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Quasideterminants
The determinant is a main organizing tool in commutative linear algebra. In
this review we present a theory of the quasideterminants defined for matrices
over a division algebra. We believe that the notion of quasideterminants should
be one of main organizing tools in noncommutative algebra giving them the same
role determinants play in commutative algebra.Comment: amstex; final version; to appear in Advances in Mat
Effective-Medium Theory for the Normal State in Orientationally Disordered Fullerides
An effective-medium theory for studying the electronic structure of the
orientationally disordered A3C60 fullerides is developed and applied to study
various normal-state properties. The theory is based on a cluster-Bethe-lattice
method in which the disordered medium is modelled by a three-band Bethe
lattice, into which we embed a molecular cluster whose scattering properties
are treated exactly. Various single-particle properties and the
frequency-dependent conductivity are calculated in this model, and comparison
is made with numerical calculations for disordered lattices, and with
experiment.Comment: 12 pages + 2 figures, REVTeX 3.
Convergent expansions for properties of the Heisenberg model for CaVO
We have carried out a wide range of calculations for the Heisenberg
model with nearest- and second-neighbor interactions on a two-dimensional
lattice which describes the geometry of the vanadium ions in the spin-gap
system CaVO. The methods used were convergent high-order perturbation
expansions (``Ising'' and ``Plaquette'' expansions at , as well as
high-temperature expansions) for quantities such as the uniform susceptibility,
sublattice magnetization, and triplet elementary excitation spectrum.
Comparison with the data for CaVO indicates that its magnetic
properties are well described by nearest-neighbor exchange of about 200K in
conjunction with second-neighbor exchange of about 100K.Comment: Uses REVTEX macros. Four pages in two-column format, five postscript
figures. Files packaged using uufile
The twistor geometry of three-qubit entanglement
A geometrical description of three qubit entanglement is given. A part of the
transformations corresponding to stochastic local operations and classical
communication on the qubits is regarded as a gauge degree of freedom. Entangled
states can be represented by the points of the Klein quadric a space
known from twistor theory. It is shown that three-qubit invariants are
vanishing on special subspaces of . An invariant vanishing for the
class is proposed. A geometric interpretation of the canonical
decomposition and the inequality for distributed entanglement is also given.Comment: 4 pages RevTeX
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