Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity properties of the eigenvalues. The methods are also used to examine further the pattern of eigenvalue degeneracies observed by Dorey et al. in [1,2].Comment: 22 pages, 13 figures. Added references, minor revision

The theory of international business: the role of economic models

This paper reviews the scope for economic modelling in international business studies. It argues for multi-level theory based on classic internalisation theory. It present a systems approach that encompasses both firm-level and industry-level analysis

Cost effective, experimentally robust differential-expression analysis for human/mammalian, pathogen and dual-species transcriptomics.

As sequencing read length has increased, researchers have quickly adopted longer reads for their experiments. Here, we examine 14 pathogen or host-pathogen differential gene expression data sets to assess whether using longer reads is warranted. A variety of data sets was used to assess what genomic attributes might affect the outcome of differential gene expression analysis including: gene density, operons, gene length, number of introns/exons and intron length. No genome attribute was found to influence the data in principal components analysis, hierarchical clustering with bootstrap support, or regression analyses of pairwise comparisons that were undertaken on the same reads, looking at all combinations of paired and unpaired reads trimmed to 36, 54, 72 and 101 bp. Read pairing had the greatest effect when there was little variation in the samples from different conditions or in their replicates (e.g. little differential gene expression). But overall, 54 and 72 bp reads were typically most similar. Given differences in costs and mapping percentages, we recommend 54 bp reads for organisms with no or few introns and 72 bp reads for all others. In a third of the data sets, read pairing had absolutely no effect, despite paired reads having twice as much data. Therefore, single-end reads seem robust for differential-expression analyses, but in eukaryotes paired-end reads are likely desired to analyse splice variants and should be preferred for data sets that are acquired with the intent to be community resources that might be used in secondary data analyses

Geological setting and petrochemistry of early Middle Devonian volcanic and gabbroic rocks in the Guysborough area, Nova Scotia

Mapping, petrological studies, and U-Pb dating of volcanic and plutonic units have provided a new understanding of the stratigraphy and paleotectonic setting of rocks in the Guysborough area. From base to top, the stratigraphic sequence is interpreted to consist of: (1) volcanic flows and pyroclastic rocks, with minor interlayered sedimentary rocks (Sunnyville Formation), (2) varied conglomerate (Glenkeen Formation), (3) quartz wacke with minor interlayered quartz arenite and conglomerate, and (4) massive to shaly or laminated siltstone. These volcanic and sedimentary units arc intruded by small gabbroic plutons, sills, and dykes. All the units are early Middle Devonian, based on a U-Pb (zircon) age of 389 ± 2 Ma for rhyolitic tuff from the Sunnyville Formation, and a preliminary U-Pb (baddelcyite) age of ca. 38S Ma for one of the gabbroic plutons in the siltstone unit. Based on whole-rock chemistry, the mafic volcanic and gabbroic rocks are similar, and formed in a continental within-plate setting. However, the rocks in the eastern part of the map area are more alkalic than those in the west, which are dominantly tholeiitic. The mafic magmas are interpreted to have formed by partial melting of the subcontinental upper mantle and to have evolved by crystal fractionation processes; the more alkalic magmas in the east may represent lesser amounts of partial melting in that area. This interpretation is consistent with the presence of felsic volcanic rocks only in the western part of the area. They may represent crustal melts formed as a result of mafic magma underplating of the crust. The regional tectonic significance of these igneous rocks is not yet resolved, but they are clearly older than Late Devonian to Carboniferous igneous units elsewhere in northern mainland Nova Scotia and in Cape Breton Island with which they were previously assumed to be correlative. RÉSUMÉ Des travaux de cartographic, des études pétrologiques et la datation au U-Pb d'unités volcaniques et plutoniques ont permis une meilleure compréhension de la stratigraphic et du cadre paléotcctonique des roches du secteur de Guysborough. On interprèts la composition de la séquence stratigraphique comme suit, de sa base à son sommet : 1) des écoulements volcaniques et des roches pyroclastiques, avec une proportion mineure de roches sédimentaires intercalécs (Formation Sunnyville); 2) un conglomerat diversify (Formation Glenkeen); 3) de la wacke qurtzeuse avec une présence mineure de conglomerat et de quartzite sédimentaire interstratifies; et 4) des siltstones massifs à schistcux ou feuilletés. Ces unités volcaniques et sédimentaires sont pénétries par de petits dykes, filons-couches et plutons gabbrolques. Toutes les unités remontent au début du Dévonien moyen d'apres une datation au U-Pb (zircon) situant a 389+2 Ma le tuf rhyolitique de la Formation Sunnyville ainsi qu'une datation au U-Pb (baddeleyite) situant provisoirement l'un des plutons gabbrolques de l'unité de siltstones a environ 38S Ma. D'après la chimie des roches, les roches volcanomaflques et gabbrolques sont semblabes et elles se sont formées dans un cadre intra-plaque continental. Les roches de la partie orientate du secteur cartographique sont cependant plus alcalines que celles de l'ouest, en predominance tholéeiitiques. Selon l'interprétation avancée, les magmas mafiques se seraient formes par suite d'une fonte partielle du manteau sous-continental supérieur et ils auraient évolué au moyen de processus de différenciation magmatique; les magmas plus alcalins de l'est pourraient représentor une fonte partielle moins importante dans ce secteur. Cette interprétation est compatible avec la présence de roches volcano-felsiques limitée a la partie ouest du secteur. Elles pourraient représentor des éléments crustaux fondus formés par suite d'une remontée de magma mafique sous les plaques de la croûte. On n'a pas encore déterminé ('importance tectonique régionale dc ces roches ignées, mais elles sont clairement plus anciennes que les unités ignées du Dévonien supérieur au Carbonifère des autres régions de L'intérieur de la Nouvelle-Écosse et de l'ile du Cap-Breton avec lesquelles on les supposait auparavant corrélatives. [Traduit par la rédaction

Identification of observables in quantum toboggans

Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of states. The recipe is extended here to quantum toboggans. In the first step the tobogganic integration path is rectified and the Schroedinger equation is given the generalized eigenvalue-problem form. In the second step the general double-series representation of the eligible metric operators is derived.Comment: 25 p

Probing Nonlocal Spatial Correlations in Quantum Gases with Ultra-long-range Rydberg Molecules

We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the order of the thermal de Broglie wavelength for temperatures around 1 $\mu$K. We observe bunching for a single-component Bose gas of $^{84}$Sr and anti-bunching due to Pauli exclusion at short distances for a polarized Fermi gas of $^{87}$Sr, revealing the effects of quantum statistics.Comment: 6 pages, 5 figure

Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear sigma-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited state TBA equations agree within numerical precision.Comment: numerical results adde

Excited states nonlinear integral equations for an integrable anisotropic spin 1 chain

We propose a set of nonlinear integral equations to describe on the excited states of an integrable the spin 1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study on the supersymmetric sine-Gordon model.Comment: 15 pages, 2 Figures, typos correcte

A variational approach for the Quantum Inverse Scattering Method

We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability through the existence of a set of conserved operators. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC). The Hamiltonians considered describe systems with interacting Cooper pairs and a bosonic degree of freedom. We obtain general exact solvability requirements which include seven subcases which have previously appeared in the literature.Comment: 18 pages, no eps figure

Ground-state properties of the attractive one-dimensional Bose-Hubbard model

We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties like the gap between the ground and first excited energy levels, and the incremental ground-state wavefunction overlaps are used to locate different regimes. Using mean-field theory we predict that there are two distinct crossovers connected to spontaneous symmetry breaking of the ground state. The first crossover arises in an analysis valid for large L with finite N, where L is the number of lattice sites and N is the total particle number. An alternative approach valid for large N with finite L yields a second crossover. For small system sizes we numerically investigate the model and observe that there are signatures of both crossovers. We compare with exact results from Bethe ansatz methods in several limiting cases to explore the validity for these numerical and mean-field schemes. The results indicate that for finite attractive systems there are generically three ground-state phases of the model.Comment: 17 pages, 12 figures, Phys.Rev.B(accepted), minor changes and updated reference