9,702 research outputs found
A Markov Chain Monte Carlo approach for measurement of jet precession in radio-loud active galactic nuclei
© 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.Jet precession can reveal the presence of binary systems of supermassive black holes. The ability to accurately measure the parameters of jet precession from radio-loud AGN is important for constraining the binary supermassive black hole population, which are expected as a result of hierarchical galaxy evolution. The age, morphology, and orientation along the line of sight of a given source often result in uncertainties regarding jet path. This paper presents a new approach for efficient determination of precession parameters using a 2D MCMC curve-fitting algorithm which provides us a full posterior probability distribution on the fitted parameters. Applying the method to Cygnus A, we find evidence for previous suggestions that the source is precessing. Interpreted in the context of binary black holes leads to a constraint of parsec scale and likely sub-parsec orbital separation for the putative supermassive binary.Peer reviewe
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
The symmetry algebras of certain families of quantum spin chains are
considered in detail. The simplest examples possess m states per site (m\geq2),
with nearest-neighbor interactions with U(m) symmetry, under which the sites
transform alternately along the chain in the fundamental m and its conjugate
representation \bar{m}. We find that these spin chains, even with {\em
arbitrary} coefficients of these interactions, have a symmetry algebra A_m much
larger than U(m), which implies that the energy eigenstates fall into sectors
that for open chains (i.e., free boundary conditions) can be labeled by j=0, 1,
>..., L, for the 2L-site chain, such that the degeneracies of all eigenvalues
in the jth sector are generically the same and increase rapidly with j. For
large j, these degeneracies are much larger than those that would be expected
from the U(m) symmetry alone. The enlarged symmetry algebra A_m(2L) consists of
operators that commute in this space of states with the Temperley-Lieb algebra
that is generated by the set of nearest-neighbor interaction terms; A_m(2L) is
not a Yangian. There are similar results for supersymmetric chains with
gl(m+n|n) symmetry of nearest-neighbor interactions, and a richer
representation structure for closed chains (i.e., periodic boundary
conditions). The symmetries also apply to the loop models that can be obtained
from the spin chains in a spacetime or transfer matrix picture. In the loop
language, the symmetries arise because the loops cannot cross. We further
define tensor products of representations (for the open chains) by joining
chains end to end. The fusion rules for decomposing the tensor product of
representations labeled j_1 and j_2 take the same form as the Clebsch-Gordan
series for SU(2). This and other structures turn the symmetry algebra \cA_m
into a ribbon Hopf algebra, and we show that this is ``Morita equivalent'' to
the quantum group U_q(sl_2) for m=q+q^{-1}. The open-chain results are extended
to the cases |m|< 2 for which the algebras are no longer semisimple; these
possess continuum limits that are critical (conformal) field theories, or
massive perturbations thereof. Such models, for open and closed boundary
conditions, arise in connection with disordered fermions, percolation, and
polymers (self-avoiding walks), and certain non-linear sigma models, all in two
dimensions. A product operation is defined in a related way for the
Temperley-Lieb representations also, and the fusion rules for this are related
to those for A_m or U_q(sl_2) representations; this is useful for the continuum
limits also, as we discuss in a companion paper
Associative-algebraic approach to logarithmic conformal field theories
We set up a strategy for studying large families of logarithmic conformal
field theories by using the enlarged symmetries and non--semi-simple
associative algebras appearing in their lattice regularizations (as discussed
in a companion paper). Here we work out in detail two examples of theories
derived as the continuum limit of XXZ spin-1/2 chains, which are related to
spin chains with supersymmetry algebras gl() and gl(),
respectively, with open (or free) boundary conditions in all cases. These
theories can also be viewed as vertex models, or as loop models. Their
continuum limits are boundary conformal field theories (CFTs) with central
charge and respectively, and in the loop interpretation they
describe dense polymers and the boundaries of critical percolation clusters,
respectively. We also discuss the case of dilute (critical) polymers as another
boundary CFT with . Within the supersymmetric formulations, these boundary
CFTs describe the fixed points of certain nonlinear sigma models that have a
supercoset space as the target manifold, and of Landau-Ginzburg field theories.
The submodule structures of indecomposable representations of the Virasoro
algebra appearing in the boundary CFT, representing local fields, are derived
from the lattice. A central result is the derivation of the fusion rules for
these fields
Kondo effect in a double quantum-dot molecule under the effect of an electric and magnetic field
Electron tunneling through a double quantum dot molecule, in the Kondo
regime, under the effect of a magnetic field and an applied voltage, is
studied. This system possesses a complex response to the applied fields
characterized by a tristable solution for the conductance. The different nature
of the solutions are studied in and out thermodynamical equilibrium. It is
shown that the interdot coupling and the fields can be used to control the
region of multistability. The mean-field slave-boson formalism is used to
obtain the solution of the problem.Comment: 5 pages, 4 figures. To appear in Sol. State Com
Bimodule structure in the periodic gl(1|1) spin chain
This paper is second in a series devoted to the study of periodic super-spin
chains. In our first paper at 2011, we have studied the symmetry algebra of the
periodic gl(1|1) spin chain. In technical terms, this spin chain is built out
of the alternating product of the gl(1|1) fundamental representation and its
dual. The local energy densities - the nearest neighbor Heisenberg-like
couplings - provide a representation of the Jones Temperley Lieb (JTL) algebra.
The symmetry algebra is then the centralizer of JTL, and turns out to be
smaller than for the open chain, since it is now only a subalgebra of U_q sl(2)
at q=i, dubbed U_q^{odd} sl(2). A crucial step in our associative algebraic
approach to bulk logarithmic conformal field theory (LCFT) is then the analysis
of the spin chain as a bimodule over U_q^{odd} sl(2) and JTL. While our
ultimate goal is to use this bimodule to deduce properties of the LCFT in the
continuum limit, its derivation is sufficiently involved to be the sole subject
of this paper. We describe representation theory of the centralizer and then
use it to find a decomposition of the periodic gl(1|1) spin chain over JTL for
any even number N of tensorands and ultimately a corresponding bimodule
structure. Applications of our results to the analysis of the bulk LCFT will
then be discussed in the third part of this series.Comment: latex, 42 pp., 13 figures + 5 figures in color, many comments adde
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