179 research outputs found
Information Gathering in Ad-Hoc Radio Networks with Tree Topology
We study the problem of information gathering in ad-hoc radio networks
without collision detection, focussing on the case when the network forms a
tree, with edges directed towards the root. Initially, each node has a piece of
information that we refer to as a rumor. Our goal is to design protocols that
deliver all rumors to the root of the tree as quickly as possible. The protocol
must complete this task within its allotted time even though the actual tree
topology is unknown when the computation starts. In the deterministic case,
assuming that the nodes are labeled with small integers, we give an O(n)-time
protocol that uses unbounded messages, and an O(n log n)-time protocol using
bounded messages, where any message can include only one rumor. We also
consider fire-and-forward protocols, in which a node can only transmit its own
rumor or the rumor received in the previous step. We give a deterministic
fire-and- forward protocol with running time O(n^1.5), and we show that it is
asymptotically optimal. We then study randomized algorithms where the nodes are
not labelled. In this model, we give an O(n log n)-time protocol and we prove
that this bound is asymptotically optimal
Coupling a quantum dot, fermionic leads and a microwave cavity on-chip
We demonstrate a hybrid architecture consisting of a quantum dot circuit
coupled to a single mode of the electromagnetic field. We use single wall
carbon nanotube based circuits inserted in superconducting microwave cavities.
By probing the nanotube-dot using a dispersive read-out in the Coulomb blockade
and the Kondo regime, we determine an electron-photon coupling strength which
should enable circuit QED experiments with more complex quantum dot circuits.Comment: 4 pages, 4 figure
Entanglement in gapless resonating valence bond states
We study resonating-valence-bond (RVB) states on the square lattice of spins
and of dimers, as well as SU(N)-invariant states that interpolate between the
two. These states are ground states of gapless models, although the
SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its
spinful sector. We show that the gapless behavior in spin and dimer RVB states
is qualitatively similar by studying the R\'enyi entropy for splitting a torus
into two cylinders, We compute this exactly for dimers, showing it behaves
similarly to the familiar one-dimensional log term, although not identically.
We extend the exact computation to an effective theory believed to interpolate
among these states. By numerical calculations for the SU(2) RVB state and its
SU(N)-invariant generalizations, we provide further support for this belief. We
also show how the entanglement entropy behaves qualitatively differently for
different values of the R\'enyi index , with large values of proving a
more sensitive probe here, by virtue of exhibiting a striking even/odd effect.Comment: 44 pages, 14 figures, published versio
Series expansions of the percolation probability for directed square and honeycomb lattices
We have derived long series expansions of the percolation probability for
site and bond percolation on directed square and honeycomb lattices. For the
square bond problem we have extended the series from 41 terms to 54, for the
square site problem from 16 terms to 37, and for the honeycomb bond problem
from 13 terms to 36. Analysis of the series clearly shows that the critical
exponent is the same for all the problems confirming expectations of
universality. For the critical probability and exponent we find in the square
bond case, , , in the
square site case , ,
and in the honeycomb bond case , . In addition we have obtained accurate estimates for the critical
amplitudes. In all cases we find that the leading correction to scaling term is
analytic, i.e., the confluent exponent .Comment: LaTex with epsf, 26 pages, 2 figures and 2 tables in Postscript
format included (uufiled). LaTeX version of tables also included for the
benefit of those without access to PS printers (note that the tables should
be printed in landscape mode). Accepted by J. Phys.
Counting a black hole in Lorentzian product triangulations
We take a step toward a nonperturbative gravitational path integral for
black-hole geometries by deriving an expression for the expansion rate of null
geodesic congruences in the approach of causal dynamical triangulations. We
propose to use the integrated expansion rate in building a quantum horizon
finder in the sum over spacetime geometries. It takes the form of a counting
formula for various types of discrete building blocks which differ in how they
focus and defocus light rays. In the course of the derivation, we introduce the
concept of a Lorentzian dynamical triangulation of product type, whose
applicability goes beyond that of describing black-hole configurations.Comment: 42 pages, 11 figure
Associahedra via spines
An associahedron is a polytope whose vertices correspond to triangulations of
a convex polygon and whose edges correspond to flips between them. Using
labeled polygons, C. Hohlweg and C. Lange constructed various realizations of
the associahedron with relevant properties related to the symmetric group and
the classical permutahedron. We introduce the spine of a triangulation as its
dual tree together with a labeling and an orientation. This notion extends the
classical understanding of the associahedron via binary trees, introduces a new
perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's
original approach, and sheds light upon the combinatorial and geometric
properties of the resulting realizations of the associahedron. It also leads to
noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction
Switchable Coupling of Vibrations to Two-Electron Carbon-Nanotube Quantum Dot States
We report transport measurements on a quantum dot in a partly suspended
carbon nanotube. Electrostatic tuning allows us to modify and even switch 'on'
and 'off' the coupling to the quantized stretching vibration across several
charge states. The magnetic-field dependence indicates that only the
two-electron spin-triplet excited state couples to the mechanical motion,
indicating mechanical coupling to both the valley degree of freedom and the
exchange interaction, in contrast to standard models
Higher-Order Airy Scaling in Deformed Dyck Paths
21 pages, 8 figure
Vicious walkers, friendly walkers and Young tableaux II: With a wall
We derive new results for the number of star and watermelon configurations of
vicious walkers in the presence of an impenetrable wall by showing that these
follow from standard results in the theory of Young tableaux, and combinatorial
descriptions of symmetric functions. For the problem of -friendly walkers,
we derive exact asymptotics for the number of stars and watermelons both in the
absence of a wall and in the presence of a wall.Comment: 35 pages, AmS-LaTeX; Definitions of n-friendly walkers clarified; the
statement of Theorem 4 and its proof were correcte
Geometric phases in adiabatic Floquet theory, abelian gerbes and Cheon's anholonomy
We study the geometric phase phenomenon in the context of the adiabatic
Floquet theory (the so-called the Floquet theory). A double
integration appears in the geometric phase formula because of the presence of
two time variables within the theory. We show that the geometric phases are
then identified with horizontal lifts of surfaces in an abelian gerbe with
connection, rather than with horizontal lifts of curves in an abelian principal
bundle. This higher degree in the geometric phase gauge theory is related to
the appearance of changes in the Floquet blocks at the transitions between two
local charts of the parameter manifold. We present the physical example of a
kicked two-level system where these changes are involved via a Cheon's
anholonomy. In this context, the analogy between the usual geometric phase
theory and the classical field theory also provides an analogy with the
classical string theory.Comment: This new version presents a more complete geometric structure which
is topologically non trivia
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