Theory for Superconducting Properties of the Cuprates: Doping Dependence of the Electronic Excitations and Shadow States

The superconducting phase of the 2D one-band Hubbard model is studied within the FLEX approximation and by using an Eliashberg theory. We investigate the doping dependence of $T_c$, of the gap function $\Delta ({\bf k},\omega)$ and of the effective pairing interaction. Thus we find that $T_c$ becomes maximal for $13 \; \%$ doping. In {\it overdoped} systems $T_c$ decreases due to the weakening of the antiferromagnetic correlations, while in the {\it underdoped} systems due to the decreasing quasi particle lifetimes. Furthermore, we find {\it shadow states} below $T_c$ which affect the electronic excitation spectrum and lead to fine structure in photoemission experiments.Comment: 10 pages (REVTeX) with 5 figures (Postscript

Modular classes of Poisson-Nijenhuis Lie algebroids

The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

The Structure of Conserved Charges in Open Spin Chains

We study the local conserved charges in integrable spin chains of the XYZ type with nontrivial boundary conditions. The general structure of these charges consists of a bulk part, whose density is identical to that of a periodic chain, and a boundary part. In contrast with the periodic case, only charges corresponding to interactions of even number of spins exist for the open chain. Hence, there are half as many charges in the open case as in the closed case. For the open spin-1/2 XY chain, we derive the explicit expressions of all the charges. For the open spin-1/2 XXX chain, several lowest order charges are presented and a general method of obtaining the boundary terms is indicated. In contrast with the closed case, the XXX charges cannot be described in terms of a Catalan tree pattern.Comment: 22 pages, harvmac.tex (minor clarifications and reference corrections added

Impact of a Distributed Intelligent System in a Large Scale Safety Critical System

Safety critical large scale systems are complex, physically extensive socio-technical systems, extending over a range of domains, and are of interest because of the enormous catastrophic potential on their constituents, bystanders and the environment. Often, failures in such systems are traced to human error, as well as to unforeseen and unanticipated combinations of causal factors arising from the size, scope and complexity of the systems. Technologies developed to support these systems are often distributed, supporting subsystems with specific local requirements

The Effect of Concussion History on Lower Extremity Musculoskeletal Injury in Collegiate Athletes: A Critically Appraised Topic

Concussions can cause a multitude of both acute and chronic symptoms including headache, blurred vision, dizziness, nausea, double vision, memory loss, balance problems, cognitive and neurological dysfunction. The majority of athletes who sustain a concussion experience documented recovery from self-reported symptoms, neurocognitive impairments, and balance dysfunction within 7-10 days post-injury. However, there is evidence to suggest that measurable neuromuscular deficits remain in athletes beyond clinical recovery of a concussion and exceed return to play criteria fulfillment. Deficiencies in neuromuscular control has been associated with musculoskeletal injury, but limited research has explored whether neuromuscular control insufficiencies secondary to concussion are correlated with risk of orthopedic injury. Focused clinical question: Are collegiate athletes with a history of concussion at a higher risk of sustaining a lower extremity injury than collegiate athletes without a history of concussion

PREDATOR-AVOIDANCE BEHAVIOR EXTENDS TROPHIC CASCADES TO REFUGE HABITATS

Consideration of how trait-mediated indirect interactions (TMIIs) affect community dynamics is recognized as an important focus for ecological research. Although these indirect effects have been shown to mediate trophic cascades in ecological communities, our understanding of how habitat refuge influences the strength and direction of cascading effects is limited. We examined whether or not oyster toadfish (top predator) affect mud crab (intermediate predator) foraging on juvenile hard clams (infaunal prey) in oyster reefs, a physically complex habitat that can provide refuge for both intermediate predators and basal prey. In particular, we manipulated toadfish presence in mesocosms containing experimental oyster reefs and quantified both mud crab and juvenile clam mortality. Toadfish significantly reduced mud crab foraging on clams and increased clam survivorship even though mud crabs foraging on the surface of the reef sought refuge from toadfish deeper within the oyster-shell matrix where they were more proximal to clams. This counterintuitive result suggests that toadfish suppression of mud crab foraging activity is far stronger than toadfish-avoidance behavior that potentially increases crab-clam encounter rates. Therefore, TMIIs can reinforce trophic cascades even in refuge habitats where intermediate predators and their prey are physically isolated from top predators. Determining the generality of cascading effects on lower trophic levels within refugia will require investigating how habitat refuge affects the relative importance of TMIIs

Integration of Dirac-Jacobi structures

We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures. These geometric objects generalize contact groupoids. We also explain the relationship between precontact groupoids and homogeneous presymplectic groupoids. Finally, we present some examples of precontact groupoids.Comment: 10 pages. Brief changes in the introduction. References update

Thermodyamic bounds on Drude weights in terms of almost-conserved quantities

We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki's proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C^* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain [Phys. Rev. Lett. 106, 217206 (2011)].Comment: version as accepted by Communications in Mathematical Physics (22 pages with 2 pdf-figures