Density-functional theory of quantum wires and dots in a strong magnetic field

We study the competition between the exchange and the direct Coulomb interaction near the edge of a two-dimensional electron gas in a strong magnetic field using density-functional theory in a local approximation for the exchange-energy functional. Exchange is shown to play a significant role in reducing the spatial extent of the compressible edge channel regions obtained from an electrostatic description. The transition from the incompressible edge channels of the Hartree-Fock picture to the broad, compressible strips predicted by electrostatics occurs within a narrow and experimentally accessible range of confinement strengths.Comment: 24 pages latex and 10 postscript figures in self extracting fil

Random Dirac operators with time-reversal symmetry

Quasi-one-dimensional stochastic Dirac operators with an odd number of channels, time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and Goldsheid-Margulis to the analysis of random products of matrices in the group SO$^*(2L)$, and then a version of Kotani theory for these operators. Absence of singular spectrum can be shown by adapting an argument of Jaksic-Last if the potential contains random Dirac peaks with absolutely continuous distribution.Comment: parts of introduction made more precise, corrections as follow-up on referee report

A general formula of the effective potential in 5D SU(N) gauge theory on orbifold

We show a general formula of the one loop effective potential of the 5D SU(N) gauge theory compactified on an orbifold, $S^1/Z_2$. The formula shows the case when there are fundamental, (anti-)symmetric tensor and adjoint representational bulk fields. Our calculation method is also applicable when there are bulk fields belonging to higher dimensional representations. The supersymmetric version of the effective potential with Scherk-Schwarz breaking can be obtained straightforwardly. We also show some examples of effective potentials in SU(3), SU(5) and SU(6) models with various boundary conditions, which are reproduced by our general formula.Comment: 22 pages;minor corrections;references added;typos correcte

Ensemble density functional theory of the fractional quantum Hall effect

We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with semiclassical and Hartree-Fock calculations, and with small system numerical diagonalizations. This establishes the usefulness of density functional theory to study the fractional quantum Hall effect, which opens up the possibility of studying inhomegeneous systems with many more electrons than has heretofore been possible.Comment: Improved discussion of ensemble density functional theory. 4 pages plus 3 postscript figures, uses latex with revtex. Contact [email protected]

Schroedingers equation with gauge coupling derived from a continuity equation

We consider a statistical ensemble of particles of mass m, which can be described by a probability density \rho and a probability current \vec{j} of the form \rho \nabla S/m. The continuity equation for \rho and \vec{j} implies a first differential equation for the basic variables \rho and S. We further assume that this system may be described by a linear differential equation for a complex state variable \chi. Using this assumptions and the simplest possible Ansatz \chi(\rho,S) Schroedingers equation for a particle of mass m in an external potential V(q,t) is deduced. All calculations are performed for a single spatial dimension (variable q) Using a second Ansatz \chi(\rho,S,q,t) which allows for an explict q,t-dependence of \chi, one obtains a generalized Schroedinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schroeodingers equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for an non-unique external q,t-dependence of \chi, one obtains Schroedingers equation with electromagnetic potentials \vec{A}, \phi in the familiar gauge coupling form. A possible source of the non-uniqueness is pointed out.Comment: 25 pages, no figure

Node-weighted Steiner tree and group Steiner tree in planar graphs

We improve the approximation ratios for two optimization problems in planar graphs. For node-weighted Steiner tree, a classical network-optimization problem, the best achievable approximation ratio in general graphs is Θ [theta] (logn), and nothing better was previously known for planar graphs. We give a constant-factor approximation for planar graphs. Our algorithm generalizes to allow as input any nontrivial minor-closed graph family, and also generalizes to address other optimization problems such as Steiner forest, prize-collecting Steiner tree, and network-formation games. The second problem we address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimum-weight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is O(log3 [superscript 3] n), or O(log2 [superscript 2] n) when the host graph is a tree. We obtain an O(log n polyloglog n) approximation algorithm for the special case where the graph is planar embedded and each group is the set of nodes on a face. We obtain the same approximation ratio for the minimum-weight tour that must visit each group

Shifting states, shifting services: Linking regime shifts to changes in ecosystem services of shallow lakes

Shallow lakes can shift between stable states as a result of anthropogenic or natural drivers. Four common stable states differ in dominant groups of primary producers: submerged, floating, or emergent macrophytes or phytoplankton. Shifts in primary producer dominance affect key supporting, provisioning, regulating, and cultural ecosystem services supplied by lakes. However, links between states and services are often neglected or unknown in lake management, resulting in conflicts and additional costs. Here, we identify major shallow lake ecosystem services and their links to Sustainable Development Goals (SDGs), compare service provisioning among the four ecosystem states and discuss potential trade-offs. We identified 39 ecosystem services potentially provided by shallow lakes. Submerged macrophytes facilitate most of the supporting (86%) and cultural (63%) services, emergent macrophytes facilitate most regulating services (60%), and both emergent and floating macrophytes facilitate most provisioning services (63%). Phytoplankton dominance supports fewer ecosystem services, and contributes most to provisioning services (42%). The shallow lake ecosystem services we identified could be linked to 10 different SDGs, notably zero hunger (SDG 2), clean water and sanitation (SDG 6), sustainable cities and communities (SDG 11), and climate action (SDG13). We highlighted several trade-offs (1) among ecosystem services, (2) within ecosystem services, and (3) between ecosystem services across ecosystems. These trade-offs can have significant ecological and economic consequences that may be prevented by early identification in water quality management. In conclusion, common stable states in shallow lakes provide a different and diverse set of ecosystem services with numerous links to the majority of SDGs. Conserving and restoring ecosystem states should account for potential trade-offs between ecosystem services and preserving the natural value of shallow lakes

Spontaneous Coherence and Collective Modes in Double-Layer Quantum Dot Systems

We study the ground state and the collective excitations of parabolically-confined double-layer quantum dot systems in a strong magnetic field. We identify parameter regimes where electrons form maximum density droplet states, quantum-dot analogs of the incompressible states of the bulk integer quantum Hall effect. In these regimes the Hartree-Fock approximation and the time-dependent Hartree-Fock approximations can be used to describe the ground state and collective excitations respectively. We comment on the relationship between edge excitations of dots and edge magneto-plasmon excitations of bulk double-layer systems.Comment: 20 pages (figures included) and also available at http://fangio.magnet.fsu.edu/~jhu/Paper/qdot_cond.ps, replaced to fix figure

Role of electrostatic interactions in amyloid beta-protein (Abeta) oligomer formation: A discrete molecular dynamics study

Pathological folding and oligomer formation of the amyloid beta-protein (Abeta) are widely perceived as central to Alzheimer's disease (AD). Experimental approaches to study Abeta self-assembly are problematic, because most relevant aggregates are quasi-stable and inhomogeneous. We apply a discrete molecular dynamics (DMD) approach combined with a four-bead protein model to study oligomer formation of the amyloid beta-protein (Abeta). We address the differences between the two most common Abeta alloforms, Abeta40 and Abeta42, which oligomerize differently in vitro. We study how the presence of electrostatic interactions (EIs) between pairs of charged amino acids affects Abeta40 and Abeta42 oligomer formation. Our results indicate that EIs promote formation of larger oligomers in both Abeta40 and Abeta42. The Abeta40 size distribution remains unimodal, whereas the Abeta42 distribution is trimodal, as observed experimentally. Abeta42 folded structure is characterized by a turn in the C-terminus that is not present in Abeta40. We show that the same C-terminal region is also responsible for the strongest intermolecular contacts in Abeta42 pentamers and larger oligomers. Our results suggest that this C-terminal region plays a key role in the formation of Abeta42 oligomers and the relative importance of this region increases in the presence of EIs. These results suggest that inhibitors targeting the C-terminal region of Abeta42 oligomers may be able to prevent oligomer formation or structurally modify the assemblies to reduce their toxicity.Comment: Accepted for publication at Biophysical Journa

Progressive transformation of a flux rope to an ICME

The solar wind conditions at one astronomical unit (AU) can be strongly disturbed by the interplanetary coronal mass ejections (ICMEs). A subset, called magnetic clouds (MCs), is formed by twisted flux ropes that transport an important amount of magnetic flux and helicity which is released in CMEs. At 1 AU from the Sun, the magnetic structure of MCs is generally modeled neglecting their expansion during the spacecraft crossing. However, in some cases, MCs present a significant expansion. We present here an analysis of the huge and significantly expanding MC observed by the Wind spacecraft during 9 and 10 November, 2004. After determining an approximated orientation for the flux rope using the minimum variance method, we precise the orientation of the cloud axis relating its front and rear magnetic discontinuities using a direct method. This method takes into account the conservation of the azimuthal magnetic flux between the in- and out-bound branches, and is valid for a finite impact parameter (i.e., not necessarily a small distance between the spacecraft trajectory and the cloud axis). Moreover, using the direct method, we find that the ICME is formed by a flux rope (MC) followed by an extended coherent magnetic region. These observations are interpreted considering the existence of a previous larger flux rope, which partially reconnected with its environment in the front. These findings imply that the ejected flux rope is progressively peeled by reconnection and transformed to the observed ICME (with a remnant flux rope in the front part).Comment: Solar Physics (in press