Finite temperature dynamics of the Anderson model

The recently introduced local moment approach (LMA) is extended to encompass single-particle dynamics and transport properties of the Anderson impurity model at finite-temperature, T. While applicable to arbitrary interaction strengths, primary emphasis is given to the strongly correlated Kondo regime (characterized by the T=0 Kondo scale $\omega_{\rm K}$). In particular the resultant universal scaling behaviour of the single-particle spectrum D(\omega; T) \equiv F(\frac{\w}{\omega_{\rm K}}; \frac{T}{\omega_{\rm K}}) within the LMA is obtained in closed form; leading to an analytical description of the thermal destruction of the Kondo resonance on all energy scales. Transport properties follow directly from a knowledge of $D(\omega; T)$. The $T / \omega_{\rm K}$-dependence of the resulting resistivity $\rho(T)$, which is found to agree rather well with numerical renormalization group calculations, is shown to be asymptotically exact at high temperatures; to concur well with the Hamann approximation for the s-d model down to $T/\omega_{\rm K} \sim 1$, and to cross over smoothly to the Fermi liquid form $\rho (T) - \rho (0) \propto -(T/\omega_{\rm K})^2$ in the low-temperature limit. The underlying approach, while naturally approximate, is moreover applicable to a broad range of quantum impurity and related models

Linear polarization sensitivity of SeGA detectors

Parity is a key observable in nuclear spectroscopy. Linear polarization measurements of $\gamma$-rays are a probe to access the parities of energy levels. Utilizing the segmentation of detectors in the Segmented Germanium Array (SeGA) at the NSCL and analyzing the positions of interaction therein allows the detectors to be used as Compton polarimeters. Unlike other segmented detectors, SeGA detectors are irradiated from the side to utilize the transversal segmentation for better Doppler corrections. Sensitivity in such an orientation has previously been untested. A linear polarization sensitivity $Q \approx 0.14$ has been measured in the 350-keV energy range for SeGA detectors using $\alpha$-$\gamma$ correlations from a \nuc{249}{Cf} source.Comment: 7 pages, 9 figure

Charging axisymmetric space-times with cosmological constant

Ernst's solution generating technique for adding electromagnetic charge to axisymmetric space-times in general relativity is generalised in presence of the cosmological constant. Ernst equations for complex potentials are found and they are traced back to an affective dual complex dynamical system, whose symmetries are studied. In particular this method is able to generate charged, asymptotically (A)dS black holes from their uncharged version: as an example, it is shown explicitly how to pass from the Kerr-(A)dS to the Kerr-Newman-(A)dS metric. A new solution describing a magnetic universe in presence of the cosmological constant is also generated.Comment: 15 pages, v2: typos correcte

The Influence of Boron (B), Tin (Sn), Copper (Cu), and Manganese (Mn) on the Microstructure of Spheroidal Graphite Irons

Most spheroidal graphite irons (SGIs) have a matrix consisting of ferrite, pearlite, or a mix of the two. To achieve the desired matrix composition, pearlite promoters such as Mn, Cu, or Sn, are added to the molten metal. Among these elements, Sn is the most potent pearlite promoter. However, each has a different impact on the solidification, graphite precipitation, eutectoid transformation, and ultimately the final structure of the material. Research has shown that B promotes ferrite in fully pearlitic grades where Cu and Mn were used to promote pearlite. The present work investigates the effect of B in SGI with additions of Sn, Cu, and Mn, and the effects of varying amounts of the different pearlite promoters on the matrix composition. The results show that Mn alone at levels of approximately 0.9 wt% is not enough to promote a fully pearlitic matrix, while 0.5 wt% Cu combined with 0.67 wt% Mn is sufficient. Likewise, a fully pearlitic microstructure can be obtained by alloying with 0.06 wt% Sn and 0.67 wt% Mn. B was found to promote ferrite in fully pearlitic SGI alloyed with Sn or Cu. However, in the absence of those elements, B promoted pearlite when alloyed with just Mn. Graphite protrusions were observed on the graphite nodule surface only for B-added alloys with Sn and Cu. In these cases, it is believed B promotes ferrite by changing the growth mechanism of graphite after solidification from spherical to lamellar. However, a different graphite morphology is observed when B is added with just Mn. Thermal analysis data is in agreement with the microstructural observations regarding the ferrite promoting effect of B

Functional renormalization group approach to zero-dimensional interacting systems

We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We truncate the hierarchy of flow equations such that the results are at least correct up to second order perturbation theory in the coupling. For the anharmonic oscillator energies and spectra obtained within two different functional renormalization group schemes are compared to numerically exact results, perturbation theory, and the mean field approximation. Even at large coupling the results obtained using the functional renormalization group agree quite well with the numerical exact solution. The better of the two schemes is used to calculate spectra of the single impurity Anderson model, which then are compared to the results of perturbation theory and the numerical renormalization group. For small to intermediate couplings the functional renormalization group gives results which are close to the ones obtained using the very accurate numerical renormalization group method. In particulare the low-energy scale (Kondo temperature) extracted from the functional renormalization group results shows the expected behavior.Comment: 22 pages, 8 figures include

Dynamic and spectral mixing in nanosystems

In the framework of simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The reservoir states are formed by three sequences with rationally independent periodicities typical for vibrational states in many nanosize systems. We show that quantum evolution of the system is determined by a dimensionless parameter which is characteristic number of the reservoir states relevant for the initial vibrational level dynamics. Our semi-quantitative analytic results are confirmed by numerical solution of the equation of motion. We anticipate that predicted in the paper both kinds of stochastic-like behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing) can be observed by femtosecond spectroscopy methods in nanosystems.Comment: 6 pages, 4 figure

Designing for emergence and innovation: Redesigning design

We reveal the surprising and counterintuitive truth that the design process, in and of itself, is not always on the forefront of innovation. Design is a necessary but not a sufficient condition for the success of new products and services. We intuitively sense a connection between innovative design and emergence. The nature of design, emergence and innovation to understand their interrelationships and interdependencies is examined. We propose that design must harness the process of emergence; for it is only through the bottom-up and massively iterative unfolding of emergence that new and improved products and services are successfully refined, introduced and diffused into the marketplace. The relationships among design, emergence and innovation are developed. What designers can learn from nature about emergence and evolution that will impact the design process is explored. We examine the roles that design and emergence play in innovation. How innovative organizations can incorporate emergence into their design process is explored. We demarcate the boundary between invention and innovation. We also articulate the similarities and differences of design and emergence. We then develop the following three hypotheses: Hypothesis 1: “An innovative design is an emergent design.” Hypothesis 2: “A homeostatic relationship between design and emergence is a required condition for innovation.”Hypothesis 3: “Since design is a cultural activity and culture is an emergent phenomenon, it follows that design leading to innovation is also an emergent phenomenon” We provide a number of examples of how design and emergence have worked together and led to innovation. Examples include the tool making of early man; the evolutionary chain of the six languages speech, writing, math, science, computing and the Internet; the Gutenberg printing press and techniques of collaborative filtering associated with the Internet. We close by describing the relationship between human and naturally “designed” systems and the notion a key element of a design is its purpose as is the case with a living organism

Non-equilibrium Differential Conductance through a Quantum Dot in a Magnetic Field

We derive an exact expression for the differential conductance for a quantum dot in an arbitrary magnetic field for small bias voltage. The derivation is based on the symmetric Anderson model using renormalized perturbation theory and is valid for all values of the on-site interaction $U$ including the Kondo regime. We calculate the critical magnetic field for the splitting of the Kondo resonance to be seen in the differential conductivity as function of bias voltage. Our calculations for small field show that the peak position of the component resonances in the differential conductance are reduced substantially from estimates using the equilibrium Green's function. We conclude that it is important to take the voltage dependence of the local retarded Green's function into account in interpreting experimental resultsComment: 8 pages, 4 figures; Replaced by a fully revised version with minor corrections in the tex

Expected length of the longest common subsequence for large alphabets

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe