544 research outputs found
Directed abelian algebras and their applications to stochastic models
To each directed acyclic graph (this includes some D-dimensional lattices)
one can associate some abelian algebras that we call directed abelian algebras
(DAA). On each site of the graph one attaches a generator of the algebra. These
algebras depend on several parameters and are semisimple. Using any DAA one can
define a family of Hamiltonians which give the continuous time evolution of a
stochastic process. The calculation of the spectra and ground state
wavefunctions (stationary states probability distributions) is an easy
algebraic exercise. If one considers D-dimensional lattices and choose
Hamiltonians linear in the generators, in the finite-size scaling the
Hamiltonian spectrum is gapless with a critical dynamic exponent . One
possible application of the DAA is to sandpile models. In the paper we present
this application considering one and two dimensional lattices. In the one
dimensional case, when the DAA conserves the number of particles, the
avalanches belong to the random walker universality class (critical exponent
). We study the local densityof particles inside large
avalanches showing a depletion of particles at the source of the avalanche and
an enrichment at its end. In two dimensions we did extensive Monte-Carlo
simulations and found .Comment: 14 pages, 9 figure
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
A refined Razumov-Stroganov conjecture II
We extend a previous conjecture [cond-mat/0407477] relating the
Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to
refined numbers of alternating sign matrices. By considering the O(1) loop
model on a semi-infinite cylinder with dislocations, we obtain the generating
function for alternating sign matrices with prescribed positions of 1's on
their top and bottom rows. This seems to indicate a deep correspondence between
observables in both models.Comment: 21 pages, 10 figures (3 in text), uses lanlmac, hyperbasics and epsf
macro
The "topological" charge for the finite XX quantum chain
It is shown that an operator (in general non-local) commutes with the
Hamiltonian describing the finite XX quantum chain with certain non-diagonal
boundary terms. In the infinite volume limit this operator gives the
"topological" charge.Comment: 5 page
Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
The raise and peel model of a one-dimensional fluctuating interface (model A)
is extended by considering one source (model B) or two sources (model C) at the
boundaries. The Hamiltonians describing the three processes have, in the
thermodynamic limit, spectra given by conformal field theory. The probability
of the different configurations in the stationary states of the three models
are not only related but have interesting combinatorial properties. We show
that by extending Pascal's triangle (which gives solutions to linear relations
in terms of integer numbers), to an hexagon, one obtains integer solutions of
bilinear relations. These solutions give not only the weights of the various
configurations in the three models but also give an insight to the connections
between the probability distributions in the stationary states of the three
models. Interestingly enough, Pascal's hexagon also gives solutions to a
Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few
references are adde
Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
We quantize the superstring on the AdS_2 x S^2 background with Ramond-Ramond
flux using a PSU(1,1|2)/U(1) x U(1) sigma model with a WZ term. One-loop
conformal invariance of the model is guaranteed by a general mechanism which
holds for coset spaces G/H where G is Ricci-flat and H is the invariant locus
of a Z_4 automorphism of G. This mechanism gives conformal theories for the
PSU(1,1|2) x PSU(2|2)/SU(2) x SU(2) and PSU(2,2|4)/SO(4,1) x SO(5) coset
spaces, suggesting our results might be useful for quantizing the superstring
on AdS_3 x S^3 and AdS_5 x S^5 backgrounds.Comment: 34 pages, 4 figures, harvmac big mode ; typos corrected, clarified
the choice of the real form
Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems
A representation theory of the quantized Poincar\'e (-Poincar\'e)
algebra (QPA) is developed. We show that the representations of this algebra
are closely connected with the representations of the non-deformed Poincar\'e
algebra. A theory of tensor operators for QPA is considered in detail.
Necessary and sufficient conditions are found in order for scalars to be
invariants. Covariant components of the four-momenta and the Pauli-Lubanski
vector are explicitly constructed.These results are used for the construction
of some q-relativistic equations. The Wigner-Eckart theorem for QPA is proven.Comment: 18 page
Homological algebra for osp(1/2n)
We discuss several topics of homological algebra for the Lie superalgebra
osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical
results although the cohomology is not given by the kernel of the Kostant
quabla operator. Based on this cohomology we can derive strong
Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules.
Then we state the Bott-Borel-Weil theorem which follows immediately from the
Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally
we calculate the projective dimension of irreducible and Verma modules in the
category O
Major depressive disorder is characterized by greater reward network activation to monetary than pleasant image rewards
Anhedonia, the loss of interest or pleasure in normally rewarding activities, is a hallmark feature of unipolar Major Depressive Disorder (MDD). A growing body of literature has identified frontostriatal dysfunction during reward anticipation and outcomes in MDD. However, no study to date has directly compared responses to different types of rewards such as pleasant images and monetary rewards in MDD. To investigate the neural responses to monetary and pleasant image rewards in MDD, a modified Monetary Incentive Delay task was used during fMRI scanning to assess neural responses during anticipation and receipt of monetary and pleasant image rewards. Participants included nine adults with MDD and thirteen affectively healthy controls. The MDD group showed lower activation than controls when anticipating monetary rewards in right orbitofrontal cortex and subcallosal cortex, and when anticipating pleasant image rewards in paracingulate and supplementary motor cortex. The MDD group had relatively greater activation in right putamen when anticipating monetary versus pleasant image rewards, relative to the control group. Results suggest reduced reward network activation in MDD when anticipating rewards, as well as relatively greater hypoactivation to pleasant image than monetary rewards
A deformed analogue of Onsager's symmetry in the XXZ open spin chain
The XXZ open spin chain with general integrable boundary conditions is shown
to possess a q-deformed analogue of the Onsager's algebra as fundamental
non-abelian symmetry which ensures the integrability of the model. This
symmetry implies the existence of a finite set of independent mutually
commuting nonlocal operators which form an abelian subalgebra. The transfer
matrix and local conserved quantities, for instance the Hamiltonian, are
expressed in terms of these nonlocal operators. It follows that Onsager's
original approach of the planar Ising model can be extended to the XXZ open
spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected,
clarifications in the text; v3: minor changes in references, version to
appear in JSTA
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