1,951 research outputs found
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 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 chain. The thermal
conductivity of this model has , i.e. it is infinite for zero frequency . The weight
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
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
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
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 -Schmidt witnesses and -positive maps. The
results are therefore presented in a general framework.Comment: published version, some proofs are more detailed, mistakes remove
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
Lie algebroid foliations and -Dirac structures
We prove some general results about the relation between the 1-cocycles of an
arbitrary Lie algebroid over and the leaves of the Lie algebroid
foliation on associated with . Using these results, we show that a
-Dirac structure induces on every leaf of its
characteristic foliation a -Dirac structure , which comes
from a precontact structure or from a locally conformal presymplectic structure
on . In addition, we prove that a Dirac structure on can be obtained from and we discuss the relation between the leaves of
the characteristic foliations of and .Comment: 25 page
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