Information theory of quantum systems with some hydrogenic applications

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.Comment: 9 pages, 3 figure

Particle-vortex dynamics in noncommutative space

We study the problem of a charged particle in the presence of a uniform magnetic field plus a vortex in noncommutative planar space considering the two possible non-commutative extensions of the corresponding Hamiltonian, namely the ``fundamental'' and the ``antifundamental'' representations. Using a Fock space formalism we construct eigenfunctions and eigenvalues finding in each case half of the states existing in the ordinary space case. In the limit of $\theta \to 0$ we recover the two classes of states found in ordinary space, relevant for the study of anyon physics.Comment: 13 pages, no figures, plain LaTeX. References adde

Streamlined islands and the English Channel megaflood hypothesis

Recognising ice-age catastrophic megafloods is important because they had significant impact on large-scale drainage evolution and patterns of water and sediment movement to the oceans, and likely induced very rapid, short-term effects on climate. It has been previously proposed that a drainage system on the floor of the English Channel was initiated by catastrophic flooding in the Pleistocene but this suggestion has remained controversial. Here we examine this hypothesis through an analysis of key landform features. We use a new compilation of multi- and single-beam bathymetry together with sub-bottom profiler data to establish the internal structure, planform geometry and hence origin of a set of 36 mid-channel islands. Whilst there is evidence of modern-day surficial sediment processes, the majority of the islands can be clearly demonstrated to be formed of bedrock, and are hence erosional remnants rather than depositional features. The islands display classic lemniscate or tear-drop outlines, with elongated tips pointing downstream, typical of streamlined islands formed during high-magnitude water flow. The length-to-width ratio for the entire island population is 3.4 ± 1.3 and the degree-of-elongation or k-value is 3.7 ± 1.4. These values are comparable to streamlined islands in other proven Pleistocene catastrophic flood terrains and are distinctly different to values found in modern-day rivers. The island geometries show a correlation with bedrock type: with those carved from Upper Cretaceous chalk having larger length-to-width ratios (3.2 ± 1.3) than those carved into more mixed Paleogene terrigenous sandstones, siltstones and mudstones (3.0 ± 1.5). We attribute these differences to the former rock unit having a lower skin friction which allowed longer island growth to achieve minimum drag. The Paleogene islands, although less numerous than the Chalk islands, also assume more perfect lemniscate shapes. These lithologies therefore reached island equilibrium shape more quickly but were also susceptible to total erosion. Our observations support the hypothesis that the islands were initially carved by high-water volume flows via a unique catastrophic drainage of a pro-glacial lake in the southern North Sea at the Dover Strait rather than by fluvial erosion throughout the Pleistocene

Entanglement of two qubits mediated by one-dimensional plasmonic waveguides

We investigate qubit-qubit entanglement mediated by plasmons supported by one-dimensional waveguides. We explore both the situation of spontaneous formation of entanglement from an unentangled state and the emergence of driven steady-state entanglement under continuous pumping. In both cases, we show that large values for the concurrence are attainable for qubit-qubit distances larger than the operating wavelength by using plasmonic waveguides that are currently available.Comment: 4 pages, 4 figures. Minor Changes. Journal Reference added. Highlighted in Physic

Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements

If we distribute n qubits between two parties, which quantum pure states and distributions of qubits would allow all-versus-nothing (or Greenberger-Horne-Zeilinger-like) proofs of Bell's theorem using only single-qubit measurements? We show a necessary and sufficient condition for the existence of these proofs for any number of qubits, and provide all distinct proofs up to n=7 qubits. Remarkably, there is only one distribution of a state of n=4 qubits, and six distributions, each for a different state of n=6 qubits, which allow these proofs.Comment: REVTeX4, 4 pages, 2 figure