Small gain theorems for large scale systems and construction of ISS Lyapunov functions

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a general formulation of ISS, the cases of summation, maximization and separation with respect to external gains are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio

Hall effect in heavy-fermion metals

The heavy fermion systems present a unique platform in which strong electronic correlations give rise to a host of novel, and often competing, electronic and magnetic ground states. Amongst a number of potential experimental tools at our disposal, measurements of the Hall effect have emerged as a particularly important one in discerning the nature and evolution of the Fermi surfaces of these enigmatic metals. In this article, we present a comprehensive review of Hall effect measurements in the heavy-fermion materials, and examine the success it has had in contributing to our current understanding of strongly correlated matter. Particular emphasis is placed on its utility in the investigation of quantum critical phenomena which are thought to drive many of the exotic electronic ground states in these systems. This is achieved by the description of measurements of the Hall effect across the putative zero-temperature instability in the archetypal heavy-fermion metal YbRh$_2$Si$_2$. Using the Ce$M$In$_5$ (with $M =$ Co, Ir) family of systems as a paradigm, the influence of (antiferro-)magnetic fluctuations on the Hall effect is also illustrated. This is compared to prior Hall effect measurements in the cuprates and other strongly correlated systems to emphasize on the generality of the unusual magnetotransport in materials with non-Fermi liquid behavior.Comment: manuscript accepted in Adv. Phy

Ecological Observations on Predatory Coccinellidae (Coleoptera) in Southwestern Michigan

Ecological observations on habitat utilization by thirteen species of predatory Coccinellidae were made at a southern Michigan site during 1989 and 1990. Most of species were common during both years and used both agricul- tural and uncultivated habitats. Coccinella septempunctata and Coleomegilla maculata, were the most abundant in agricultural crops (alfalfa, maize, soy- bean and triticale), whereas Adalia bipunctata and Cycloneda munda, were the most abundant in deciduous and bushy habitats

Lifshitz transitions and quasiparticle de-renormalization in YbRh2_2Si2_2

We study the effect of magnetic fields up to 15 T on the heavy fermion state of YbRh$_2$Si$_2$ via Hall effect and magnetoresistance measurements down to 50 mK. Our data show anomalies at three different characteristic fields. We compare our data to renormalized band structure calculations through which we identify Lifshitz transitions associated with the heavy fermion bands. The Hall measurements indicate that the de-renormalization of the quasiparticles, {\it i.e} the destruction of the local Kondo singlets, occurs smoothly while the Lifshitz transitions occur within rather confined regions of the magnetic field.Comment: 7 pages, 5 figure

Hybridization gap and Fano resonance in SmB6{_6}

We present results of Scanning Tunneling Microscopy and Spectroscopy (STS) measurements on the "Kondo insulator" SmB$_6$. The vast majority of surface areas investigated was reconstructed but, infrequently, also patches of varying size of non-reconstructed, Sm- or B-terminated surfaces were found. On the smallest patches, clear indications for the hybridization gap and inter-multiplet transitions were observed. On non-reconstructed surface areas large enough for coherent co-tunneling we were able to observe clear-cut Fano resonances. Our locally resolved STS indicated considerable finite conductance on all surfaces independent of their structure.Comment: 5 pages, 4 figure

Magnetotransport in the CeIrIn5{_5} system: The influence of antiferromagnetic fluctuations

We present an overview of magnetotransport measurements on the heavy-fermion superconductor CeIrIn$_5$. Sensitive measurements of the Hall effect and magnetoresistance (MR) are used to elucidate the low temperature phase diagram of this system. The normal-state magnetotransport is highly anomalous, and experimental signatures of a pseudogap-like precursor state to superconductivity as well as evidence for two distinct scattering times governing the Hall effect and the MR are observed. Our observations point out the influence of antiferromagnetic fluctuations on the magnetotransport in this class of materials. The implications of these findings, both in the context of unconventional superconductivity in heavy-fermion systems as well as in relation to the high temperature superconducting cuprates are discussed

Solitonic spin-liquid state due to the violation of the Lifshitz condition in Fe1+y_{1+y}Te

A combination of phenomenological analysis and M\"ossbauer spectroscopy experiments on the tetragonal Fe$_{1+y}$Te system indicates that the magnetic ordering transition in compounds with higher Fe-excess, $y\ge$ 0.11, is unconventional. Experimentally, a liquid-like magnetic precursor with quasi-static spin-order is found from significantly broadened M\"ossbauer spectra at temperatures above the antiferromagnetic transition. The incommensurate spin-density wave (SDW) order in Fe$_{1+y}$Te is described by a magnetic free energy that violates the weak Lifshitz condition in the Landau theory of second-order transitions. The presence of multiple Lifshitz invariants provides the mechanism to create multidimensional, twisted, and modulated solitonic phases.Comment: 5 pages, 2 figure