A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also giv...

We discuss the crossover from the quantum critical, z =1, to the quantum disordered regime in high-Tc materials in relation to the experimental data on the nuclear relaxation, bulk susceptibility, and inelastic neutron scattering. In our scenario, the spin excitations develop a gap ∆∼1/ξ well above Tc, which is supplemented by the quasiparticle gap below Tc. The above experiments yield consiste...

We show that minimizers of free discontinuity problems with energy dependent on jump integrals and Dirichlet boundary conditions are smooth provided a smallness condition is imposed on data. We examine several examples, including elastic-plastic beam and plate with free yield lines and deformable body with free damage. In all cases there is a gap between the condition for solvability (safe load...

The spin density wave phase transition in chromium has been studied by angle-resolved photoemission on a (110) surface. The electronic band structure is shown to exhibit backfolding in the antiferromagnetic state. Direct spectroscopic evidence is obtained on the gradual opening of an energy gap at the Fermi level. The gap extends almost isotropically around the G point, its magnitude reaching 2...

Two established frameworks account for the onset of a gap in a superconducting system: one is based on spontaneous symmetry breaking via the Anderson-Higgs-Kibble mechanism, and the other is based on the recently developed paradigm of topological order. We show that, on manifolds with non trivial topology, both mechanisms yield a degeneracy of the ground state arising only from the incompressib...

In iterative schemes of identification and control one of the particular and important choices to make is the choice for a model uncertainty structure, capturing the uncertainty concerning the estimated plant model. This is typically done in some normbounded form, in order to guarantee robust stability and/or robust performance when redesigning the controller. Structures that are used in the re...

Both rainfed and irrigated soybean production are important in Nebraska (western US Corn Belt), accounting for a respective 48 and 52% of the state’s soybean production of 7 Mt on a respective 55 and 45% share of the state soybean area of 1.9 Mha. To date, no assessment of factors that may account for regional and inter-annual variation in yield and irrigation amount has been performed. To acco...

Cell to cell communication, through the transmission of small molecules (Mr less than 1200), probably occurs via a membrane specialization, the gap junction. A procedure has been developed for the isolation of gap junctions from rat liver without the use of exogenous proteases. Plasma membranes were prepared from 45 to 50 rat livers (about 500 g) by a procedure which provided a 10% yield with a...

Given a graphH with at least one edge, let gap H (n) denote the maximum difference between the numbers of edges in two n-vertex edge-maximal graphs with no minor H . We show that for exactly four connected graphs H (with at least two vertices), the class of graphs with no minor H is pure, that is, gap H (n) = 0 for all n > 1; and for each connected graph H (with at least two vertices) we have t...