294 research outputs found
Mixing length scales of low temperature spin plaquettes models
Plaquette models are short range ferromagnetic spin models that play a key
role in the dynamic facilitation approach to the liquid glass transition. In
this paper we perform a rigorous study of the thermodynamic properties of two
dimensional plaquette models, the square and triangular plaquette models. We
prove that for any positive temperature both models have a unique infinite
volume Gibbs measure with exponentially decaying correlations. We analyse the
scaling of three a priori different static correlation lengths in the small
temperature regime, the mixing, cavity and multispin correlation lengths.
Finally, using the symmetries of the model we determine an exact self
similarity property for the infinite volume Gibbs measure.Comment: 33 pages, 9 figure
A scanning microcavity for in-situ control of single-molecule emission
We report on the fabrication and characterization of a scannable Fabry-Perot
microcavity, consisting of a curved micromirror at the end of an optical fiber
and a planar distributed Bragg reflector. Furthermore, we demonstrate the
coupling of single organic molecules embedded in a thin film to well-defined
resonator modes. We discuss the choice of cavity parameters that will allow
sufficiently high Purcell factors for enhancing the zero-phonon transition
between the vibrational ground levels of the electronic excited and ground
states.Comment: 8 page
Universality for one-dimensional hierarchical coalescence processes with double and triple merges
We consider one-dimensional hierarchical coalescence processes (in short
HCPs) where two or three neighboring domains can merge. An HCP consists of an
infinite sequence of stochastic coalescence processes: each process occurs in a
different "epoch" and evolves for an infinite time, while the evolutions in
subsequent epochs are linked in such a way that the initial distribution of
epoch coincides with the final distribution of epoch . Inside each
epoch a domain can incorporate one of its neighboring domains or both of them
if its length belongs to a certain epoch-dependent finite range. Assuming that
the distribution at the beginning of the first epoch is described by a renewal
simple point process, we prove limit theorems for the domain length and for the
position of the leftmost point (if any). Our analysis extends the results
obtained in [Ann. Probab. 40 (2012) 1377-1435] to a larger family of models,
including relevant examples from the physics literature [Europhys. Lett. 27
(1994) 175-180, Phys. Rev. E (3) 68 (2003) 031504]. It reveals the presence of
a common abstract structure behind models which are apparently very different,
thus leading to very similar limit theorems. Finally, we give here a full
characterization of the infinitesimal generator for the dynamics inside each
epoch, thus allowing us to describe the time evolution of the expected value of
regular observables in terms of an ordinary differential equation.Comment: Published in at http://dx.doi.org/10.1214/12-AAP917 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem
Jamming, or dynamical arrest, is a transition at which many particles stop
moving in a collective manner. In nature it is brought about by, for example,
increasing the packing density, changing the interactions between particles, or
otherwise restricting the local motion of the elements of the system. The onset
of collectivity occurs because, when one particle is blocked, it may lead to
the blocking of a neighbor. That particle may then block one of its neighbors,
these effects propagating across some typical domain of size named the
dynamical correlation length. When this length diverges, the system becomes
immobile. Even where it is finite but large the dynamics is dramatically
slowed. Such phenomena lead to glasses, gels, and other very long-lived
nonequilibrium solids. The bootstrap percolation models are the simplest
examples describing these spatio-temporal correlations. We have been able to
solve one such model in two dimensions exactly, exhibiting the precise
evolution of the jamming correlations on approach to arrest. We believe that
the nature of these correlations and the method we devise to solve the problem
are quite general. Both should be of considerable help in further developing
this field.Comment: 17 pages, 4 figure
Fractional moment bounds and disorder relevance for pinning models
We study the critical point of directed pinning/wetting models with quenched
disorder. The distribution K(.) of the location of the first contact of the
(free) polymer with the defect line is assumed to be of the form
K(n)=n^{-\alpha-1}L(n), with L(.) slowly varying. The model undergoes a
(de)-localization phase transition: the free energy (per unit length) is zero
in the delocalized phase and positive in the localized phase. For \alpha<1/2 it
is known that disorder is irrelevant: quenched and annealed critical points
coincide for small disorder, as well as quenched and annealed critical
exponents. The same has been proven also for \alpha=1/2, but under the
assumption that L(.) diverges sufficiently fast at infinity, an hypothesis that
is not satisfied in the (1+1)-dimensional wetting model considered by Forgacs
et al. (1986) and Derrida et al. (1992), where L(.) is asymptotically constant.
Here we prove that, if 1/21, then quenched and annealed
critical points differ whenever disorder is present, and we give the scaling
form of their difference for small disorder. In agreement with the so-called
Harris criterion, disorder is therefore relevant in this case. In the marginal
case \alpha=1/2, under the assumption that L(.) vanishes sufficiently fast at
infinity, we prove that the difference between quenched and annealed critical
points, which is known to be smaller than any power of the disorder strength,
is positive: disorder is marginally relevant. Again, the case considered by
Forgacs et al. (1986) and Derrida et al. (1992) is out of our analysis and
remains open.Comment: 20 pages, 1 figure; v2: few typos corrected, references revised. To
appear on Commun. Math. Phy
Glass transition in granular media
In the framework of schematic hard spheres lattice models for granular media
we investigate the phenomenon of the ``jamming transition''. In particular,
using Edwards' approach, by analytical calculations at a mean field level, we
derive the system phase diagram and show that ``jamming'' corresponds to a
phase transition from a ``fluid'' to a ``glassy'' phase, observed when
crystallization is avoided. Interestingly, the nature of such a ``glassy''
phase turns out to be the same found in mean field models for glass formers.Comment: 7 pages, 4 figure
Resolution limits of quantum ghost imaging
Quantum ghost imaging uses photon pairs produced from parametric downconversion to enable an alternative method of image acquisition. Information from either one of the photons does not yield an image, but an image can be obtained by harnessing the correlations between them. Here we present an examination of the resolution limits of such ghost imaging systems. In both conventional imaging and quantum ghost imaging the resolution of the image is limited by the point-spread function of the optics associated with the spatially resolving detector. However, whereas in conventional imaging systems the resolution is limited only by this point spread function, in ghost imaging we show that the resolution can be further degraded by reducing the strength of the spatial correlations inherent in the downconversion process
Single-molecule study for a graphene-based nano-position sensor
In this study we lay the groundwork for a graphene-based fundamental ruler at
the nanoscale. It relies on the efficient energy-transfer mechanism between
single quantum emitters and low-doped graphene monolayers. Our experiments,
conducted with dibenzoterrylene (DBT) molecules, allow going beyond ensemble
analysis due to the emitter photo-stability and brightness. A quantitative
characterization of the fluorescence decay-rate modification is presented and
compared to a simple model, showing agreement with the dependence, a
genuine manifestation of a dipole interacting with a 2D material. With DBT
molecules, we can estimate a potential uncertainty in position measurements as
low as 5nm in the range below 30nm
Experimental limits of ghost diffraction: Popper’s thought experiment
Quantum ghost diffraction harnesses quantum correlations to record diffraction or interference features using photons that have never interacted with the diffractive element. By designing an optical system in which the diffraction pattern can be produced by double slits of variable width either through a conventional diffraction scheme or a ghost diffraction scheme, we can explore the transition between the case where ghost diffraction behaves as conventional diffraction and the case where it does not. For conventional diffraction the angular extent increases as the scale of the diffracting object is reduced. By contrast, we show that no matter how small the scale of the diffracting object, the angular extent of the ghost diffraction is limited (by the transverse extent of the spatial correlations between beams). Our study is an experimental realisation of Popper’s thought experiment on the validity of the Copenhagen interpretation of quantum mechanics. We discuss the implication of our results in this context and explain that it is compatible with, but not proof of, the Copenhagen interpretation
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