8,079 research outputs found
Formality and Star Products
These notes, based on the mini-course given at the PQR2003 Euroschool held in
Brussels in 2003, aim to review Kontsevich's formality theorem together with
his formula for the star product on a given Poisson manifold. A brief
introduction to the employed mathematical tools and physical motivations is
also given.Comment: 49 pages, 9 figures; proceedings of the PQR2003 Euroschool. Version 2
has minor correction
High dimensional measurement device independent quantum key distribution on two dimensional subspaces
Quantum key distribution (QKD) provides ultimate cryptographic security based
on the laws of quantum mechanics. For point-to-point QKD protocols, the
security of the generated key is compromised by detector side channel attacks.
This problem can be solved with measurement device independent QKD (mdi-QKD).
However, mdi-QKD has shown limited performances in terms of the secret key
generation rate, due to post-selection in the Bell measurements. We show that
high dimensional (Hi-D) encoding (qudits) improves the performance of current
mdi-QKD implementations. The scheme is proven to be unconditionally secure even
for weak coherent pulses with decoy states, while the secret key rate is
derived in the single photon case. Our analysis includes phase errors,
imperfect sources and dark counts to mimic real systems. Compared to the
standard bidimensional case, we show an improvement in the key generation rate.Comment: 6 pages, 3 figure
Contraction analysis of switched Filippov systems via regularization
We study incremental stability and convergence of switched (bimodal) Filippov
systems via contraction analysis. In particular, by using results on
regularization of switched dynamical systems, we derive sufficient conditions
for convergence of any two trajectories of the Filippov system between each
other within some region of interest. We then apply these conditions to the
study of different classes of Filippov systems including piecewise smooth (PWS)
systems, piecewise affine (PWA) systems and relay feedback systems. We show
that contrary to previous approaches, our conditions allow the system to be
studied in metrics other than the Euclidean norm. The theoretical results are
illustrated by numerical simulations on a set of representative examples that
confirm their effectiveness and ease of application.Comment: Preprint submitted to Automatic
Anomalous screening of an electrostatic field at the surface of niobium nitride
The interaction between an electric field and the electric charges in a
material is described by electrostatic screening, which in metallic systems is
commonly thought to be confined within a distance of the order of the
Thomas-Fermi length. The validity of this picture, which holds for surface
charges up to , has been recently questioned by
several experimental results when dealing with larger surface charges, such as
those routinely achieved via the ionic gating technique. Whether these results
can be accounted for in a purely electrostatic picture is still debated. In
this work, we tackle this issue by calculating the spatial dependence of the
charge carrier density in thin slabs of niobium nitride via an ab initio
density functional theory approach in the field-effect transistor
configuration. We find that perturbations induced by surface charges are mainly screened within the first layer, while
those induced by larger surface charges can
penetrate over multiple atomic layers, in reasonable agreement with the
available experimental data. Furthermore, we show that a significant
contribution to the screening of large fields is associated not only to the
accumulation layer of the induced charge carriers at the surface, but also to
the polarization of the pre-existing charge density of the undoped system.Comment: 8 pages, 4 figure
Hydrodynamic oscillations and variable swimming speed in squirmers close to repulsive walls
We present a lattice Boltzmann study of the hydrodynamics of a fully resolved
squirmer, radius R, confined in a slab of fluid between two no-slip walls. We
show that the coupling between hydrodynamics and short-range repulsive
interactions between the swimmer and the surface can lead to hydrodynamic
trapping of both pushers and pullers at the wall, and to hydrodynamic
oscillations in the case of a pusher. We further show that a pusher moves
significantly faster when close to a surface than in the bulk, whereas a puller
undergoes a transition between fast motion and a dynamical standstill according
to the range of the repulsive interaction. Our results critically require
near-field hydrodynamics; they further suggest that it should be possible to
control density and speed of squirmers at a surface by tuning the range of
steric and electrostatic swimmer-wall interactions.Comment: 5 + 8 pages, 4 + 4 Figure
- …