661 research outputs found
LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies
We extend the classical LR characterization of chirotopes of finite planar
families of points to chirotopes of finite planar families of pairwise disjoint
convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a
chirotope of finite planar families of pairwise disjoint convex bodies if and
only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the
set of 3-subsets of J is a chirotope of finite planar families of pairwise
disjoint convex bodies. Our main tool is the polarity map, i.e., the map that
assigns to a convex body the set of lines missing its interior, from which we
derive the key notion of arrangements of double pseudolines, introduced for the
first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio
Deformed Algebras from Inverse Schwinger Method
We consider a problem which may be viewed as an inverse one to the Schwinger
realization of Lie algebra, and suggest a procedure of deforming the
so-obtained algebra. We illustrate the method through a few simple examples
extending Schwinger's construction. As results, various q-deformed
algebras are (re-)produced as well as their undeformed counterparts. Some
extensions of the method are pointed out briefly.Comment: 14 pages, Jeonju University Report, Late
Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology
In this paper we determine the representation type of some algebras of
infinite matrices continuously controlled at infinity by a compact metrizable
space. We explicitly classify their finitely presented modules in the finite
and tame cases. The algebra of row-column-finite (or locally finite) matrices
over an arbitrary field is one of the algebras considered in this paper, its
representation type is shown to be finite.Comment: 33 page
Morse theory of the moment map for representations of quivers
The results of this paper concern the Morse theory of the norm-square of the
moment map on the space of representations of a quiver. We show that the
gradient flow of this function converges, and that the Morse stratification
induced by the gradient flow co-incides with the Harder-Narasimhan
stratification from algebraic geometry. Moreover, the limit of the gradient
flow is isomorphic to the graded object of the
Harder-Narasimhan-Jordan-H\"older filtration associated to the initial
conditions for the flow. With a view towards applications to Nakajima quiver
varieties we construct explicit local co-ordinates around the Morse strata and
(under a technical hypothesis on the stability parameter) describe the negative
normal space to the critical sets. Finally, we observe that the usual Kirwan
surjectivity theorems in rational cohomology and integral K-theory carry over
to this non-compact setting, and that these theorems generalize to certain
equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's
comments. To appear in Geometriae Dedicat
Out-of-Equilibrium Admittance of Single Electron Box Under Strong Coulomb Blockade
We study admittance and energy dissipation in an out-of-equlibrium single
electron box. The system consists of a small metallic island coupled to a
massive reservoir via single tunneling junction. The potential of electrons in
the island is controlled by an additional gate electrode. The energy
dissipation is caused by an AC gate voltage. The case of a strong Coulomb
blockade is considered. We focus on the regime when electron coherence can be
neglected but quantum fluctuations of charge are strong due to Coulomb
interaction. We obtain the admittance under the specified conditions. It turns
out that the energy dissipation rate can be expressed via charge relaxation
resistance and renormalized gate capacitance even out of equilibrium. We
suggest the admittance as a tool for a measurement of the bosonic distribution
corresponding collective excitations in the system
Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure
The spin-orbit interaction affects the electronic structure of solids in
various ways. Topological insulators are one example where the spin-orbit
interaction leads the bulk bands to have a non-trivial topology, observable as
gapless surface or edge states. Another example is the Rashba effect, which
lifts the electron-spin degeneracy as a consequence of spin-orbit interaction
under broken inversion symmetry. It is of particular importance to know how
these two effects, i.e. the non-trivial topology of electronic states and
Rashba spin splitting, interplay with each other. Here we show, through
sophisticated first-principles calculations, that BiTeI, a giant bulk Rashba
semiconductor, turns into a topological insulator under a reasonable pressure.
This material is shown to exhibit several unique features such as, a highly
pressure-tunable giant Rashba spin splitting, an unusual pressure-induced
quantum phase transition, and more importantly the formation of strikingly
different Dirac surface states at opposite sides of the material.Comment: 5 figures are include
One-dimensional Topological Edge States of Bismuth Bilayers
The hallmark of a time-reversal symmetry protected topologically insulating
state of matter in two-dimensions (2D) is the existence of chiral edge modes
propagating along the perimeter of the system. To date, evidence for such
electronic modes has come from experiments on semiconducting heterostructures
in the topological phase which showed approximately quantized values of the
overall conductance as well as edge-dominated current flow. However, there have
not been any spectroscopic measurements to demonstrate the one-dimensional (1D)
nature of the edge modes. Among the first systems predicted to be a 2D
topological insulator are bilayers of bismuth (Bi) and there have been recent
experimental indications of possible topological boundary states at their
edges. However, the experiments on such bilayers suffered from irregular
structure of their edges or the coupling of the edge states to substrate's bulk
states. Here we report scanning tunneling microscopy (STM) experiments which
show that a subset of the predicted Bi-bilayers' edge states are decoupled from
states of Bi substrate and provide direct spectroscopic evidence of their 1D
nature. Moreover, by visualizing the quantum interference of edge mode
quasi-particles in confined geometries, we demonstrate their remarkable
coherent propagation along the edge with scattering properties that are
consistent with strong suppression of backscattering as predicted for the
propagating topological edge states.Comment: 15 pages, 5 figures, and supplementary materia
Hierarchical information clustering by means of topologically embedded graphs
We introduce a graph-theoretic approach to extract clusters and hierarchies
in complex data-sets in an unsupervised and deterministic manner, without the
use of any prior information. This is achieved by building topologically
embedded networks containing the subset of most significant links and analyzing
the network structure. For a planar embedding, this method provides both the
intra-cluster hierarchy, which describes the way clusters are composed, and the
inter-cluster hierarchy which describes how clusters gather together. We
discuss performance, robustness and reliability of this method by first
investigating several artificial data-sets, finding that it can outperform
significantly other established approaches. Then we show that our method can
successfully differentiate meaningful clusters and hierarchies in a variety of
real data-sets. In particular, we find that the application to gene expression
patterns of lymphoma samples uncovers biologically significant groups of genes
which play key-roles in diagnosis, prognosis and treatment of some of the most
relevant human lymphoid malignancies.Comment: 33 Pages, 18 Figures, 5 Table
Universal Resistances of the Quantum RC circuit
We examine the concept of universal quantized resistance in the AC regime
through the fully coherent quantum RC circuit comprising a cavity (dot)
capacitively coupled to a gate and connected via a single spin-polarized
channel to a reservoir lead. As a result of quantum effects such as the Coulomb
interaction in the cavity and global phase coherence, we show that the charge
relaxation resistance is identical for weak and large transmissions and
it changes from to when the frequency (times ) exceeds
the level spacing of the cavity; is the Planck constant and the
electron charge. For large cavities, we formulate a correspondence between the
charge relaxation resistance and the Korringa-Shiba relation of the
Kondo model. Furthermore, we introduce a general class of models, for which the
charge relaxation resistance is universal. Our results emphasize that the
charge relaxation resistance is a key observable to understand the dynamics of
strongly correlated systems.Comment: 12 pages, 3 figure
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