1,544 research outputs found
Exotic plasma as classical Hall Liquid
A non-relativistic plasma model endowed with an ``exotic'' structure
associated with the two-parameter central extension of the planar Galilei group
is constructed. Introducing a Chern-Simons statistical gauge field provides us
with a self-consistent system; when the magnetic field takes a critical value
determined by the extension parameters, the fluid becomes incompressible and
moves collectively, according to the Hall law.Comment: 11 pages, LaTex, no figures. Revised version: Some details better
explained. To appear in Int. Journ. Mod. Phys.
Failure of mean-field approach in out-of-equilibrium Anderson model
To explore the limitations of the mean field approximation, frequently used
in \textit{ab initio} molecular electronics calculations, we study an
out-of-equilibrium Anderson impurity model in a scattering formalism. We find
regions in the parameter space where both magnetic and non-magnetic solutions
are stable. We also observe a hysteresis in the non-equilibrium magnetization
and current as a function of the applied bias voltage. The mean field method
also predicts incorrectly local moment formation for large biases and a spin
polarized current, and unphysical kinks appear in various physical quantities.
The mean field approximation thus fails in every region where it predicts local
moment formation.Comment: 5 pages, 5 figure
Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
While sign-coherent 4-dimensional structures cannot dominate topological
charge fluctuations in the QCD vacuum at all scales due to reflection
positivity, it is possible that enhanced coherence exists over extended
space-time regions of lower dimension. Using the overlap Dirac operator to
calculate topological charge density, we present evidence for such structure in
pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium
configuration is dominated by two oppositely-charged sign-coherent connected
structures (``sheets'') covering about 80% of space-time. Each sheet is built
from elementary 3-d cubes connected through 2-d faces, and approximates a
low-dimensional curved manifold (or possibly a fractal structure) embedded in
the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18%
of the most intense space-time points organized into a global long-range
structure, involving connected parts spreading over maximal possible distances.
We find that the skeleton is locally 1-dimensional and propose that its
geometrical properties might be relevant for understanding the possible role of
topological charge fluctuations in the physics of chiral symmetry breaking.Comment: 4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations
provided, figure and references added, published versio
Non-equilibrium transport theory of the singlet-triplet transition: perturbative approach
We use a simple iterative perturbation theory to study the singlet-triplet
(ST) transition in lateral and vertical quantum dots, modeled by the
non-equilibrium two-level Anderson model. To a great surprise, the region of
stable perturbation theory extends to relatively strong interactions, and this
simple approach is able to reproduce all experimentally-observed features of
the ST transition, including the formation of a dip in the differential
conductance of a lateral dot indicative of the two-stage Kondo effect, or the
maximum in the linear conductance around the transition point. Choosing the
right starting point to the perturbation theory is, however, crucial to obtain
reliable and meaningful results
Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge
configurations at non-zero temperature and compare periodic and anti-periodic
temporal boundary conditions for the fermions. It is demonstrated that for the
different boundary conditions often the modes are localized at different
space-time points and have different sizes. Our observations are consistent
with patterns expected for Kraan - van Baal solutions of the classical
Yang-Mills equations. These solutions consist of constituent monopoles and the
zero-modes are localized on different constituents for different boundary
conditions. Our findings indicate that the excitations of the QCD vacuum are
more structured than simple instanton-like lumps.Comment: Remarks added. To appear in Phys. Rev.
On three-rowed Chomp
Chomp is a 50 year-old game played on a partially ordered set P. It has been in the center of interest of several mathematicians since then. Even when P is simply a 3 × n lattice, we have almost no information about the winning strategy. In this paper we present a new approach and a cubic algorithm for computing the winning positions for this case. We also prove that from the initial positions there are infinitely many winning moves in the third row
On three-rowed Chomp
Chomp is a 50 year-old game played on a partially ordered set P. It has been in the center of interest of several mathematicians since then. Even when P is simply a 3 × n lattice, we have almost no information about the winning strategy. In this paper we present a new approach and a cubic algorithm for computing the winning positions for this case. We also prove that from the initial positions there are infinitely many winning moves in the third row
Invariance Conditions for Nonlinear Dynamical Systems
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to
invariance condition of dynamical system, submitted to Applied Mathematics and
Computation}] proposed a novel unified approach to study, i.e., invariance
conditions, sufficient and necessary conditions, under which some convex sets
are invariant sets for linear dynamical systems.
In this paper, by utilizing analogous methodology, we generalize the results
for nonlinear dynamical systems. First, the Theorems of Alternatives, i.e., the
nonlinear Farkas lemma and the \emph{S}-lemma, together with Nagumo's Theorem
are utilized to derive invariance conditions for discrete and continuous
systems. Only standard assumptions are needed to establish invariance of
broadly used convex sets, including polyhedral and ellipsoidal sets. Second, we
establish an optimization framework to computationally verify the derived
invariance conditions. Finally, we derive analogous invariance conditions
without any conditions
Local Chirality of Low-Lying Dirac Eigenmodes and the Instanton Liquid Model
The reasons for using low-lying Dirac eigenmodes to probe the local structure
of topological charge fluctuations in QCD are discussed, and it is pointed out
that the qualitative double-peaked behavior of the local chiral orientation
probability distribution in these modes is necessary, but not sufficient for
dominance of instanton-like fluctuations. The results with overlap Dirac
operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm
to a~0.12 fm are reported, and it is found that the size and density of local
structures responsible for double-peaking of the distribution are in
disagreement with the assumptions of the Instanton Liquid Model. More
generally, our results suggest that vacuum fluctuations of topological charge
are not effectively dominated by locally quantized (integer-valued) lumps in
QCD.Comment: 29 pages, 13 figures; v2: minor improvements in presentation, results
and conclusions unchanged, version to appear in PR
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