51,418 research outputs found
Quasi-Spin Graded-Fermion Formalism and Branching Rules
The graded-fermion algebra and quasi-spin formalism are introduced and
applied to obtain the branching rules for the
"two-column" tensor irreducible representations of gl(m|n), for the case . In the case m < n, all such irreducible representations of gl(m|n)
are shown to be completely reducible as representations of osp(m|n). This is
also shown to be true for the case m=n except for the "spin-singlet"
representations which contain an indecomposable representation of osp(m|n) with
composition length 3. These branching rules are given in fully explicit form.Comment: 19 pages, Latex fil
Magnetic Excitations of Stripes and Checkerboards in the Cuprates
We discuss the magnetic excitations of well-ordered stripe and checkerboard
phases, including the high energy magnetic excitations of recent interest and
possible connections to the "resonance peak" in cuprate superconductors. Using
a suitably parametrized Heisenberg model and spin wave theory, we study a
variety of magnetically ordered configurations, including vertical and diagonal
site- and bond-centered stripes and simple checkerboards. We calculate the
expected neutron scattering intensities as a function of energy and momentum.
At zero frequency, the satellite peaks of even square-wave stripes are
suppressed by as much as a factor of 34 below the intensity of the main
incommensurate peaks. We further find that at low energy, spin wave cones may
not always be resolvable experimentally. Rather, the intensity as a function of
position around the cone depends strongly on the coupling across the stripe
domain walls. At intermediate energy, we find a saddlepoint at for
a range of couplings, and discuss its possible connection to the "resonance
peak" observed in neutron scattering experiments on cuprate superconductors. At
high energy, various structures are possible as a function of coupling strength
and configuration, including a high energy square-shaped continuum originally
attributed to the quantum excitations of spin ladders. On the other hand, we
find that simple checkerboard patterns are inconsistent with experimental
results from neutron scattering.Comment: 11 pages, 13 figures, for high-res figs, see
http://physics.bu.edu/~yaodx/spinwave2/spinw2.htm
Magnetic Excitations of Stripes Near a Quantum Critical Point
We calculate the dynamical spin structure factor of spin waves for weakly
coupled stripes. At low energy, the spin wave cone intensity is strongly peaked
on the inner branches. As energy is increased, there is a saddlepoint followed
by a square-shaped continuum rotated 45 degree from the low energy peaks. This
is reminiscent of recent high energy neutron scattering data on the cuprates.
The similarity at high energy between this semiclassical treatment and quantum
fluctuations in spin ladders may be attributed to the proximity of a quantum
critical point with a small critical exponent .Comment: 4+ pages, 5 figures, published versio
Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups
We introduce the quasi-Hopf superalgebras which are graded versions of
Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum
supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting
the normal quantum supergroups by twistors which satisfy the graded shifted
cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the
supersymmetric case. Two types of elliptic quantum supergroups are defined,
that is the face type and the vertex type
(and ), where is any
Kac-Moody superalgebra with symmetrizable generalized Cartan matrix. It appears
that the vertex type twistor can be constructed only for
in a non-standard system of simple roots, all of which are fermionic.Comment: 22 pages, Latex fil
Quantum affine algebras and universal R-matrix with spectral parameter, II
This paper is an extended version of our previous short letter \cite{ZG2} and
is attempted to give a detailed account for the results presented in that
paper. Let be the quantized nontwisted affine Lie algebra
and be the corresponding quantum simple Lie algebra. Using the
previous obtained universal -matrix for and
, we determine the explicitly spectral-dependent universal
-matrix for and . We apply these spectral-dependent
universal -matrix to some concrete representations. We then reproduce the
well-known results for the fundamental representations and we are also able to
derive for the first time the extreamly explicit and compact formula of the
spectral-dependent -matrix for the adjoint representation of , the
simplest nontrival case when the tensor product of the representations is {\em
not} multiplicity-free.Comment: 22 page
A Wake Model for Free-Streamline Flow Theory, Part II. Cavity Flows Past Obstacles of Arbitrary Profile
In Part I of this paper a free-streamline wake model was introduced to treat the fully and partially developed wake flow or cavity flow past an oblique flat plate. This theory is generalized here to investigate the cavity flow past an obstacle of arbitrary profile at an arbitrary cavitation
number. Consideration is first given to the cavity flow past a polygonal obstacle whose wetted sides may be concave towards the flow and may also possess some gentle convex corners. The general case of curved walls is then obtained by a limiting process. The analysis in this general case leads to a set of two functional equations for which several
methods of solution are developed and discussed.
As a few typical examples the analysis is carried out in detail for the specific cases of wedges, two-step wedges, flapped hydrofoils, and inclined circular arc plate. For these cases the present theory is found in good agreement with the experimental results available
A wake model for free-streamline flow theory. Part 2. Cavity flows past obstacles of arbitrary profile
In Part 1 of this paper a free-streamline wake model mas introduced to treat the fully and partially developed wake flow or cavity flow past an oblique flat plate. This theory is generalized here to investigate the cavity flow past an obstacle of arbitrary profile at an arbitrary cavitation number. Consideration is first given to the cavity flow past a polygonal obstacle whose wetted sides may be concave
towards the flow and may also possess some gentle convex corners. The general case of curved walls is then obtained by a limiting process. The analysis in this general case leads to a set of two funnctional equations for which several methods of solutioii are developed and discussed.
As a few typictbl examples the analysis is carried out in detail for the specific cases of wedges, two-step wedges, flapped hydrofoils, and inclined circular arc plates. For these cases the present theory is found to be in good agreement with the experimental results available
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