12,573 research outputs found
Helical scattering and valleytronics in bilayer graphene
We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating regions of different pseudospin polarization, and is associated with the helical winding of the pseudospin vector across the interface, which breaks the reflection symmetry in each valley. Electrons are transmitted with a preferred direction of up to 60° over a large energetic range in one of the valleys, and down to −60° in the other. In a Y-junction geometry, this can be used to create and detect valley polarization
Equivalences on Acyclic Orientations
The cyclic and dihedral groups can be made to act on the set Acyc(Y) of
acyclic orientations of an undirected graph Y, and this gives rise to the
equivalence relations ~kappa and ~delta, respectively. These two actions and
their corresponding equivalence classes are closely related to combinatorial
problems arising in the context of Coxeter groups, sequential dynamical
systems, the chip-firing game, and representations of quivers.
In this paper we construct the graphs C(Y) and D(Y) with vertex sets Acyc(Y)
and whose connected components encode the equivalence classes. The number of
connected components of these graphs are denoted kappa(Y) and delta(Y),
respectively. We characterize the structure of C(Y) and D(Y), show how delta(Y)
can be derived from kappa(Y), and give enumeration results for kappa(Y).
Moreover, we show how to associate a poset structure to each kappa-equivalence
class, and we characterize these posets. This allows us to create a bijection
from Acyc(Y)/~kappa to the union of Acyc(Y')/~kappa and Acyc(Y'')/~kappa, Y'
and Y'' denote edge deletion and edge contraction for a cycle-edge in Y,
respectively, which in turn shows that kappa(Y) may be obtained by an
evaluation of the Tutte polynomial at (1,0).Comment: The original paper was extended, reorganized, and split into two
papers (see also arXiv:0802.4412
Cycle Equivalence of Graph Dynamical Systems
Graph dynamical systems (GDSs) can be used to describe a wide range of
distributed, nonlinear phenomena. In this paper we characterize cycle
equivalence of a class of finite GDSs called sequential dynamical systems SDSs.
In general, two finite GDSs are cycle equivalent if their periodic orbits are
isomorphic as directed graphs. Sequential dynamical systems may be thought of
as generalized cellular automata, and use an update order to construct the
dynamical system map.
The main result of this paper is a characterization of cycle equivalence in
terms of shifts and reflections of the SDS update order. We construct two
graphs C(Y) and D(Y) whose components describe update orders that give rise to
cycle equivalent SDSs. The number of components in C(Y) and D(Y) is an upper
bound for the number of cycle equivalence classes one can obtain, and we
enumerate these quantities through a recursion relation for several graph
classes. The components of these graphs encode dynamical neutrality, the
component sizes represent periodic orbit structural stability, and the number
of components can be viewed as a system complexity measure
On Enumeration of Conjugacy Classes of Coxeter Elements
In this paper we study the equivalence relation on the set of acyclic
orientations of a graph Y that arises through source-to-sink conversions. This
source-to-sink conversion encodes, e.g. conjugation of Coxeter elements of a
Coxeter group. We give a direct proof of a recursion for the number of
equivalence classes of this relation for an arbitrary graph Y using edge
deletion and edge contraction of non-bridge edges. We conclude by showing how
this result may also be obtained through an evaluation of the Tutte polynomial
as T(Y,1,0), and we provide bijections to two other classes of acyclic
orientations that are known to be counted in the same way. A transversal of the
set of equivalence classes is given.Comment: Added a few results about connections to the Tutte polynomia
Coxeter Groups and Asynchronous Cellular Automata
The dynamics group of an asynchronous cellular automaton (ACA) relates
properties of its long term dynamics to the structure of Coxeter groups. The
key mathematical feature connecting these diverse fields is involutions.
Group-theoretic results in the latter domain may lead to insight about the
dynamics in the former, and vice-versa. In this article, we highlight some
central themes and common structures, and discuss novel approaches to some open
and open-ended problems. We introduce the state automaton of an ACA, and show
how the root automaton of a Coxeter group is essentially part of the state
automaton of a related ACA.Comment: 10 pages, 4 figure
Semiclassical transport in nearly symmetric quantum dots. I. Symmetry breaking in the dot
We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry, or fourfold symmetry. In this work—the first of a pair of articles—we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields, and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter gamma_asym. However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot's boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot's boundary smaller than a lead-width is deformed an arbitrarily large distance
Order Independence in Asynchronous Cellular Automata
A sequential dynamical system, or SDS, consists of an undirected graph Y, a
vertex-indexed list of local functions F_Y, and a permutation pi of the vertex
set (or more generally, a word w over the vertex set) that describes the order
in which these local functions are to be applied. In this article we
investigate the special case where Y is a circular graph with n vertices and
all of the local functions are identical. The 256 possible local functions are
known as Wolfram rules and the resulting sequential dynamical systems are
called finite asynchronous elementary cellular automata, or ACAs, since they
resemble classical elementary cellular automata, but with the important
distinction that the vertex functions are applied sequentially rather than in
parallel. An ACA is said to be pi-independent if the set of periodic states
does not depend on the choice of pi, and our main result is that for all n>3
exactly 104 of the 256 Wolfram rules give rise to a pi-independent ACA. In 2005
Hansson, Mortveit and Reidys classified the 11 symmetric Wolfram rules with
this property. In addition to reproving and extending this earlier result, our
proofs of pi-independence also provide significant insight into the dynamics of
these systems.Comment: 18 pages. New version distinguishes between functions that are
pi-independent but not w-independen
Detecting planets in protoplanetary disks: A prospective study
We investigate the possibility to find evidence for planets in circumstellar
disks by infrared and submillimeter interferometry. We present simulations of a
circumstellar disk around a solar-type star with an embedded planet of 1
Jupiter mass. The three-dimensional (3D) density structure of the disk results
from hydrodynamical simulations. On the basis of 3D radiative transfer
simulations, images of this system were calculated. The intensity maps provide
the basis for the simulation of the interferometers VLTI (equipped with the
mid-infrared instrument MIDI) and ALMA. While MIDI/VLTI will not provide the
possibility to distinguish between disks with or without a gap on the basis of
visibility measurements, ALMA will provide the necessary basis for a direct gap
detection.Comment: 5 page
Semiclassical transport in nearly symmetric quantum dots II: symmetry-breaking due to asymmetric leads
In this work - the second of a pair of articles - we consider transport
through spatially symmetric quantum dots with leads whose widths or positions
do not obey the spatial symmetry. We use the semiclassical theory of transport
to find the symmetry-induced contributions to weak localization corrections and
universal conductance fluctuations for dots with left-right, up-down, inversion
and four-fold symmetries. We show that all these contributions are suppressed
by asymmetric leads, however they remain finite whenever leads intersect with
their images under the symmetry operation. For an up-down symmetric dot, this
means that the contributions can be finite even if one of the leads is
completely asymmetric. We find that the suppression of the contributions to
universal conductance fluctuations is the square of the suppression of
contributions to weak localization. Finally, we develop a random-matrix theory
model which enables us to numerically confirm these results.Comment: (18pages - 9figures) This is the second of a pair of articles (v3
typos corrected - including in equations
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