552 research outputs found
The Maslov index and nondegenerate singularities of integrable systems
We consider integrable Hamiltonian systems in R^{2n} with integrals of motion
F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical
points of F where rank dF = n-1 and which have definite linear stability. The
set of nondegenerate singularities is a codimension-two symplectic submanifold
invariant under the flow. We show that the Maslov index of a closed curve is a
sum of contributions +/- 2 from the nondegenerate singularities it is encloses,
the sign depending on the local orientation and stability at the singularities.
For one-freedom systems this corresponds to the well-known formula for the
Poincar\'e index of a closed curve as the oriented difference between the
number of elliptic and hyperbolic fixed points enclosed. We also obtain a
formula for the Liapunov exponent of invariant (n-1)-dimensional tori in the
nondegenerate singular set. Examples include rotationally symmetric n-freedom
Hamiltonians, while an application to the periodic Toda chain is described in a
companion paper.Comment: 27 pages, 1 figure; published versio
Slow epidemic extinction in populations with heterogeneous infection rates
We explore how heterogeneity in the intensity of interactions between people
affects epidemic spreading. For that, we study the
susceptible-infected-susceptible model on a complex network, where a link
connecting individuals and is endowed with an infection rate
proportional to the intensity of their contact
, with a distribution taken from face-to-face experiments
analyzed in Cattuto (PLoS ONE 5, e11596, 2010). We find an extremely
slow decay of the fraction of infected individuals, for a wide range of the
control parameter . Using a distribution of width we identify two
large regions in the space with anomalous behaviors, which are
reminiscent of rare region effects (Griffiths phases) found in models with
quenched disorder. We show that the slow approach to extinction is caused by
isolated small groups of highly interacting individuals, which keep epidemic
alive for very long times. A mean-field approximation and a percolation
approach capture with very good accuracy the absorbing-active transition line
for weak (small ) and strong (large ) disorder, respectively
Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain
The n-particle periodic Toda chain is a well known example of an integrable
but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold
singularities of the Toda chain, ie points where there exist k independent
linear relations amongst the gradients of the integrals of motion, coincide
with points where there are k (doubly) degenerate eigenvalues of
representatives L and Lbar of the two inequivalent classes of Lax matrices
(corresponding to degenerate periodic or antiperiodic solutions of the
associated second-order difference equation). The singularities are shown to be
nondegenerate, so that Sigma_k is a codimension-2k symplectic submanifold.
Sigma_k is shown to be of elliptic type, and the frequencies of transverse
oscillations under Hamiltonians which fix Sigma_k are computed in terms of
spectral data of the Lax matrices. If mu(C) is the (even) Maslov index of a
closed curve C in the regular component of R^{2n}, then (-1)^{\mu(C)/2} is
given by the product of the holonomies (equal to +/- 1) of the even- (or odd-)
indexed eigenvector bundles of L and Lmat.Comment: 25 pages; published versio
Magnetic Field Dependence of the Level Spacing of a Small Electron Droplet
The temperature dependence of conductance resonances is used to measure the
evolution with the magnetic field of the average level spacing
of a droplet containing electrons created by lateral confinement of a
two-dimensional electron gas in GaAs. becomes very small (eV) near two critical magnetic fields at which the symmetry of the
droplet changes and these decreases of are predicted by
Hartree-Fock (HF) for charge excitations. Between the two critical fields,
however, the largest measured eV is an order of
magnitude smaller than predicted by HF but comparable to the Zeeman splitting
at this field, which suggests that the spin degrees of freedom are important.
PACS: 73.20.Dx, 73.20.MfComment: 11 pages of text in RevTeX, 4 figures in Postscript (files in the
form of uuencoded compressed tar file
Maslov Indices and Monodromy
We prove that for a Hamiltonian system on a cotangent bundle that is
Liouville-integrable and has monodromy the vector of Maslov indices is an
eigenvector of the monodromy matrix with eigenvalue 1. As a corollary the
resulting restrictions on the monodromy matrix are derived.Comment: 6 page
Detection of Intracellular Bacterial Communities in Human Urinary Tract Infection
Analyzing urine specimens from women with bladder infections, Scott Hultgren and colleagues find evidence for intracellular bacterial communities, which have been associated with recurrent urinary tract infections in mice
Cloaked Facebook pages: Exploring fake Islamist propaganda in social media
This research analyses cloaked Facebook pages that are created to spread political propaganda by cloaking a user profile and imitating the identity of a political opponent in order to spark hateful and aggressive reactions. This inquiry is pursued through a multi-sited online ethnographic case study of Danish Facebook pages disguised as radical Islamist pages, which provoked racist and anti-Muslim reactions as well as negative sentiments towards refugees and immigrants in Denmark in general. Drawing on Jessie Daniels’ critical insights into cloaked websites, this research furthermore analyses the epistemological, methodological and conceptual challenges of online propaganda. It enhances our understanding of disinformation and propaganda in an increasingly interactive social media environment and contributes to a critical inquiry into social media and subversive politics
Measuring Temperature Gradients over Nanometer Length Scales
When a quantum dot is subjected to a thermal gradient, the temperature of
electrons entering the dot can be determined from the dot's thermocurrent if
the conductance spectrum and background temperature are known. We demonstrate
this technique by measuring the temperature difference across a 15 nm quantum
dot embedded in a nanowire. This technique can be used when the dot's energy
states are separated by many kT and will enable future quantitative
investigations of electron-phonon interaction, nonlinear thermoelectric
effects, and the effciency of thermoelectric energy conversion in quantum dots.Comment: 6 pages, 5 figure
Detection of Coulomb Charging around an Antidot in the Quantum Hall Regime
We have detected oscillations of the charge around a potential hill (antidot)
in a two-dimensional electron gas as a function of a large magnetic field B.
The field confines electrons around the antidot in closed orbits, the areas of
which are quantised through the Aharonov-Bohm effect. Increasing B reduces each
state's area, pushing electrons closer to the centre, until enough charge
builds up for an electron to tunnel out. This is a new form of the Coulomb
blockade seen in electrostatically confined dots. Addition and excitation
spectra in DC bias confirm the Coulomb blockade of tunnelling.Comment: 4 pages, 4 Postscript figure
Leading off-diagonal contribution to the spectral form factor of chaotic quantum systems
We semiclassically derive the leading off-diagonal correction to the spectral
form factor of quantum systems with a chaotic classical counterpart. To this
end we present a phase space generalization of a recent approach for uniformly
hyperbolic systems (M. Sieber and K. Richter, Phys. Scr. T90, 128 (2001); M.
Sieber, J. Phys. A: Math. Gen. 35, L613 (2002)). Our results coincide with
corresponding random matrix predictions. Furthermore, we study the transition
from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 8 pages, 2 figures; J. Phys. A: Math. Gen. (accepted for publication
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