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 $d$, where $d$ 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 ${\bf CP}^3$. 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 $n$-qubit ones related to Grassmannians of $l$-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 ${\bf CP}^3$ 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 $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field $W_\mu$ 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 $\delta$-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