of state is reasonable, the calculated value for the Ashcroft radius for s-electrons agrees remarkably with the ab initio estimate. The atomic-like orbitals minimizing the total energy are somewhat more extended than the real atomic wave-functions.     

Note on the difference between the a-cyclic and c-cyclic version of the XY model

The transverse susceptibility of the c-cyclic version of the one-dimensional XY model with respect to an infinitesimal magnetic field in the x-direction is investigated in more detail. Special attention is paid to the c-cyclic version of the one-dimensional Ising model. The c-cyclic susceptibility χ_xx is evaluated explicitly. The autocorrelation function of the magnetization M_x turns out to be time dependent in the c-cyclic Ising model.     

Anomalous behavior of the surface tension at the interface of the metallic and insulating phases in the vicinity of the metal-insulator phase transition in a magnetic field

Mean-field equations describing the metal-insulator (MI) transition are formulated. They involve two coupled order parameters characterizing this transition: (i) a scalar order parameter describing the density change accompanying the transition from the insulating state to the metallic one and (ii) an order parameter (a two-component vector) describing the electron density in the metallic or semimetallic phase affected by the applied magnetic field. Two components of this vector correspond to different possible spin states of electrons in the applied magnetic field. The transition in the density of metallic and insulating phases being a first order phase transition is treated in terms of the Cahn-Hilliard-type gradient expansion. The transition in the electron density is a second order phase described by the Ginzburg-Landau-type functional. The coupling of these two parameters is described by the term linearly dependent on the electron density n in the metal with the proportionality factor being a function of the density of the metallic phase. The derived equations are solved in the case of the MI interface in the presence of both parallel and perpendicular uniform magnetic fields. The calculated surface tension Σ_mi between the metallic and insulating phases has a singular behavior. In the limit of zero electron density n ? 0, Σ_mi ～ n ^3/2. Near the MI transition point T _c(h) in the applied magnetic field, Σ_mi ～ [T - T _c(h)]^3/2. The singular behavior of the surface tension at the MI interface results in the clearly pronounced hysteresis accompanying the transition from the insulating to metallic state and vice versa.     

On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay ratet ^–5/4) ast+ to that of the compressible Navier-Stokes equation for the corresponding initial data.     

Effect of the frustration to the ground state energy and entropy of the spin-glass in the random bond Ising model on the square lattice

The energies and the entropies of the spin-glass state and the paramagnetic state at T = 0 of the random-bond Ising mixture of the ferromagnetic bond (concentration p) and the antiferromagnetic bond (concentration 1 ? p) on the square lattice are calculated by the method of the square approximation in the simple version. A self-consistent relation that the partial trace of the normalized density matrix of the square cluster is equal to that of the vertex ($\text{tr}\text{(}{}_{\mathrm{jkl}}\text{?}\text{?}{}^{\mathrm{(4)}}\text{(i,j,k,l) =}\text{?}\text{?}{}^{\mathrm{(1)}}\text{(i)}$) leads to an integral equation for the distribution function of the effective fields, and it is solved exactly at T = 0. The symmetric solution of the integral equation contains the paramagnetic state and two spin-glass states, SG1 and SG2. The energies and the entropies of these states are obtained as functions of the concentration p. The values of the energies per spin at $\text{p =}\text{1}\text{2}$ are -0.75|E_F|, -0.72746|E_F|, -0.72543|E_F|, and correspond to a minimum, a saddle point, and a maximum, respectively, and the values of the entropies are 0, 0.082886k_B, and 0.054457k_B, respectively. The present results are compared with those of the pair approximation and discussed.