Adiabatic Geometric Phase for a General Quantum States

A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems. Furthermore, this new phase is related to Hannay's angles as we find that these angles, a classical concept, can arise naturally in quantum systems. The results are demonstrated with a two-level model.Comment: 4 pages, 2 figure

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

Locked and Unlocked Polygonal Chains in 3D

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D with a polynomial number of moves.Comment: To appear in Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 199

Work-related psychological health and psychological type among lead elders within the Newfrontiers network of churches in the United Kingdom

Building on a series of recent studies concerned with assessing work-related psychological health and psychological type among various groups of church leaders, this study reports new data provided by 134 Lead Elders within the Newfrontiers network of churches in the United Kingdom who completed the Francis Psychological Type Scales (FPTS) together with the two scales of the Francis Burnout Inventory (FBI) concerned with emotional exhaustion and satisfaction in ministry. Compared with other groups of church leaders, Lead Elders within the Newfrontiers network of churches reported lower levels of emotional exhaustion and higher levels of satisfaction in ministry. Compared with other groups of church leaders, there was a higher proportion of extraverts among Lead Elders within the Newfrontiers network of churches. There was only a weak association between psychological type and burnout

THE INTRODUCED SABELLID POLYCHAETE TEREBRASABELLA HETEROUNCINATA IN CALIFORNIA: TRANSMISSION, METHODS OF CONTROL AND SURVEY FOR PRESENCE IN NATIVE GASTROPOD POPULATIONS

The sabellid polychaete Terebrasabella heterouncinata (Fitzhugh & Rouse 1999) has a unique life history in which larvae settle on the edge of gastropod shells and rely on shell deposition to create a tube with an opening to the exterior. This worm was accidentally imported to California, USA on abalone from South Africa in the 1980s and spread with abalone shipments to most culture facilities and some public aquaria throughout the state. Its ability to infest California's native gastropods has sparked concern regarding potential establishment in intertidal habitats adjacent to facilities that held sabellid-positive abalone. We examined the ability of T. heterouncinata to transmit between individual turban snails, Tegula funebralis. We found that transmission between T.funebralis did occur, but at a significantly slower rate than that between red abalone Haliotis rufescens. During 2002 to 2006 native gastropods (turban snails and limpets) were collected at most sabellid-exposed sites and no T. heterouncinata were detected; it thus appears that this species has not become established in California. Freshwater exposure was examined as a method to kill T. heterouncinala in shell fragments that may remain after abalone are removed from production or display units. Freshwater immersion for up to 8 hours but not 16 or 32 h resulted in survival of adults and/or larvae resident in brood chambers. In a similar study, motile T. heterouncinata larvae were found to survive up to 32 see of freshwater exposure, whereas none survived a 64-sec exposure. These data can be used by abalone culture and display facilities to establish reliable sanitization procedures to prevent T. heterouncinata transmission or reinfestation

Quantum indistinguishability from general representations of SU(2n)

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-particle configuration space. It is shown how families of such bundles can be constructed from irreducible representations of the group SU(2n). The construction of Berry and Robbins, which leads to a definite connection between spin and statistics (the physically correct connection), is shown to correspond to the completely symmetric representations. The spin-statistics connection is typically broken for general SU(2n) representations, which may admit, for a given value of spin, both bose and fermi statistics, as well as parastatistics. The determination of the allowed values of the spin and statistics reduces to the decomposition of certain zero-weight representations of a (generalised) Weyl group of SU(2n). A formula for this decomposition is obtained using the Littlewood-Richardson theorem for the decomposition of representations of U(m+n) into representations of U(m)*U(n).Comment: 32 pages, added example section 4.