Asymptotic properties of the development of conformally flat data near spatial infinity

Certain aspects of the behaviour of the gravitational field near null and spatial infinity for the developments of asymptotically Euclidean, conformally flat initial data sets are analysed. Ideas and results from two different approaches are combined: on the one hand the null infinity formalism related to the asymptotic characteristic initial value problem and on the other the regular Cauchy initial value problem at spatial infinity which uses Friedrich's representation of spatial infinity as a cylinder. The decay of the Weyl tensor for the developments of the class of initial data under consideration is analysed under some existence and regularity assumptions for the asymptotic expansions obtained using the cylinder at spatial infinity. Conditions on the initial data to obtain developments satisfying the Peeling Behaviour are identified. Further, the decay of the asymptotic shear on null infinity is also examined as one approaches spatial infinity. This decay is related to the possibility of selecting the Poincar\'e group out of the BMS group in a canonical fashion. It is found that for the class of initial data under consideration, if the development peels, then the asymptotic shear goes to zero at spatial infinity. Expansions of the Bondi mass are also examined. Finally, the Newman-Penrose constants of the spacetime are written in terms of initial data quantities and it is shown that the constants defined at future null infinity are equal to those at past null infinity.Comment: 24 pages, 1 figur

Summary of Munoz v. Branch Banking & Trust Co., 131 Nev. Adv. Op. No. 23 (Apr. 30, 2015)

NRS 40.459(1)(c)’s limitation on the amount of deficiency judgment that a successor can recover conflicts with the federal Financial Institutions Reform, Recovery and Enforcement Act’s (“FIRREA”) purpose of facilitating the transfer of assets of failed banks to other institutions. Because NRS 40.459(1)(c) limits the value a successor can recover on a deficiency judgment, its application to assets transferred by the Federal Deposit Insurance Corporation (“FDIC”) frustrates FIRREA’s purpose. Therefore, NRS 40.459(1)(c) is preempted by FIRREA to the extent that NRS 40.459(1)(c) limits deficiency judgment that may be obtained from loans transferred by the FDIC

Summary of Logan v. Abe, 131 Nev. Adv. Op. No. 31 (Jun. 4, 2015)

A party incurs an expense even if a third party pays the expense on the party’s behalf, as long as the party would otherwise be legally obligated to pay the expense. Thus, costs and reasonable attorney fees that a third party paid on behalf of a litigant can be recovered under NRS 17.115(4) and NRCP 68(f)(2). In addition, a party can recover expert witness fees even if the expert did not testify at trial and was not deposed

A rigidity property of asymptotically simple spacetimes arising from conformally flat data

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.Comment: 37 page

Summary of State v. Beaudion, 131 Nev. Adv. Op. No. 48 (Jul. 2, 2015)

NRS 172.241 affords the target of a grand jury investigation the opportunity to testify before them unless, after holding “a closed hearing on the matter,” the district court determines that adequate cause exists to withhold target notice. NRS 172.241(3) specifies that “[t]he district attorney may apply to the court for a determination that adequate cause exists to withhold notice, if the district attorney.... [d]etermines” that the target poses a flight risk, cannot be located or, as relevant here, “that the notice may endanger the life or property of other persons.” Accordingly, NRS 172.241’s procedure for withholding notice is met if the State presents sufficient evidence to the district court, through written application and/or at oral argument, should the court require it, to allow the court to conclude by written order that that adequate cause to withhold notice of the grand jury proceedings exists

Optical spectroscopy of rare-earth ions doped KY(WO4)2 thin films

KY(WO4)2 thin films doped with Dy3+, Tb3+, Yb3+, were grown onto KY(WO4)2 substrates using liquid-phase epitaxy. Spectroscopic investigations of the grown layers were performed. Obtained results were compared with spectra given for bulk crystals. Upconversion experiments after direct Yb3+ excitation in Dy3+-Yb3+ and Tb3+-Yb3+ codoped layers will be also presented

Strongly interacting confined quantum systems in one dimension

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and anti-ferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.Comment: 11 pages, 2 figures, including methods, final versio

Fractional energy states of strongly-interacting bosons in one dimension

We study two-component bosonic systems with strong inter-species and vanishing intra-species interactions. A new class of exact eigenstates is found with energies that are {\it not} sums of the single-particle energies with wave functions that have the characteristic feature that they vanish over extended regions of coordinate space. This is demonstrated in an analytically solvable model for three equal mass particles, two of which are identical bosons, which is exact in the strongly-interacting limit. We numerically verify our results by presenting the first application of the stochastic variational method to this kind of system. We also demonstrate that the limit where both inter- and intra-component interactions become strong must be treated with extreme care as these limits do not commute. Moreover, we argue that such states are generic also for general multi-component systems with more than three particles. The states can be probed using the same techniques that have recently been used for fermionic few-body systems in quasi-1D.Comment: 6 pages, 4 figures, published versio

Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension

The paper examines a trapped one-dimensional system of multicomponent spinless fermions that interact with a zero-range two-body potential. We show that when the repulsion between particles is very large the system can be approached analytically. To illustrate this analytical approach we consider a simple system of three distinguishable particles, which can be addressed experimentally. For this system we show that for infinite repulsion the energy spectrum is sixfold degenerate. We also show that this degeneracy is partially lifted for finitely large repulsion for which we find and describe corresponding wave functions.Comment: Paper in connection with the 22nd European Conference on Few-Body Problems in Physics, Krakow, Poland, 9-13 September 201

Lattice oscillator model, scattering theory and a many-body problem

We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring.Comment: 3 Figures. Version accepted in J. Phys.