Hubbard Models as Fusion Products of Free Fermions

A class of recently introduced su(n) `free-fermion' models has recently been used to construct generalized Hubbard models. I derive an algebra defining the `free-fermion' models and give new classes of solutions. I then introduce a conjugation matrix and give a new and simple proof of the corresponding decorated Yang-Baxter equation. This provides the algebraic tools required to couple in an integrable way two copies of free-fermion models. Complete integrability of the resulting Hubbard-like models is shown by exhibiting their L and R matrices. Local symmetries of the models are discussed. The diagonalization of the free-fermion models is carried out using the algebraic Bethe Ansatz.Comment: 14 pages, LaTeX. Minor modification

On higher analogues of Courant algebroids

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle $TM\oplus\wedge^nT^*M$ for an $m$-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an $(n+1)$-vector field $\pi$ is closed under the higher-order Dorfman bracket iff $\pi$ is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on $\wedge^nT^*M$. The graph of an $(n+1)$-form $\omega$ is closed under the higher-order Dorfman bracket iff $\omega$ is a premultisymplectic structure of order $n$, i.e. \dM\omega=0. Furthermore, there is a Lie algebroid structure on the admissible bundle $A\subset\wedge^{n}T^*M$. In particular, for a 2-plectic structure, it induces the Lie 2-algebra structure given in \cite{baez:classicalstring}.Comment: 13 page

Effects of Electronic Correlations on the Thermoelectric Power of the Cuprates

We show that important anomalous features of the normal-state thermoelectric power S of high-Tc materials can be understood as being caused by doping dependent short-range antiferromagnetic correlations. The theory is based on the fluctuation-exchange approximation applied to Hubbard model in the framework of the Kubo formalism. Firstly, the characteristic maximum of S as function of temperature can be explained by the anomalous momentum dependence of the single-particle scattering rate. Secondly, we discuss the role of the actual Fermi surface shape for the occurrence of a sign change of S as a function of temperature and doping.Comment: 4 pages, with eps figure

Spectral properties of entanglement witnesses

Entanglement witnesses are observables which when measured, detect entanglement in a measured composed system. It is shown what kind of relations between eigenvectors of an observable should be fulfilled, to allow an observable to be an entanglement witness. Some restrictions on the signature of entaglement witnesses, based on an algebraic-geometrical theorem will be given. The set of entanglement witnesses is linearly isomorphic to the set of maps between matrix algebras which are positive, but not completely positive. A translation of the results to the language of positive maps is also given. The properties of entanglement witnesses and positive maps express as special cases of general theorems for $k$-Schmidt witnesses and $k$-positive maps. The results are therefore presented in a general framework.Comment: published version, some proofs are more detailed, mistakes remove

Genotypic diversity effects on biomass production in native perennial bioenergy cropping systems

Citation: Morris, G. P., Hu, Z., Grabowski, P. P., Borevitz, J. O., de Graaff, M. A., Miller, R. M., & Jastrow, J. D. (2016). Genotypic diversity effects on biomass production in native perennial bioenergy cropping systems. GCB Bioenergy. doi:10.1111/gcbb.12309Article: Version of RecordThe perennial grass species that are being developed as biomass feedstock crops harbor extensive genotypic diversity, but the effects of this diversity on biomass production are not well understood. We investigated the effects of genotypic diversity in switchgrass (Panicum virgatum) and big bluestem (Andropogon gerardii) on perennial biomass cropping systems in two experiments conducted over 2008-2014 at a 5.4-ha fertile field site in northeastern Illinois, USA. We varied levels of switchgrass and big bluestem genotypic diversity using various local and nonlocal cultivars - under low or high species diversity, with or without nitrogen inputs - and quantified establishment, biomass yield, and biomass composition. In one experiment ('agronomic trial'), we compared three switchgrass cultivars in monoculture to a switchgrass cultivar mixture and three different species mixtures, with or without N fertilization. In another experiment ('diversity gradient'), we varied diversity levels in switchgrass and big bluestem (1, 2, 4, or 6 cultivars per plot), with one or two species per plot. In both experiments, cultivar mixtures produced yields equivalent to or greater than the best cultivars. In the agronomic trial, the three switchgrass mixture showed the highest production overall, though not significantly different than best cultivar monoculture. In the diversity gradient, genotypic mixtures had one-third higher biomass production than the average monoculture, and none of the monocultures were significantly higher yielding than the average mixture. Year-to-year variation in yields was lowest in the three-cultivar switchgrass mixtures and Cave-In-Rock (the southern Illinois cultivar) and also reduced in the mixture of switchgrass and big bluestem relative to the species monocultures. The effects of genotypic diversity on biomass composition were modest relative to the differences among species and genotypes. Our findings suggest that local genotypes can be included in biomass cropping systems without compromising yields and that genotypic mixtures could help provide high, stable yields of high-quality biomass feedstocks. © 2015 John Wiley & Sons Ltd

Poisson quasi-Nijenhuis structures with background

We define the Poisson quasi-Nijenhuis structures with background on Lie algebroids and we prove that to any generalized complex structure on a Courant algebroid which is the double of a Lie algebroid is associated such a structure. We prove that any Lie algebroid with a Poisson quasi-Nijenhuis structure with background constitutes, with its dual, a quasi-Lie bialgebroid. We also prove that any pair $(\pi,\omega)$ of a Poisson bivector and a 2-form induces a Poisson quasi-Nijenhuis structure with background and we observe that particular cases correspond to already known compatibilities between $\pi$ and $\omega$.Comment: 11 pages, submitted to Letters in Mathematical Physic

Theory of Spin Fluctuation-Induced Superconductivity Based on a d-p Model. II. -Superconducting State-

The superconducting state of a two-dimensional d-p model is studied from the spin fluctuation point of view by using a strong coupling theory. The fluctuation exchange (FLEX) approximatoin is employed to calculate the spin fluctuations and the superconducting gap functions self-consistently in the optimal- and over-doped regions of hole concentration. The gap function has a symmetry of d_{x^2 - y^2} type and develops below the transition temperature T_c more rapidly than in the BCS model. Its saturation value at the maximum is about 10 T_c. When the spin fluctuation-induced superconductivity is well stabilized at low temperatures in the optimal regime, the imaginary part of the antiferromagnetic spin susceptibility shows a very sharp resonance peak reminiscent of the 41 meV peak observed in the neutron scattering experiment on YBCO. The one-particle spectral density around k=(pi,0) shows sharp quasi-particle peaks followed by dip and hump structures bearing resemblance to the features observed in the angle-resolved photoemission experiment. With increasing doping concentration these features gradually disappear.Comment: 13 pages(LaTeX), 20 eps figure

Theory for Dynamical Short Range Order and Fermi Surface Volume in Strongly Correlated Systems

Using the fluctuation exchange approximation of the one band Hubbard model, we discuss the origin of the changing Fermi surface volume in underdoped cuprate systems due to the transfer of occupied states from the Fermi surface to its shadow, resulting from the strong dynamical antiferromagnetic short range correlations. The momentum and temperature dependence of the quasi particle scattering rate shows unusual deviations from the conventional Fermi liquid like behavior. Their consequences for the changing Fermi surface volume are discussed. Here, we investigate in detail which scattering processes might be responsible for a violation of the Luttinger theorem. Finally, we discuss the formation of hole pockets near half filling.Comment: 5 pages, Revtex, 4 postscript figure

The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature

Motivated by recent investigations of transport properties of strongly correlated 1d models and thermal conductivity measurements of quasi 1d magnetic systems we present results for the integrable spin-1/2 $XXZ$ chain. The thermal conductivity $\kappa(\omega)$ of this model has $\Re\kappa(\omega)=\tilde\kappa \delta(\omega)$, i.e. it is infinite for zero frequency $\omega$. The weight $\tilde\kappa$ of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low and high temperature limits are studied analytically.Comment: 12 page