Quantum Critical Behavior in Kondo Systems

This article briefly reviews three topics related to the quantum critical behavior of certain heavy-fermion systems. First, we summarize an extended dynamical mean-field theory for the Kondo lattice, which treats on an equal footing the quantum fluctuations associated with the Kondo and RKKY couplings. The dynamical mean-field equations describe an effective Kondo impurity model with an additional coupling to vector bosons. Two types of quantum phase transition appear to be possible within this approach---the first a conventional spin-density-wave transition, the second driven by local physics. For the second type of transition to be realized, the effective impurity model must have a quantum critical point exhibiting an anomalous local spin susceptibility. In the second part of the paper, such a critical point is shown to occur in two variants of the Kondo impurity problem. Finally, we propose an operational test for the existence of quantum critical behavior driven by local physics. Neutron scattering results suggest that CeCu$_{6-x}$Au$_x$ passes this test.Comment: 6 pages, 4 eps figures, REVTeX (epsf style

Occurrence of Escherichia coli O157 in a river used for fresh produce irrigation in Nigeria

Concerns about the persistence of Escherichia coli O157 in irrigation waters and its transmission to fresh produce makes investigation of irrigation waters imperative. The prevalence of this pathogen and seasonal levels of water quality parameters in Kubanni River were studied, using standard methods, over a 10-month period. Detection rate for E. coli O157 confirmed by slide agglutination was 2.1%. Faecal coliform counts (FCC) exceeded acceptable limits and was significantly higher in the dry season than during the rainy season (p<0.05). Remarkably, nitrate level was significantly higher in the rainy season than dry season (p<0.05). A significant (p<0.05) correlation was established between FCC and each of nitrate (r = 0.25), biochemical oxygen demand (r = 0.51) and electrical conductivity (r = 0.55). It was concluded that the Kubanni River represents a potential public health risk, being unfit for fresh produce irrigation. Perhaps, this is the first report on the isolation of E. coli O157 from water sources in Nigeria

Spatial Correlations in Dynamical Mean Field Theory

We further develop an extended dynamical mean field approach introduced earlier. It goes beyond the standard $D=\infty$ dynamical mean field theory by incorporating quantum fluctuations associated with intersite (RKKY-like) interactions. This is achieved by scaling the intersite interactions to the same power in 1/D as that for the kinetic terms. In this approach, a correlated lattice problem is reduced to a single-impurity Anderson model with additional self-consistent bosonic baths. Here, we formulate the approach in terms of perturbation expansions. We show that the two-particle vertex functions are momentum-dependent, while the single-particle self-energy remains local. In spite of this, the approach is conserving. Finally, we also determine the form of a momentum-dependent dynamical susceptibility; the resulting expression relates it to the corresponding Weiss field, local correlation function and (momentum-dependent) intersite coupling.Comment: 28 pages, REVTEX, 8 figures include

An Analytical Approach to Neuronal Connectivity

This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional orthogonal lattice with parameter $\Delta$, it is possible to obtain the accurate number of connections and cycles of any length from the autoconvolution function as well as from the respective spectral density derived from the adjacency matrix. It is shown that neuronal shape plays an important role in defining the spatial spread of network connections. In addition, most such networks are characterized by the interesting phenomenon where the connections are progressively shifted along the spatial domain where the network is embedded. It is also shown that the number of cycles follows a power law with their respective length. Morphological measurements for characterization of the spatial distribution of connections, including the adjacency matrix spectral density and the lacunarity of the connections, are suggested. The potential of the proposed approach is illustrated with respect to digital images of real neuronal cells.Comment: 4 pages, 6 figure

Requiring Teachers to have Mental Health Training

Mental illness is a growing problem in America, with 1 in 5 students suffering with mental health issues. This leads to an increase in the likelihood of violence and conflict, and ultimately the situation can escalate into a school shooting. This solution aims to prevent tragic events like this from happening, and addresses the UN Sustainable Development goal of quality education and health and well-being. Though more direct efforts could be taken such as tightening gun control, these types of laws are difficult to pass. Therefore, our policy is to require teachers to have mental health training so that they will be able to recognize problems in students, and reach out before the problem worsens

The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335

Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators

We discuss the general theoretical arguments advanced earlier for the T=0 global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing between the established and the conjectured. In addition to the well-known phase of a paramagnetic metal with a "large" Fermi surface (P_L), there is also an antiferromagnetic phase with a "small" Fermi surface (AF_S). We provide the details of the derivation of a quantum non-linear sigma-model (QNLsM) representation of the Kondo lattice Hamiltonian, which leads to an effective field theory containing both low-energy fermions in the vicinity of a Fermi surface and low-energy bosons near zero momentum. An asymptotically exact analysis of this effective field theory is made possible through the development of a renormalization group procedure for mixed fermion-boson systems. Considerations on how to connect the AF_S and P_L phases lead to a global phase diagram, which not only puts into perspective the theory of local quantum criticality for antiferromagnetic heavy fermion metals, but also provides the basis to understand the surprising recent experiments in chemically-doped as well as pressurized YbRh2Si2. We point out that the AF_S phase still occurs for the case of an equal number of spin-1/2 local moments and conduction electrons. This observation raises the prospect for a global phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally, we discuss the connection between the Kondo breakdown physics discussed here for the Kondo lattice systems and the non-Fermi liquid behavior recently studied from a holographic perspective.Comment: (v3) leftover typos corrected. (v2) Published version. 32 pages, 4 figures. Section 7, on the connection between the Kondo lattice systems and the holographic models of non-Fermi liquid, is expanded. (v1) special issue of JLTP on quantum criticalit