18,219 research outputs found
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
Low-energy parameters and spin gap of a frustrated spin- Heisenberg antiferromagnet with on the honeycomb lattice
The coupled cluster method is implemented at high orders of approximation to
investigate the zero-temperature phase diagram of the frustrated
spin- ---- antiferromagnet on the honeycomb lattice.
The system has isotropic Heisenberg interactions of strength ,
and between nearest-neighbour, next-nearest-neighbour and
next-next-nearest-neighbour pairs of spins, respectively. We study it in the
case , in the window
that contains the classical tricritical point (at ) of maximal frustration, appropriate to the limiting value of the spin quantum number. We present results for the magnetic
order parameter , the triplet spin gap , the spin stiffness
and the zero-field transverse magnetic susceptibility for the
two collinear quasiclassical antiferromagnetic (AFM) phases with N\'{e}el and
striped order, respectively. Results for and are given for the
three cases , and , while those for
and are given for the two cases and . On
the basis of all these results we find that the spin- and spin-1
models both have an intermediate paramagnetic phase, with no discernible
magnetic long-range order, between the two AFM phases in their phase
diagrams, while for there is a direct transition between them. Accurate
values are found for all of the associated quantum critical points. While the
results also provide strong evidence for the intermediate phase being gapped
for the case , they are less conclusive for the case . On
balance however, at least the transition in the latter case at the striped
phase boundary seems to be to a gapped intermediate state
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
New space research frequency band proposals in the 20- to 40.5-GHz range
Future space research communications systems may require spectra above 20 GHz. Frequency bands above 20 GHz are identified that are suitable for space research. The selection of the proper bands depends on consideration of interference with other radio services, adequate bandwidths, link performance, and technical requirements for practical implementation
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
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
The Physics of Bicycling
Faculty reflection on VCU Great Bike Race Book course.
Course Description: The science of bicycling will be explored by measuring and observing key physical principles of the cyclist
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
The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation
The quantum many-body bound-state problem in its computationally successful
coupled cluster method (CCM) representation is reconsidered. In conventional
practice one factorizes the ground-state wave functions which live in the "physical" Hilbert space using
an elementary ansatz for plus a formal expansion of in an
operator basis of multi-configurational creation operators. In our paper a
reinterpretation of the method is proposed. Using parallels between the CCM and
the so called quasi-Hermitian, alias three-Hilbert-space (THS), quantum
mechanics, the CCM transition from the known microscopic Hamiltonian (denoted
by usual symbol ), which is self-adjoint in , to its
effective lower-case isospectral avatar , is assigned a
THS interpretation. In the opposite direction, a THS-prescribed, non-CCM,
innovative reinstallation of Hermiticity is shown to be possible for the CCM
effective Hamiltonian , which only appears manifestly non-Hermitian in
its own ("friendly") Hilbert space . This goal is achieved via
an ad hoc amendment of the inner product in , thereby yielding
the third ("standard") Hilbert space . Due to the resulting
exact unitary equivalence between the first and third spaces, , the indistinguishability of predictions
calculated in these alternative physical frameworks is guaranteed.Comment: 15 page
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