2,265 research outputs found
The su(N) XX model
The natural su(N) generalization of the XX model is introduced and analyzed.
It is defined in terms of the characterizing properties of the usual XX model:
the existence of two infinite sequences of mutually commuting conservation laws
and the existence of two infinite sequences of mastersymmetries. The
integrability of these models, which cannot be obtained in a degenerate limit
of the su(N)-XXZ model, is established in two ways: by exhibiting their R
matrix and from a direct construction of the commuting conservation laws. We
then diagonalize the conserved laws by the method of the algebraic Bethe
Ansatz. The resulting spectrum is trivial in a certain sense; this provides
another indication that the su(N) XX model is the natural generalization of the
su(2) model. The application of these models to the construction of an
integrable ladder, that is, an su(N) version of the Hubbard model, is
mentioned.Comment: 16 pages, TeX and harvmac (option b). Minor corrections, accepted for
publication in Nuclear Physics
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
Division Algebras and Extended N=2,4,8 SuperKdVs
The first example of an N=8 supersymmetric extension of the KdV equation is
here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It
corresponds to the unique N=8 solution based on a generalized hamiltonian
dynamics with (generalized) Poisson brackets given by the Non-associative N=8
Superconformal Algebra. The complete list of inequivalent classes of
parametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associative
N=8 SCA" is also furnished. Furthermore, a fundamental domain characterizing
the class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" is
given.Comment: 14 pages, LaTe
The Schroedinger operator as a generalized Laplacian
The Schroedinger operators on the Newtonian space-time are defined in a way
which make them independent on the class of inertial observers. In this picture
the Schroedinger operators act not on functions on the space-time but on
sections of certain one-dimensional complex vector bundle -- the Schroedinger
line bundle. This line bundle has trivializations indexed by inertial observers
and is associated with an U(1)-principal bundle with an analogous list of
trivializations -- the Schroedinger principal bundle. For the Schroedinger
principal bundle a natural differential calculus for `wave forms' is developed
that leads to a natural generalization of the concept of Laplace-Beltrami
operator associated with a pseudo-Riemannian metric. The free Schroedinger
operator turns out to be the Laplace-Beltrami operator associated with a
naturally distinguished invariant pseudo-Riemannian metric on the Schroedinger
principal bundle. The presented framework is proven to be strictly related to
the frame-independent formulation of analytical Newtonian mechanics and
Hamilton-Jacobi equations, that makes a bridge between the classical and
quantum theory.Comment: 19 pages, a remark, an example and references added - the version to
appear in J. Phys. A: Math. and Theo
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
for an -dimensional manifold. As an application, we revisit Nambu-Poisson
structures and multisymplectic structures. We prove that the graph of an
-vector field is closed under the higher-order Dorfman bracket iff
is a Nambu-Poisson structure. Consequently, there is an induced Leibniz
algebroid structure on . The graph of an -form is
closed under the higher-order Dorfman bracket iff is a
premultisymplectic structure of order , i.e. \dM\omega=0. Furthermore,
there is a Lie algebroid structure on the admissible bundle
. In particular, for a 2-plectic structure, it induces
the Lie 2-algebra structure given in \cite{baez:classicalstring}.Comment: 13 page
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 -Schmidt witnesses and -positive maps. The
results are therefore presented in a general framework.Comment: published version, some proofs are more detailed, mistakes remove
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 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 and
.Comment: 11 pages, submitted to Letters in Mathematical Physic
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
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
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