11,453 research outputs found
Supersymmetry on Jacobstahl lattices
It is shown that the construction of Yang and Fendley (2004 {\it J. Phys. A:
Math.Gen. {\bf 37}} 8937) to obtainsupersymmetric systems, leads not to the
open XXZ chain with anisotropy but to systems having
dimensions given by Jacobstahl sequences.For each system the ground state is
unique. The continuum limit of the spectra of the Jacobstahl systems coincide,
up to degeneracies, with that of the invariant XXZ chain for
. The relation between the Jacobstahl systems and the open XXZ
chain is explained.Comment: 6 pages, 0 figure
The two-boundary Temperley-Lieb algebra
We study a two-boundary extension of the Temperley-Lieb algebra which has
recently arisen in statistical mechanics. This algebra lies in a quotient of
the affine Hecke algebra of type C and has a natural diagrammatic
representation. The algebra has three parameters and, for generic values of
these, we determine its representation theory.
We use the action of the centre of the affine Hecke algebra to show that all
irreducible representations lie within a finite dimensional diagrammatic
quotient. These representations are fully characterised by an additional
parameter related to the action of the centre. For generic values of this
parameter there is a unique representation of dimension 2^N and we show that it
is isomorphic to a tensor space representation. We construct a basis in which
the Gram matrix is diagonal and use this to discuss the irreducibility of this
representation.Comment: 45 pages Latex, 21 eps figures, revised versio
New Models for UO2 Fuel Structure Evolution under Irradiation in Fast Reactors
On the base of analysis of experimental observations and critical assessment
of existing models for oxide fuel structure evolution under operation
conditions of fast reactors, new models for fuel restructuring and coring are
proposed. The restructuring model describes coherent motion in the temperature
gradient of various voids (gas bubbles, sintering pores and large lenticular
pores) and grain boundaries, to which the voids are attached. As a result, the
model explains elongation of thermally growing equiaxed grains and formation of
columnar grains, and predicts a rapid formation of extended columnar grain zone
during a relatively short initial period of fast reactor irradiation. The
coring model describes formation and growth of the central void in the fuel
pellet, activated by mass transport from the inner to the outer zone of the
pellet under stresses induced by inhomogeneous fuel densification in the
initial period of irradiation.Comment: 17 pages, 7 Figure
Structure of the two-boundary XXZ model with non-diagonal boundary terms
We study the integrable XXZ model with general non-diagonal boundary terms at
both ends. The Hamiltonian is considered in terms of a two boundary extension
of the Temperley-Lieb algebra.
We use a basis that diagonalizes a conserved charge in the one-boundary case.
The action of the second boundary generator on this space is computed. For the
L-site chain and generic values of the parameters we have an irreducible space
of dimension 2^L. However at certain critical points there exists a smaller
irreducible subspace that is invariant under the action of all the bulk and
boundary generators. These are precisely the points at which Bethe Ansatz
equations have been formulated. We compute the dimension of the invariant
subspace at each critical point and show that it agrees with the splitting of
eigenvalues, found numerically, between the two Bethe Ansatz equations.Comment: 9 pages Latex. Minor correction
Equivalences between spin models induced by defects
The spectrum of integrable spin chains are shown to be independent of the
ordering of their spins. As an application we introduce defects (local spin
inhomogeneities in homogenous chains) in two-boundary spin systems and, by
changing their locations, we show the spectral equivalence of different
boundary conditions. In particular we relate certain nondiagonal boundary
conditions to diagonal ones.Comment: 14 pages, 16 figures, LaTeX, Extended versio
Parallelization of adaptive MC Integrators
Monte Carlo (MC) methods for numerical integration seem to be embarassingly
parallel on first sight. When adaptive schemes are applied in order to enhance
convergence however, the seemingly most natural way of replicating the whole
job on each processor can potentially ruin the adaptive behaviour. Using the
popular VEGAS-Algorithm as an example an economic method of semi-micro
parallelization with variable grain-size is presented and contrasted with
another straightforward approach of macro-parallelization. A portable
implementation of this semi-micro parallelization is used in the xloops-project
and is made publicly available.Comment: 10 pages, LaTeX2e, 1 pstricks-figure included and 2 eps-figures
inserted via epsfig. To appear in Comput. Phys. Commu
Boundary energy of the general open XXZ chain at roots of unity
We have recently proposed a Bethe Ansatz solution of the open spin-1/2 XXZ
quantum spin chain with general integrable boundary terms (containing six free
boundary parameters) at roots of unity. We use this solution, together with an
appropriate string hypothesis, to compute the boundary energy of the chain in
the thermodynamic limit.Comment: 22 pages, 6 figures; v2: some comments, a reference and a footnote
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Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
We show that from the spectra of the U_q (sl(2)) symmetric XXZ spin-1/2
finite quantum chain at Delta=-1/2 (q=e^{pi i/3}) one can obtain the spectra of
certain XXZ quantum chains with diagonal and non-diagonal boundary conditions.
Similar observations are made for Delta=0 (q=e^{pi i/2}). In the finite-size
scaling limit the relations among the various spectra are the result of
identities satisfied by known character functions. For the finite chains the
origin of the remarkable spectral identities can be found in the representation
theory of one and two boundaries Temperley-Lieb algebras at exceptional points.
Inspired by these observations we have discovered other spectral identities
between chains with different boundary conditions.Comment: 29 page
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