Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries

We determine the autonomous three dimensional Newtonian systems which admit Lie point symmetries and the three dimensional autonomous Newtonian Hamiltonian systems, which admit Noether point symmetries. We apply the results in order to determine the two dimensional Hamiltonian dynamical systems which move in a space of constant non-vanishing curvature and are integrable via Noether point symmetries. The derivation of the results is geometric and can be extended naturally to higher dimensions.Comment: Accepted for publication in Journal of Physics A: Math. and Theor.,13 page

Tunnelling in quantum superlattices with variable lacunarity

Quantum fractal superlattices are microelectronic devices consisting of a series of thin layers of two semiconductor materials deposited alternately on each other over a substrate following the rules of construction of a fractal set, here, a symmetrical polyadic Cantor fractal. The scattering properties of electrons in these superlattices may be modeled by using that of quantum particles in piecewise constant potential wells. The twist plots representing the reflection coefficient as function of the lacunarity parameter show the appearance of black curves with perfectly transparent tunnelling which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for these reflection-less curves are derived using the transfer matrix method. Comparison with the numerical results show their good accuracy.Comment: 12 pages, 3 figure

Generalizing the autonomous Kepler Ermakov system in a Riemannian space

We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov dynamical system to three dimensions using the sl(2,R) invariance of Noether symmetries and determine all three dimensional autonomous Hamiltonian Kepler Ermakov dynamical systems which are Liouville integrable via Noether symmetries. Subsequently we generalize the autonomous Kepler Ermakov system in a Riemannian space which admits a gradient homothetic vector by the requirements (a) that it admits a first integral (the Riemannian Ermakov invariant) and (b) it has sl(2,R) invariance. We consider both the non-Hamiltonian and the Hamiltonian systems. In each case we compute the Riemannian Ermakov invariant and the equations defining the dynamical system. We apply the results in General Relativity and determine the autonomous Hamiltonian Riemannian Kepler Ermakov system in the spatially flat Friedman Robertson Walker spacetime. We consider a locally rotational symmetric (LRS) spacetime of class A and discuss two cosmological models. The first cosmological model consists of a scalar field with exponential potential and a perfect fluid with a stiff equation of state. The second cosmological model is the f(R) modified gravity model of {\Lambda}_{bc}CDM. It is shown that in both applications the gravitational field equations reduce to those of the generalized autonomous Riemannian Kepler Ermakov dynamical system which is Liouville integrable via Noether integrals.Comment: Reference [25] update, 21 page

A transfer matrix method for the analysis of fractal quantum potentials

The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential

Atomic time-of-arrival measurements with a laser of finite beam width

A natural approach to measure the time of arrival of an atom at a spatial region is to illuminate this region with a laser and detect the first fluorescence photons produced by the excitation of the atom and subsequent decay. We investigate the actual physical content of such a measurement in terms of atomic dynamical variables, taking into account the finite width of the laser beam. Different operation regimes are identified, in particular the ones in which the quantum current density may be obtained.Comment: 7 figure

The Numbers Behind Mushroom Biodiversity

Fungi are among the most diverse groups of organisms on Earth. with a global diversity estimated at 0.8 million to 5.1 million species. They play fundamental ecological roles as decomposers, mutualists, and pathogens, growing in almost all habitats and being important as sources of food and health benefits, income, and to maintain forest health. Global assessment of wild edible fungi indicate the existence of 2327 useful wild species; 2166 edible and 1069 used as food; 470 medicinal species. Several million tonnes are collected, consumed, and sold each year in over 80 countries. The major mushroom-producing countries in 2012 were China, Italy, USA, and The Netherlands, with 80% of the world production, 64% of which came from China. The European Union produces 24% of the world production. Italy is the largest European producer, Poland is the largest exporter, UK the largest importer.Fungi are difficult to preserve and fossilize and due to the poor preservation of most fungal structures, it has been difficult to interpret the fossil record of fungi. Hyphae, the vegetative bodies of fungi, bear few distinctive morphological characteristicss, and organisms as diverse as cyanobacteria, eukaryotic algal groups, and oomycetes can easily be mistaken for them (Taylor & Taylor 1993). Fossils provide minimum ages for divergences and genetic lineages can be much older than even the oldest fossil representative found. According to Berbee and Taylor (2010), molecular clocks (conversion of molecular changes into geological time) calibrated by fossils are the only available tools to estimate timing of evolutionary events in fossil‐poor groups, such as fungi. The arbuscular mycorrhizal symbiotic fungi from the division Glomeromycota, generally accepted as the phylogenetic sister clade to the Ascomycota and Basidiomycota, have left the most ancient fossils in the Rhynie Chert of Aberdeenshire in the north of Scotland (400 million years old). The Glomeromycota and several other fungi have been found associated with the preserved tissues of early vascular plants (Taylor et al. 2004a). Fossil spores from these shallow marine sediments from the Ordovician that closely resemble Glomeromycota spores and finely branched hyphae arbuscules within plant cells were clearly preserved in cells of stems of a 400 Ma primitive land plant, Aglaophyton, from Rhynie chert 455–460 Ma in age (Redecker et al. 2000; Remy et al. 1994) and from roots from the Triassic (250–199 Ma) (Berbee & Taylor 2010; Stubblefield et al. 1987).info:eu-repo/semantics/publishedVersio