An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

The infinite-$U$ single impurity Anderson model for rare earth alloys is examined with a new set of self-consistent coupled integral equations, which can be embedded in the large $N$ expansion scheme ($N$ is the local spin degeneracy). The finite temperature impurity density of states (DOS) and the spin-fluctuation spectra are calculated exactly up to the order $O(1/N^2)$. The presented conserving approximation goes well beyond the $1/N$-approximation ({\em NCA}) and maintains local Fermi-liquid properties down to very low temperatures. The position of the low lying Abrikosov-Suhl resonance (ASR) in the impurity DOS is in accordance with Friedel's sum rule. For $N=2$ its shift toward the chemical potential, compared to the {\em NCA}, can be traced back to the influence of the vertex corrections. The width and height of the ASR is governed by the universal low temperature energy scale $T_K$. Temperature and degeneracy $N$-dependence of the static magnetic susceptibility is found in excellent agreement with the Bethe-Ansatz results. Threshold exponents of the local propagators are discussed. Resonant level regime ($N=1$) and intermediate valence regime ($|\epsilon_f| <\Delta$) of the model are thoroughly investigated as a critical test of the quality of the approximation. Some applications to the Anderson lattice model are pointed out.Comment: 19 pages, ReVTeX, no figures. 17 Postscript figures available on the WWW at http://spy.fkp.physik.th-darmstadt.de/~frithjof

Composite Spin-Triplet Superconductivity in an SU(2)⊗SU(2)SU(2)\otimes SU(2) Symmetric Lattice Model

The two-channel Anderson lattice model which has $SU(2)\otimes SU(2)$ symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U$_{1-x}$Th$_x$Be$_{13}$ or Pr base skutterudite compounds such as PrFe$_4$P$_{12}$ or PrOs$_4$Sb$_{12}$. Possible unconventional superconducting phases of the model are explored. They are characterized by a composite order parameter comprising of a local magnetic or quadrupolar moment and a triplet conduction electron Cooper-pair. This binding of local degrees of freedom removes the entropy of the non Fermi-liquid normal state. We find superconducting transitions in the intermediate valence regime which are suppressed in the stable moment regime. The gap function is non analytic and odd in frequency: a pseudo-gap develops in the conduction electron density of states which vanishes as $|\omega|$ close to $\omega=0$. In the strong intermediate valent regime, the gap function acquires an additional \k-dependence.Comment: 20 pages, 12 figures, latex EPJ format. Accepted for publication as Eur.Phys.J.

Comment on "Scaling feature of magnetic field induced Kondo-peak splittings"

In a recent work Zhang and coworkers (PRB 82, 075111 (2010)) studied the Zeeman splitting of the Kondo resonance for the single impurity Anderson model in a finite magnetic field $B$ with the numerical renormalization group (NRG) method. There, it was found that with increasing magnetic field $B$ the position of the Kondo resonance in the total spectral function \textit{does not} approach its position in the spin resolved spectral function. Additionally, the position of the Kondo maximum exceeded the Zeeman energy for $B/ T_K\gtrsim 5-10$, where $T_K$ is the low energy Kondo scale of the model ($g=2$, $\mu_B=k_B=\hbar=1$). In this comment we argue that both these findings are produced by an improper choice of NRG parameter values. However, we reproduce the crossover in the splitting from Kondo-like behavior to a non-universal splitting larger than the Zeeman energy, but this crossover occurs at much larger fields of the order of the charge scale.Comment: Minor revisions; same version as publishe

Spin-noise in the anisotropic central spin model

Spin-noise measurements can serve as direct probe for the microscopic decoherence mechanism of an electronic spin in semiconductor quantum dots (QD).We have calculated the spin-noise spectrum in the anisotropic central spin model using a Chebyshev expansion technique which exactly accounts for the dynamics up to an arbitrary long but fixed time in a finite size system. In the isotropic case, describing QD charged with a single electron, the short-time dynamics is in good agreement with a quasi-static approximation for the thermodynamic limit. The spin-noise spectrum, however, shows strong deviations at low frequencies with a power-law behavior. In the Ising limit, applicable to QDs with heavy-hole spins, the spin-noise spectrum exhibits a threshold behavior above the Larmor frequency. In the generic anisotropic central spin model we have found a crossover from a Gaussian type of spin-noise spectrum to a more Ising-type spectrum with increasing anisotropy in a finite magnetic field. In order to make contact with experiments, we present ensemble averaged spin-noise spectra for QD ensembles charged with single electrons or holes. The Gaussian-type noise spectrum evolves to a more Lorentzian shape spectrum with increasing spread of characteristic time-scales and g-factors of the individual QDs.Comment: 24 pages, 16 figures, submitted to PR

Airfoil large eddy breakup devices for turbulent drag reduction

It was determined from the present LaRC experiments that tandem, airfoil-shaped large eddy breakup (LEBU) devices can reduce local skin friction as much as 30 percent with a recovery region extending more than 100 boundary layer thicknesses downstream. These airfoils experience near laminar skin friction device drag and produce net drag reductions of up to 7 percent. In contrast to the thin plates used in previous experiments, these airfoils are more than 1000 time stiffer and hence have the potential to withstand the real flight environment (dynamic pressure 36 times larger than in low-speed wing tunnels). In addition, the higher Reynolds numbers of the present tests indicate drag reduction performance is at least as good (or better) as at lower Reynolds numbers

Quantum transport through a molecular level: a scattering states numerical renormalisation group study

We use the scattering states numerical renormalization group (SNRG) approach to calculate the current $I(V)$ through a single molecular level coupled to a local molecular phonon. The suppression of $I$ for asymmetric junctions with increasing electron-phonon coupling, the hallmark of the Franck-Condon blockade, is discussed. We compare the SNRG currents with recently published data obtained by an iterative summation of path integrals approach (ISPI). Our results excellently agree with the ISPI currents for small and intermediate voltages. In the linear response regime $I(V)$ approaches the current calculated from the equilibrium spectral function. We also present the temperature and voltage evolution of the non-equilibrium spectral functions for a particle-hole asymmetric junction with symmetric coupling to the lead.Comment: 7 pages, 7 figure

On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems

We propose a numerical renormalization group (NRG) approach to steady-state currents through nano-devices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce two degenerate Wilson chains for current carrying left and right-moving electrons reflecting time-reversal symmetry in the absence of a finite bias $V$. We employ the time-dependent NRG to evolve the known steady-state density operator for a non-interacting junction into the density operator of the fully interacting nano-device at finite bias. We calculate the temperature dependent current as function of $V$ and applied external magnetic field using a recently developed algorithm for non-equilibrium spectral functions.Comment: 4 pages, 6 figure

Effects of vibrational nonequilibrium on the inviscid design of an axisymmetric nozzle for hypersonic flow

An axisymmetric, hypersonic nozzle for arc-heated air is described. The method of characteristics is used to compute an inviscid nozzle contour in which vibrational nonequilibrium is approximated by the sudden-freeze technique. Chemical reactions are shown to freeze early in the nozzle expansion, and the result of vibrational and chemical freezing on the nozzle contour is demonstrated. The approximate nozzle design is analyzed by an exact calculation based on the method of characteristics for flow with vibrational nonequilibrium. Exit profiles are computed, and the usefulness of the approximate design is discussed. An analysis of the nozzle performance at off-design conditions is presented