Energy-momentum and angular momentum densities in gauge theories of gravity

In the \bar{\mbox{\rm Poincar\'{e}}} gauge theory of gravity, which has been formulated on the basis of a principal fiber bundle over the space-time manifold having the covering group of the proper orthochronous Poincar\'{e} group as the structure group, we examine the tensorial properties of the dynamical energy-momentum density ${}^{G}{\mathbf T}_{k}{}^{\mu}$ and the ` ` spin" angular momentum density ${}^{G}{\mathbf S}_{kl}{}^{\mu}$ of the gravitational field. They are both space-time vector densities, and transform as tensors under {\em global} $SL(2,C)$- transformations. Under {\em local} internal translation, ${}^{G}{\mathbf T}_{k}{}^{\mu}$ is invariant, while ${}^{G}{\mathbf S}_{kl}{}^{\mu}$ transforms inhomogeneously. The dynamical energy-momentum density ${}^{M}{\mathbf T}_{k}{}^{\mu}$ and the ` ` spin" angular momentum density ${}^{M}{\mathbf S}_{kl}{}^{\mu}$ of the matter field are also examined, and they are known to be space-time vector densities and to obey tensorial transformation rules under internal \bar{\mbox{\rm Poincar\'{e}}} gauge transformations. The corresponding discussions in extended new general relativity which is obtained as a teleparallel limit of \bar{\mbox{\rm Poincar\'{e}}} gauge theory are also given, and energy-momentum and ` ` spin" angular momentum densities are known to be well behaved. Namely, they are all space-time vector densities, etc. In both theories, integrations of these densities on a space-like surface give the total energy-momentum and {\em total} (={\em spin}+{\em orbital}) angular momentum for asymptotically flat space-time. The tensorial properties of canonical energy-momentum and ` ` extended orbital angular momentum" densities are also examined.Comment: 18 page

Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing

In the asymptotic setting, the optimal test for hypotheses testing of the maximally entangled state is derived under several locality conditions for measurements. The optimal test is obtained in several cases with the asymptotic framework as well as the finite-sample framework. In addition, the experimental scheme for the optimal test is presented

Determining Structurally Identifiable Parameter Combinations Using Subset Profiling

Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the dependencies between unidentifiable parameters. Identifiable combinations can help in model reparameterization and also in determining which parameters may be experimentally measured to recover model identifiability. Several numerical approaches to determining identifiability of differential equation models have been developed, however the question of determining identifiable combinations remains incompletely addressed. In this paper, we present a new approach which uses parameter subset selection methods based on the Fisher Information Matrix, together with the profile likelihood, to effectively estimate identifiable combinations. We demonstrate this approach on several example models in pharmacokinetics, cellular biology, and physiology

The Depressing Effect of Agricultural Institutions on the Prewar Japanese Economy

The question we address in this paper is why the Japanese miracle didn't take place until after World War II. For much of the pre-WWII period, Japan's real GNP per worker was not much more than a third of that of the U.S., with falling capital intensity. We argue that its major cause is a barrier that kept agricultural employment constant at about 14 million throughout the prewar period. In our two-sector neoclassical growth model, the barrier-induced sectoral mis-allocation of labor and a resulting disincentive for capital accumulation account well for the depressed output level. Were it not for the barrier, Japan's prewar GNP per worker would have been close to a half of the U.S. The labor barrier existed because, we argue, the prewar patriarchy, armed with paternalistic clauses in the prewar Civil Code, forced the son designated as heir to stay in agriculture.

Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation

We discuss two quantum analogues of Fisher information, symmetric logarithmic derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher information from a large deviation viewpoint of quantum estimation and prove that the former gives the true bound and the latter gives the bound of consistent superefficient estimators. In another comparison, it is shown that the difference between them is characterized by the change of the order of limits.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.st

Universal approximation of multi-copy states and universal quantum lossless data compression

We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning `approximation error' up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression

Cluster induced quenching of galaxies in the massive cluster XMMXCSJ2215.9-1738 at z~1.5 traced by enhanced metallicities inside half R200

(Abridged) We explore the massive cluster XMMXCSJ2215.9-1738 at z~1.5 with KMOS spectroscopy of Halpha and [NII] covering a region that corresponds to about one virial radius. Using published spectroscopic redshifts of 108 galaxies in and around the cluster we computed the location of galaxies in the projected velocity vs. position phase-space to separate our cluster sample into a virialized region of objects accreted longer ago (roughly inside half R200) and a region of infalling galaxies. We measured oxygen abundances for ten cluster galaxies with detected [NII] lines in the individual galaxy spectra and compared the MZR of the galaxies inside half R200 with the infalling galaxies and a field sample at similar redshifts. We find that the oxygen abundances of individual z~1.5 star-forming cluster galaxies inside half R200 are comparable, at the respective stellar mass, to the higher local SDSS metallicity values. We find that the [NII]/Halpha line ratios inside half R200 are higher by 0.2 dex and that the resultant metallicities of the galaxies in the inner part of the cluster are higher by about 0.1 dex, at a given mass, than the metallicities of infalling galaxies and of field galaxies at z~1.5. The enhanced metallicities of cluster galaxies at z~1.5 inside half R200 indicate that the density of the ICM in this massive cluster becomes high enough toward the cluster center such that the ram pressure exceeds the restoring pressure of the hot gas reservoir of cluster galaxies. This can remove the gas reservoir initiating quenching; although the galaxies continue to form stars, albeit at slightly lower rates, using the available cold gas in the disk which is not stripped.Comment: Accepted for publication in A&

Changepoint Problem in Quantumn Setting

In the changepoint problem, we determine when the distribution observed has changed to another one. We expand this problem to the quantum case where copies of an unknown pure state are being distributed. We study the fundamental case, which has only two candidates to choose. This problem is equal to identifying a given state with one of the two unknown states when multiple copies of the states are provided. In this paper, we assume that two candidate states are distributed independently and uniformly in the space of the whole pure states. The minimum of the averaged error probability is given and the optimal POVM is defined as to obtain it. Using this POVM, we also compute the error probability which depends on the inner product. These analytical results allow us to calculate the value in the asymptotic case, where this problem approaches to the usual discrimination problem

Asymptotic estimation theory for a finite dimensional pure state model

The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurement for one sample.Comment: LaTeX, 23 pages, Doctoral Thesi