Trions in a periodic potential

The group-theoretical classification of trion states is presented. It is based on considerations of products of irreducible representations of the 2D translation group. For a given BvK period N degeneracy of obtained states is N^2. Trions consist of two identical particles so the symmetrization of states with respect to particles transposition is considered. Completely antisymmetric states can be constructed by introducing antisymmetric spin functions. Two symmetry adapted bases are considered. The third possibility is postponed for the further investigations.Comment: revtex, 5 p., sub. to Physica

The role of a form of vector potential - normalization of the antisymmetric gauge

Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak are compared with those based on pure group-theoretical considerations and corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary conditions one has to be very careful since the first gauge leads to a factor system which is not normalized. A period N introduced in Brown's and Zak's papers should be considered as a magnetic one, whereas the crystal period is in fact 2N. The `normalization' procedure proposed here shows the equivalence of Brown's, Zak's, and other approaches. It also indicates the importance of the concept of magnetic cells. Moreover, it is shown that factor systems (of projective representations and central extensions) are gauge-dependent, whereas a commutator of two magnetic translations is gauge-independent. This result indicates that a form of the vector potential (a gauge) is also important in physical investigations.Comment: RevTEX, 9 pages, to be published in J. Math. Phy

Archaeology of the mound spring campsites near Lake Eyre in South Australia

This study examines the variability of the stone assemblages at the mound springs campsites in South Australia. The research area is part of the tribal territories of Arabana and Diyari people. It comprises a network of mound springs stretching for about 200 km along the south and southwest shores of Lake Eyre. These mound springs were vital for permanent occupation of this arid region in late prehistory and in the post contact period. Large campsites located near the major springs attest to the prehistoric occupation of the area. Historical accounts reveal that this occupation was abruptly terminated in early 1 8 6 0’s. Although environment and chronology are uniform for all the mound spring sites the assemblages are distinctly different. They vary in the proportions of lithic materials, tool types, and artefact size. Inter-site variability is prominent while intrasite variation is minimal. The research is focused on this fact as it provides an important clue to the nature of springs o c c u p a t i o n. It is demonstrated that the variability of the mound spring campsites reflects different tactics of use and economy of lithic materials at each site. These tactics were influenced by: a) availability of different lithic materials and b) different demands for processing organic materials. It is argued that assemblage patterning is sensitive to local circumstances, and affected by quantity and quality of resources at each site. Consequently the variability between assemblages reflects the overall organisation and strategy of land use. This study attempts not merely to reconstruct human behaviour at each site but rather to understand how this behaviour was organised on the strategic level. This level of organisation is best represented by the differential use of sites within a common settlement system. Organisation such as this suggests consistent links between groups of people in the mound springs area throughout the last thousand years

An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

Krótkie rozważania na temat cierpienia człowieka chorego

W pracy przedstawiono krótkie rozważania na temat cierpienia człowieka chorego. Zwrócono uwagę na różne definicje cierpienia. Odwołano się m.in. do definicji encyklopedycznych, czy poglądów Jana Pawła II na temat cierpienia.The paper briefly discusses the problem of the suffering of the ill. Several definitions of suffering have been brought to attention. References have been made to both encyclopaedic definitions and John Paul II’s views on suffering

Spatial clustering of interacting bugs: Levy flights versus Gaussian jumps

A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neighborhood. The spatial dynamics corresponds either to normal diffusion characterized by Gaussian jumps or to superdiffusion characterized by L\'evy flights. It is observed that in both cases periodic patterns occur for appropriate parameters of the model, indicating that the general macroscopic collective behavior of the system is more strongly influenced by the competition for the resources than by the type of spatial dynamics. However, some differences arise that are discussed.Comment: This version incorporates in the text the correction published as an Erratum in Europhysics Letters (EPL) 95, 69902 (2011) [doi: 10.1209/0295-5075/95/69902

Water bound in elytra of the Weevil Liparus glabrirostris (Küster, 1849) by NMR and sorption isotherm (Coleoptera: Curculionidae)

Scanning electron microscopy micrograms of the elytra of Liparus glabrirostris showed a different dorsal and ventral surface and a multilayered inner structure. Hydration kinetics, sorption isotherm, and proton free induction decays are measured for hydrated elytra of the weevil species Liparus glabrirostris (Coleoptera: Curculionidae) in the atmosphere with controlled humidity. Very tightly bound water fraction with the mass Δ m/$m_0$ = 0.037 ± 0.004, and very short hydration time, tightly bound water Δ m/$m_0$ = 0.034 ± 0.009, and hydration time $t_1^{h}$ = (3.31 ± 0.93) h, and finally loosely bound water fraction with $t_2^{h}$ = (25.5 ± 7.8) h were distinguished. The sorption isotherm is sigmoidal in form, with the mass of water saturating primary water binding sites equal of Δ M/$m_0$ = 0.036. The proton free induction decays show the presence of solid signal (well fitted by a Gaussian function) from elytra ($T_{2G}$* ≈ 18 μs), the immobilized water fraction ($T_{2L_1}$* ≈ 120 μs) and mobile water pool ($T_{2 L_2}$* ≈ 300 μs). The hydration dependence of the water bound in elytra of L. glabrirostris, L/S is linear showing the absence of water-soluble solid fraction and negligible content of water pool "sealed" in pores of the structure

Microbiological changes in meat and minced meat from beavers (Castor fiber L.) during refrigerated and frozen storage

This study aims to evaluate the microbiological status, pH, and water activity of European beaver meat to establish its shelf-life and microbiological safety. In this study, the microbiological profiles of meat and minced meat obtained from the carcasses of beavers were investigated. Microbial evaluation of the chilled meat was performed within 24 h after hunting, on the 7th day and 14th day, and the evaluation of the frozen meat was made during the 11th week of storage. Meat samples were analysed for total viable count (TVC), psychrotrophic bacteria count (PBC), Enterobacteriaceae count (EBC), Escherichia coli count (EC), total staphylococcal count (TSC), lactic acid bacteria count (LABC) and total yeast and mould counts (TYMC). Tests for the presence of pathogenic bacteria from the genus Salmonella and Listeria were also performed. Additionally, the pH and water activity were determined. The initial amount of TVC was 4.94 log CFU/g in meat samples and 4.80 log CFU/g in minced meat. After 14 days of storage, the TVC increased to 8.33 in meat samples and 8.08 log CFU/g in minced meat. Pathogenic bacteria such as Listeria and Salmonella were not found in the beaver meat tested. The microbiological state of meat stored frozen for 11 weeks was comparable to the state found in meat stored refrigerated for seven days regarding the number of microorganisms

The trion: two electrons plus one hole versus one electron plus one exciton

We first show that, for problems dealing with trions, it is totally hopeless to use the standard many-body description in terms of electrons and holes and its associated Feynman diagrams. We then show how, by using the description of a trion as an electron interacting with an exciton, we can obtain the trion absorption through far simpler diagrams, written with electrons and \emph{excitons}. These diagrams are quite novel because, for excitons being not exact bosons, we cannot use standard procedures designed to deal with interacting true fermions or true bosons. A new many-body formalism is necessary to establish the validity of these electron-exciton diagrams and to derive their specific rules. It relies on the ``commutation technique'' we recently developed to treat interacting close-to-bosons. This technique generates a scattering associated to direct Coulomb processes between electrons and excitons and a dimensionless ``scattering'' associated to electron exchange inside the electron-exciton pairs -- this ``scattering'' being the original part of our many-body theory. It turns out that, although exchange is crucial to differentiate singlet from triplet trions, this ``scattering'' enters the absorption explicitly when the photocreated electron and the initial electron have the same spin -- \emph{i}. \emph{e}., when triplet trions are the only ones created -- \emph{but not} when the two spins are different, although triplet trions are also created in this case. The physical reason for this rather surprising result will be given