8,467 research outputs found
Invariant and polynomial identities for higher rank matrices
We exhibit explicit expressions, in terms of components, of discriminants,
determinants, characteristic polynomials and polynomial identities for matrices
of higher rank. We define permutation tensors and in term of them we construct
discriminants and the determinant as the discriminant of order , where
is the dimension of the matrix. The characteristic polynomials and the
Cayley--Hamilton theorem for higher rank matrices are obtained there from
On the geometry of four qubit invariants
The geometry of four-qubit entanglement is investigated. We replace some of
the polynomial invariants for four-qubits introduced recently by new ones of
direct geometrical meaning. It is shown that these invariants describe four
points, six lines and four planes in complex projective space . For
the generic entanglement class of stochastic local operations and classical
communication they take a very simple form related to the elementary symmetric
polynomials in four complex variables. Moreover, their magnitudes are
entanglement monotones that fit nicely into the geometric set of -qubit ones
related to Grassmannians of -planes found recently. We also show that in
terms of these invariants the hyperdeterminant of order 24 in the four-qubit
amplitudes takes a more instructive form than the previously published
expressions available in the literature. Finally in order to understand two,
three and four-qubit entanglement in geometric terms we propose a unified
setting based on furnished with a fixed quadric.Comment: 19 page
Universal field equations for metric-affine theories of gravity
We show that almost all metric--affine theories of gravity yield Einstein
equations with a non--null cosmological constant . Under certain
circumstances and for any dimension, it is also possible to incorporate a Weyl
vector field and therefore the presence of an anisotropy. The viability
of these field equations is discussed in view of recent astrophysical
observations.Comment: 13 pages. This is a copy of the published paper. We are posting it
here because of the increasing interest in f(R) theories of gravit
Optimal signal states for quantum detectors
Quantum detectors provide information about quantum systems by establishing
correlations between certain properties of those systems and a set of
macroscopically distinct states of the corresponding measurement devices. A
natural question of fundamental significance is how much information a quantum
detector can extract from the quantum system it is applied to. In the present
paper we address this question within a precise framework: given a quantum
detector implementing a specific generalized quantum measurement, what is the
optimal performance achievable with it for a concrete information readout task,
and what is the optimal way to encode information in the quantum system in
order to achieve this performance? We consider some of the most common
information transmission tasks - the Bayes cost problem (of which minimal error
discrimination is a special case), unambiguous message discrimination, and the
maximal mutual information. We provide general solutions to the Bayesian and
unambiguous discrimination problems. We also show that the maximal mutual
information has an interpretation of a capacity of the measurement, and derive
various properties that it satisfies, including its relation to the accessible
information of an ensemble of states, and its form in the case of a
group-covariant measurement. We illustrate our results with the example of a
noisy two-level symmetric informationally complete measurement, for whose
capacity we give analytical proofs of optimality. The framework presented here
provides a natural way to characterize generalized quantum measurements in
terms of their information readout capabilities.Comment: 13 pages, 1 figure, example section extende
High-spatial-resolution observations of NH3 and CH3OH towards the massive twin cores NGC6334 I & I(N)
Molecular line observations of NH3 (J,K)=(1,1), (2,2) and CH3OH at 24.93GHz
taken with the Australian Telescope Compact Array (ATCA) toward the massive
twin cores NGC6334 I & I(N) reveal significant variations in the line emission
between the two massive cores. The UCHII region/hot core NGC6334 I exhibits
strong thermal NH3 and CH3OH emission adjacent to the UCHII region and
coincident with two mm continuum peaks observed by Hunter et al. (in prep.). In
contrast, we find neither compact NH3 nor thermal CH3OH line emission toward
NGC6334 I(N). There, the NH3 emission is distributed over a broad region (>1')
without a clear peak, and we find Class I CH3OH maser emission with peak
brightness temperatures up to 7000K. The maser emission peaks appear to be
spatially associated with the interfaces between the molecular outflows and the
ambient dense gas. Peak NH3(1,1) line brightness temperatures >= 70K in both
regions indicate gas temperatures of the same order. NH3 emission is also
detected toward the outflow in NGC6334 I resulting in an estimated rotational
temperature of Trot~19K. Furthermore, we observe CH3OH and NH3 absorption
toward the UCHII region, the velocity structure is consistent with expanding
molecular gas around the UCHII region. Thermal and kinematic effects possibly
imposed from the UCHII region on the molecular core are also discussed.Comment: Accepted for the Astrophysical Journa
Discovery of New Milky Way Star Cluster Candidates in the 2MASS Point Source Catalog II. Physical Properties of the Star Cluster CC01
Three new obscured Milky Way clusters were detected as surface density peaks
in the 2MASS point source catalog during our on-going search for hidden
globular clusters and massive Arches-like star clusters. One more cluster was
discovered serendipitously during a visual inspection of the candidates.
The first deep J, H, and Ks imaging of the cluster [IBP2002] CC01 is
presented. We estimated a cluster age of ~1-3 Myr, distance modulus of
(m-M)0=12.56+-0.08 mag (D=3.5 Kpc), and extinction of AV~7.7 mag. We also
derived the initial mass function slope for the cluster: Gamma=-2.23+-0.16. The
integration over the initial mass function yielded a total cluster mass
M_{total}<=1800+-200Msol. CC01 appears to be a regular, not very massive star
cluster, whose formation has probably been induced by the shock front from the
nearby HII region Sh2-228.Comment: 8 pages, 9 figures, accepted in A&
Three Bosons in One Dimension with Short Range Interactions I: Zero Range Potentials
We consider the three-boson problem with -function interactions in
one spatial dimension. Three different approaches are used to calculate the
phase shifts, which we interpret in the context of the effective range
expansion, for the scattering of one free particle a off of a bound pair. We
first follow a procedure outlined by McGuire in order to obtain an analytic
expression for the desired S-matrix element. This result is then compared to a
variational calculation in the adiabatic hyperspherical representation, and to
a numerical solution to the momentum space Faddeev equations. We find excellent
agreement with the exact phase shifts, and comment on some of the important
features in the scattering and bound-state sectors. In particular, we find that
the 1+2 scattering length is divergent, marking the presence of a zero-energy
resonance which appears as a feature when the pair-wise interactions are
short-range. Finally, we consider the introduction of a three-body interaction,
and comment on the cutoff dependence of the coupling.Comment: 9 figures, 2 table
A BRIEF REVIEW ON THE ADVANTAGES, HINDRANCES AND ECONOMIC FEASIBILITY OF STIRLING ENGINES AS A DISTRIBUTED GENERATION SOURCE AND COGENERATION TECHNOLOGY
The present paper aims to provide a brief review of the potentiality and economic feasibility of the Stirling engine as a distributed generation source and cogeneration technology. Another objective was the determination of hindrances which may be preventing the feasibility of the Stirling technology. With these intentions, a research based on a combination of preselected keywords was performed at the Metasearch of CAPES (Brazil's Higher Education Coordination of Personnel Perfecting). No filters in relation to the research period or to particular geographical regions were employed, thus publications until 2017’s middle were included and the research was conducted on a global level. Next, the selection of papers which contained some of the keywords was made, consisting initially of the read of the publications’ abstracts. The remaining ones were then further explored and had their relevant information incorporated, according to the scope of this work. It is worth mentioning that other accredited sources which dealt with important aspects of the topic were also included. Furthermore, a table containing some examples of products concerning the application of the Stirling engine as a distributed generation and cogeneration technology is presented. Ultimately, it is concluded that the Stirling technology, despite its advantages and suitability regarding the proposed applications, is not yet commercially feasible, having currently only a minor presence in the market. This scenario can be attributed to the need for further research and technical development as well as cost reduction
Palatini versus metric formulation in higher curvature gravity
We compare the metric and the Palatini formalism to obtain the Einstein
equations in the presence of higher-order curvature corrections that consist of
contractions of the Riemann tensor, but not of its derivatives. We find that
there is a class of theories for which the two formalisms are equivalent. This
class contains the Palatini version of Lovelock theory, but also more
Lagrangians that are not Lovelock, but respect certain symmetries. For the
general case, we find that imposing the Levi-Civita connection as an Ansatz,
the Palatini formalism is contained within the metric formalism, in the sense
that any solution of the former also appears as a solution of the latter, but
not necessarily the other way around. Finally we give the conditions the
solutions of the metric equations should satisfy in order to solve the Palatini
equations.Comment: 13 pages, latex. V2: reference added, major changes in section 3,
conclusions partially correcte
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