12,895 research outputs found
The Value-of-Information in Matching with Queues
We consider the problem of \emph{optimal matching with queues} in dynamic
systems and investigate the value-of-information. In such systems, the
operators match tasks and resources stored in queues, with the objective of
maximizing the system utility of the matching reward profile, minus the average
matching cost. This problem appears in many practical systems and the main
challenges are the no-underflow constraints, and the lack of matching-reward
information and system dynamics statistics. We develop two online matching
algorithms: Learning-aided Reward optimAl Matching () and
Dual- () to effectively resolve both challenges.
Both algorithms are equipped with a learning module for estimating the
matching-reward information, while incorporates an additional
module for learning the system dynamics. We show that both algorithms achieve
an close-to-optimal utility performance for any
, while achieves a faster convergence speed and a
better delay compared to , i.e., delay and convergence under
compared to delay and convergence under
( and are maximum estimation errors for
reward and system dynamics). Our results reveal that information of different
system components can play very different roles in algorithm performance and
provide a systematic way for designing joint learning-control algorithms for
dynamic systems
Bogoliubov transformations and exact isolated solutions for simple non-adiabatic Hamiltonians
We present a new method for finding isolated exact solutions of a class of
non-adiabatic Hamiltonians of relevance to quantum optics and allied areas.
Central to our approach is the use of Bogoliubov transformations of the bosonic
fields in the models. We demonstrate the simplicity and efficiency of this
method by applying it to the Rabi Hamiltonian.Comment: LaTeX, 16 pages, 1 figure. Minor additions and journal re
Exact isolated solutions for the two-photon Rabi Hamiltonian
The two-photon Rabi Hamiltonian is a simple model describing the interaction
of light with matter, with the interaction being mediated by the exchange of
two photons. Although this model is exactly soluble in the rotating-wave
approximation, we work with the full Hamiltonian, maintaining the
non-integrability of the model. We demonstrate that, despite this
non-integrability, there exist isolated, exact solutions for this model
analogous to the so-called Juddian solutions found for the single-photon Rabi
Hamiltonian. In so doing we use a Bogoliubov transformation of the field mode,
as described by the present authors in an earlier publication.Comment: 15 Pages, 1 Figure, Latex, minor change
Phase Transitions in the Spin-Half J_1--J_2 Model
The coupled cluster method (CCM) is a well-known method of quantum many-body
theory, and here we present an application of the CCM to the spin-half J_1--J_2
quantum spin model with nearest- and next-nearest-neighbour interactions on the
linear chain and the square lattice. We present new results for ground-state
expectation values of such quantities as the energy and the sublattice
magnetisation. The presence of critical points in the solution of the CCM
equations, which are associated with phase transitions in the real system, is
investigated. Completely distinct from the investigation of the critical
points, we also make a link between the expansion coefficients of the
ground-state wave function in terms of an Ising basis and the CCM ket-state
correlation coefficients. We are thus able to present evidence of the
breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which
is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any
bipartite lattice. For the square lattice, our best estimates of the points at
which the sign rule breaks down and at which the phase transition from the
antiferromagnetic phase to the frustrated phase occurs are, respectively, given
(to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure
High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model
In this article, we present new results of high-order coupled cluster method
(CCM) calculations, based on a N\'eel model state with spins aligned in the
-direction, for both the ground- and excited-state properties of the
spin-half {\it XXZ} model on the linear chain, the square lattice, and the
simple cubic lattice. In particular, the high-order CCM formalism is extended
to treat the excited states of lattice quantum spin systems for the first time.
Completely new results for the excitation energy gap of the spin-half {\it XXZ}
model for these lattices are thus determined. These high-order calculations are
based on a localised approximation scheme called the LSUB scheme in which we
retain all -body correlations defined on all possible locales of
adjacent lattice sites (). The ``raw'' CCM LSUB results are seen to
provide very good results for the ground-state energy, sublattice
magnetisation, and the value of the lowest-lying excitation energy for each of
these systems. However, in order to obtain even better results, two types of
extrapolation scheme of the LSUB results to the limit (i.e.,
the exact solution in the thermodynamic limit) are presented. The extrapolated
results provide extremely accurate results for the ground- and excited-state
properties of these systems across a wide range of values of the anisotropy
parameter.Comment: 31 Pages, 5 Figure
A new method for the determination of thin film porosity
Internal reflection spectroscopy may be used to determine presence of water in thin film pores. Presence of water in such pores is function of relative humidity and pore size. Thus, one can determine pore size by controlling humidity. Fluids with surface tension different from that of water can be used to detect pores
Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin- Models
We apply the microscopic coupled-cluster method (CCM) to the spin-
models on both the one-dimensional chain and the two-dimensional square
lattice. Based on a systematic approximation scheme of the CCM developed by us
previously, we carry out high-order {\it ab initio} calculations using
computer-algebraic techniques. The ground-state properties of the models are
obtained with high accuracy as functions of the anisotropy parameter.
Furthermore, our CCM analysis enables us to study their quantum critical
behavior in a systematic and unbiased manner.Comment: (to appear in PRL). 4 pages, ReVTeX, two figures available upon
request. UMIST Preprint MA-000-000
Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method
We outline how the coupled cluster method of microscopic quantum many-body
theory can be utilized in practice to give highly accurate results for the
ground-state properties of a wide variety of highly frustrated and strongly
correlated spin-lattice models of interest in quantum magnetism, including
their quantum phase transitions. The method itself is described, and it is
shown how it may be implemented in practice to high orders in a systematically
improvable hierarchy of (so-called LSUB) approximations, by the use of
computer-algebraic techniques. The method works from the outset in the
thermodynamic limit of an infinite lattice at all levels of approximation, and
it is shown both how the "raw" LSUB results are themselves generally
excellent in the sense that they converge rapidly, and how they may accurately
be extrapolated to the exact limit, , of the truncation
index , which denotes the {\it only} approximation made. All of this is
illustrated via a specific application to a two-dimensional, frustrated,
spin-half -- model on a honeycomb lattice with
nearest-neighbor and next-nearest-neighbor interactions with exchange couplings
and , respectively, where both
interactions are of the same anisotropic type. We show how the method can
be used to determine the entire zero-temperature ground-state phase diagram of
the model in the range of the frustration parameter and
of the spin-space anisotropy parameter. In particular,
we identify a candidate quantum spin-liquid region in the phase space
Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems
We study a square-lattice spin-half Heisenberg model where frustration is
introduced by competing nearest-neighbor bonds of different signs. We discuss
the influence of quantum fluctuations on the nature of the zero-temperature
phase transitions from phases with collinear magnetic order at small
frustration to phases with noncollinear spiral order at large frustration. We
use the coupled cluster method (CCM) for high orders of approximation (up to
LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to
calculate ground-state properties. The role of quantum fluctuations is examined
by comparing the ferromagnetic-spiral and the antiferromagnetic-spiral
transition within the same model. We find clear evidence that quantum
fluctuations prefer collinear order and that they may favour a first order
transition instead of a second order transition in case of no quantum
fluctuations.Comment: 6 pages, 6 Postscipt figures; Accepted for publication in Phys. Rev.
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