307 research outputs found
Developing critical analysis of explanations in physics teachers: Which direction to take?
International audienc
Photon mediated interaction between distant quantum dot circuits
Engineering the interaction between light and matter is an important goal in
the emerging field of quantum opto-electronics. Thanks to the use of cavity
quantum electrodynamics architectures, one can envision a fully hybrid
multiplexing of quantum conductors. Here, we use such an architecture to couple
two quantum dot circuits . Our quantum dots are separated by 200 times their
own size, with no direct tunnel and electrostatic couplings between them. We
demonstrate their interaction, mediated by the cavity photons. This could be
used to scale up quantum bit architectures based on quantum dot circuits or
simulate on-chip phonon-mediated interactions between strongly correlated
electrons
Nilpotency in type A cyclotomic quotients
We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree
of cyclotomic quotients of rings that categorify one-half of quantum sl(k).Comment: 19 pages, 39 eps files. v3 simplifies antigravity moves and corrects
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Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model
We study numerically and analytically the average length of reduced
(primitive) words in so-called locally free and braid groups. We consider the
situations when the letters in the initial words are drawn either without or
with correlations. In the latter case we show that the average length of the
reduced word can be increased or lowered depending on the type of correlation.
The ideas developed are used for analytical computation of the average number
of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on
request), submitted to J. Phys. (A): Math. Ge
(2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
We perform a non-perturbative sum over geometries in a (2+1)-dimensional
quantum gravity model given in terms of Causal Dynamical Triangulations.
Inspired by the concept of triangulations of product type introduced
previously, we impose an additional notion of order on the discrete, causal
geometries. This simplifies the combinatorial problem of counting geometries
just enough to enable us to calculate the transfer matrix between boundary
states labelled by the area of the spatial universe, as well as the
corresponding quantum Hamiltonian of the continuum theory. This is the first
time in dimension larger than two that a Hamiltonian has been derived from such
a model by mainly analytical means, and opens the way for a better
understanding of scaling and renormalization issues.Comment: 38 pages, 13 figure
Uniform generation in trace monoids
We consider the problem of random uniform generation of traces (the elements
of a free partially commutative monoid) in light of the uniform measure on the
boundary at infinity of the associated monoid. We obtain a product
decomposition of the uniform measure at infinity if the trace monoid has
several irreducible components-a case where other notions such as Parry
measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl
Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs
We define a function by means of the minimum weight flow on a planar graph
and prove that this function solves the ultradiscrete Toda molecule equation,
its B\"acklund transformation and the two dimensional Toda molecule equation.
The method we employ in the proof can be considered as fundamental to the
integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v
Harnessing spin precession with dissipation
International audienceNon-collinear spin transport is at the heart of spin or magnetization control in spintronics devices. The use of nanoscale conductors exhibiting quantum effects in transport could provide new paths for that purpose. Here we study non-collinear spin transport in a quantum dot. We use a device made out of a single-wall carbon nanotube connected to orthogonal ferromagnetic electrodes. In the spin transport signals, we observe signatures of out of equilibrium spin precession that are electrically tunable through dissipation. This could provide a new path to harness spin precession in nanoscale conductors
Cycle-centrality in complex networks
Networks are versatile representations of the interactions between entities
in complex systems. Cycles on such networks represent feedback processes which
play a central role in system dynamics. In this work, we introduce a measure of
the importance of any individual cycle, as the fraction of the total
information flow of the network passing through the cycle. This measure is
computationally cheap, numerically well-conditioned, induces a centrality
measure on arbitrary subgraphs and reduces to the eigenvector centrality on
vertices. We demonstrate that this measure accurately reflects the impact of
events on strategic ensembles of economic sectors, notably in the US economy.
As a second example, we show that in the protein-interaction network of the
plant Arabidopsis thaliana, a model based on cycle-centrality better accounts
for pathogen activity than the state-of-art one. This translates into
pathogen-targeted-proteins being concentrated in a small number of triads with
high cycle-centrality. Algorithms for computing the centrality of cycles and
subgraphs are available for download
Chebyshev type lattice path weight polynomials by a constant term method
We prove a constant term theorem which is useful for finding weight
polynomials for Ballot/Motzkin paths in a strip with a fixed number of
arbitrary `decorated' weights as well as an arbitrary `background' weight. Our
CT theorem, like Viennot's lattice path theorem from which it is derived
primarily by a change of variable lemma, is expressed in terms of orthogonal
polynomials which in our applications of interest often turn out to be
non-classical. Hence we also present an efficient method for finding explicit
closed form polynomial expressions for these non-classical orthogonal
polynomials. Our method for finding the closed form polynomial expressions
relies on simple combinatorial manipulations of Viennot's diagrammatic
representation for orthogonal polynomials. In the course of the paper we also
provide a new proof of Viennot's original orthogonal polynomial lattice path
theorem. The new proof is of interest because it uses diagonalization of the
transfer matrix, but gets around difficulties that have arisen in past attempts
to use this approach. In particular we show how to sum over a set of implicitly
defined zeros of a given orthogonal polynomial, either by using properties of
residues or by using partial fractions. We conclude by applying the method to
two lattice path problems important in the study of polymer physics as models
of steric stabilization and sensitized flocculation.Comment: 27 pages, 14 figure
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