599 research outputs found
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, 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
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
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, . 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
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
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
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
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