4,614 research outputs found
Theoretical Study of Carbon Clusters in Silicon Carbide Nanowires
Using first-principles methods we performed a theoretical study of carbon
clusters in silicon carbide nanowires. We examined small clusters with carbon
interstitials and antisites in hydrogen-passivated SiC nanowires growth along
the [100] and [111] directions. The formation energies of these clusters were
calculated as a function of the carbon concentration. We verified that the
energetic stability of the carbon defects in SiC nanowires depends strongly on
the composition of the nanowire surface: the energetically most favorable
configuration in carbon-coated [100] SiC nanowire is not expected to occur in
silicon-coated [100] SiC nanowire. The binding energies of some aggregates were
also obtained, and they indicate that the formation of carbon clusters in SiC
nanowires is energetically favored.Comment: 6 pages, 5 figures; 8 pages,
http://www.hindawi.com/journals/jnt/2011/203423
Finite type modules and Bethe Ansatz for quantum toroidal gl(1)
We study highest weight representations of the Borel subalgebra of the
quantum toroidal gl(1) algebra with finite-dimensional weight spaces. In
particular, we develop the q-character theory for such modules. We introduce
and study the subcategory of `finite type' modules. By definition, a module
over the Borel subalgebra is finite type if the Cartan like current \psi^+(z)
has a finite number of eigenvalues, even though the module itself can be
infinite dimensional.
We use our results to diagonalize the transfer matrix T_{V,W}(u;p) analogous
to those of the six vertex model. In our setting T_{V,W}(u;p) acts in a tensor
product W of Fock spaces and V is a highest weight module over the Borel
subalgebra of quantum toroidal gl(1) with finite-dimensional weight spaces.
Namely we show that for a special choice of finite type modules the
corresponding transfer matrices, Q(u;p) and T(u;p), are polynomials in u and
satisfy a two-term TQ relation. We use this relation to prove the Bethe Ansatz
equation for the zeroes of the eigenvalues of Q(u;p). Then we show that the
eigenvalues of T_{V,W}(u;p) are given by an appropriate substitution of
eigenvalues of Q(u;p) into the q-character of V.Comment: Latex 42 page
Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles
Let be a sequence of
skew-symmetric polynomials in satisfying , whose coefficients are symmetric Laurent polynomials in . We
call an -cycle if
holds for all .
These objects arise in integral representations for form factors of massive
integrable field theory, i.e., the SU(2)-invariant Thirring model and the
sine-Gordon model. The variables are the integration
variables and are the rapidity variables. To each
-cycle there corresponds a form factor of the above models.
Conjecturally all form-factors are obtained from the -cycles.
In this paper, we define an action of
on the space of -cycles.
There are two sectors of -cycles depending on whether is even or
odd. Using this action, we show that the character of the space of even (resp.
odd) -cycles which are polynomials in is equal to the
level irreducible character of with lowest
weight (resp. ). We also suggest a possible tensor
product structure of the full space of -cycles.Comment: 27 pages, abstract and section 3.1 revise
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