2,096,045 research outputs found
The Complex of Solutions of the Nested Bethe Ansatz. The A_2 Spin Chain
The full set of polynomial solutions of the nested Bethe Ansatz is
constructed for the case of A_2 rational spin chain. The structure and
properties of these associated solutions are more various then in the case of
usual XXX (A_1) spin chain but their role is similar
Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge
We use a de Sitter breaking graviton propagator to compute the tree order
correlator between noncoincident Weyl tensors on a locally de Sitter
background. An explicit, and very simple result is obtained, for any spacetime
dimension D, in terms of a de Sitter invariant length function and the tensor
basis constructed from the metric and derivatives of this length function. Our
answer does not agree with the one derived previously by Kouris, but that
result must be incorrect because it not transverse and lacks some of the
algebraic symmetries of the Weyl tensor. Taking the coincidence limit of our
result (with dimensional regularization) and contracting the indices gives the
expectation value of the square of the Weyl tensor at lowest order. We propose
the next order computation of this as a true test of de Sitter invariance in
quantum gravity.Comment: 31 pages, 2 tables, no figures, uses LaTex2
Ignorance is Almost Bliss: Near-Optimal Stochastic Matching With Few Queries
The stochastic matching problem deals with finding a maximum matching in a
graph whose edges are unknown but can be accessed via queries. This is a
special case of stochastic -set packing, where the problem is to find a
maximum packing of sets, each of which exists with some probability. In this
paper, we provide edge and set query algorithms for these two problems,
respectively, that provably achieve some fraction of the omniscient optimal
solution.
Our main theoretical result for the stochastic matching (i.e., -set
packing) problem is the design of an \emph{adaptive} algorithm that queries
only a constant number of edges per vertex and achieves a
fraction of the omniscient optimal solution, for an arbitrarily small
. Moreover, this adaptive algorithm performs the queries in only a
constant number of rounds. We complement this result with a \emph{non-adaptive}
(i.e., one round of queries) algorithm that achieves a
fraction of the omniscient optimum. We also extend both our results to
stochastic -set packing by designing an adaptive algorithm that achieves a
fraction of the omniscient optimal solution, again
with only queries per element. This guarantee is close to the best known
polynomial-time approximation ratio of for the
\emph{deterministic} -set packing problem [Furer and Yu, 2013]
We empirically explore the application of (adaptations of) these algorithms
to the kidney exchange problem, where patients with end-stage renal failure
swap willing but incompatible donors. We show on both generated data and on
real data from the first 169 match runs of the UNOS nationwide kidney exchange
that even a very small number of non-adaptive edge queries per vertex results
in large gains in expected successful matches
Quadratic Algebra associated with Rational Calogero-Moser Models
Classical Calogero-Moser models with rational potential are known to be
superintegrable. That is, on top of the r involutive conserved quantities
necessary for the integrability of a system with r degrees of freedom, they
possess an additional set of r-1 algebraically and functionally independent
globally defined conserved quantities. At the quantum level, Kuznetsov
uncovered the existence of a quadratic algebra structure as an underlying key
for superintegrability for the models based on A type root systems. Here we
demonstrate in a universal way the quadratic algebra structure for quantum
rational Calogero-Moser models based on any root systems.Comment: 19 pages, LaTeX2e, no figure
Further Series Studies of the Spin-1/2 Heisenberg Antiferromagnet at T=0: Magnon Dispersion and Structure Factors
We have extended our previous series studies of quantum antiferromagnets at
zero temperature by computing the one-magnon dispersion curves and various
structure factors for the linear chain, square and simple cubic lattices. Many
of these results are new; others are a substantial extension of previous work.
These results are directly comparable with neutron scattering experiments and
we make such comparisons where possible.Comment: 15 pages, 12 figures, revised versio
Phase Diagram of the J1, J2, J3 Heisenberg Models on the Honeycomb Lattice: A Series Expansion Study
We study magnetically ordered phases and their phase boundaries in the
Heisenberg models on the honeycomb lattice using series
expansions around N\'eel and different colinear and non-colinear magnetic
states. An Ising anisotropy () is introduced and
ground state energy and magnetization order parameter are calculated as a power
seies expansion in . Series extrapolation methods are used to study
properties for the Heisenberg model (). We find that at large
() there is a first order transition between N\'eel and columnar states,
in agreement with the classical answer. For , we find that the N\'eel
phase extends beyond the region of classical stability. We also find that
spiral phases are stabilized over large parameter regions, although their
spiral angles can be substantially renormalized with respect to the classical
values. Our study also shows a magnetically disordered region at intermedaite
and values.Comment: 6 pages, 9 figure
Ground state properties, excitation spectra and phase transitions in the and bilayer Heisenberg models on the honeycomb Lattice
Motivated by the observation of a disordered spin ground state in the
material BiMnONO, we study the ground state properties and
excitation spectra of the (and for comparison ) bilayer
Heisenberg model on the honeycomb lattice, with and without frustrating further
neighbor interactions. We use series expansions around the N\'eel state to
calculate properties of the magnetically ordered phase. Furthermore, series
expansions in , where is an in-plane exchange
constant and is the exchange constant between the layers are used to
study properties of the spin singlet phase. For the unfrustrated case, our
results for the phase transitions are in very good agreement with recent
Quantum Monte Carlo studies. We also obtain the excitation spectra in the
disordered phase and study the change in the critical when
frustrating exchange interactions are added to the system and find a
rapid suppression of the ordered phase with frustration. Implications for the
material BiMnONO are discussed.Comment: 5 pages, 6 figure
Theoretical Framework for Microscopic Osmotic Phenomena
The basic ingredients of osmotic pressure are a solvent fluid with a soluble
molecular species which is restricted to a chamber by a boundary which is
permeable to the solvent fluid but impermeable to the solute molecules. For
macroscopic systems at equilibrium, the osmotic pressure is given by the
classical van't Hoff Law, which states that the pressure is proportional to the
product of the temperature and the difference of the solute concentrations
inside and outside the chamber. For microscopic systems the diameter of the
chamber may be comparable to the length-scale associated with the solute-wall
interactions or solute molecular interactions. In each of these cases, the
assumptions underlying the classical van't Hoff Law may no longer hold. In this
paper we develop a general theoretical framework which captures corrections to
the classical theory for the osmotic pressure under more general relationships
between the size of the chamber and the interaction length scales. We also show
that notions of osmotic pressure based on the hydrostatic pressure of the fluid
and the mechanical pressure on the bounding walls of the chamber must be
distinguished for microscopic systems. To demonstrate how the theoretical
framework can be applied, numerical results are presented for the osmotic
pressure associated with a polymer of N monomers confined in a spherical
chamber as the bond strength is varied
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