The pollination of Tritoniopsis parviflora (Iridaceae) by the oil-collecting bee Rediviva gigas (Hymenoptera: Melittidae): the first record of oil-secretion in African Iridaceae

The Western Cape geophyte Tritoniopsis parviflora (Iridaceae: Crocoideae) has been found to secrete floral oils as well as nectar. The oils are secreted from epithelial elaiophores over much of the proximal parts of the perianth. This is the first report of oil-secretion in the subfamily Crocoideae and the first record of oil-secretion in the Old World representatives of the Iridaceae. The species is pollinated by the large oil-collecting bee Rediviva gigas (Hymenoptera: Melittidae) and is part of a guild of yellow-flowered, often fragrant species that flower in late spring and early summer, usually only after a fire the previous season. Tritoniopsis parviflora will not self-pollinate and the provision of both oil and nectar may be a strategy for ensuring pollination in populations in areas where R. gigas is not presen

Topology and Phases in Fermionic Systems

There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of exponentially localized Wannier functions. We show that by taking two copies of a gapped, free fermionic system with complex conjugate Hamiltonians, it is always possible to overcome these obstructions. This allows us to write the ground state in matrix product form using Grassman-valued bond variables, and show insensitivity of the ground state density matrix to boundary conditions.Comment: 4 pages, see also arxiv:0710.329

Relativistic entanglement of two massive particles

We describe the spin and momentum degrees of freedom of a system of two massive spin--$\tfrac{1}{2}$ particles as a 4 qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alice's and Bob's subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin- with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the 4 qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.Comment: 17 pages, 4 figure