245 research outputs found
Force--induced depinning of directed polymers
We present an approach to studying directed polymers in interaction with a
defect line and subject to a force, which pulls them away from the line. We
consider in particular the case of inhomogeneous interactions. We first give a
formula relating the free energy of these models to the free energy of the
corresponding ones in which the force is switched off. We then show how to
detect the presence of a re-entrant transition without fully solving the model.
We discuss some models in detail and show that inhomogeneous interaction, e.g.
disordered interactions, may induce the re-entrance phenomenon.Comment: 15 pages, 2 figure
Spiral model, jamming percolation and glass-jamming transitions
The Spiral Model (SM) corresponds to a new class of kinetically constrained
models introduced in joint works with D.S. Fisher [8,9]. They provide the first
example of finite dimensional models with an ideal glass-jamming transition.
This is due to an underlying jamming percolation transition which has
unconventional features: it is discontinuous (i.e. the percolating cluster is
compact at the transition) and the typical size of the clusters diverges faster
than any power law, leading to a Vogel-Fulcher-like divergence of the
relaxation time. Here we present a detailed physical analysis of SM, see [5]
for rigorous proofs. We also show that our arguments for SM does not need any
modification contrary to recent claims of Jeng and Schwarz [10].Comment: 9 pages, 7 figures, proceedings for StatPhys2
Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder
We consider disordered models of pinning of directed polymers on a defect
line, including (1+1)-dimensional interface wetting models, disordered
Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional
polymers in interaction with columnar defects. We consider also random
copolymers at a selective interface. These models are known to have a
(de)pinning transition at some critical line in the phase diagram. In this work
we prove that, as soon as disorder is present, the transition is at least of
second order: the free energy is differentiable at the critical line, and the
order parameter (contact fraction) vanishes continuously at the transition. On
the other hand, it is known that the corresponding non-disordered models can
have a first order (de)pinning transition, with a jump in the order parameter.
Our results confirm predictions based on the Harris criterion.Comment: 4 pages, 1 figure. Version 2: references added, minor changes made.
To appear on Phys. Rev. Let
Hierarchical pinning models, quadratic maps and quenched disorder
We consider a hierarchical model of polymer pinning in presence of quenched
disorder, introduced by B. Derrida, V. Hakim and J. Vannimenius in 1992, which
can be re-interpreted as an infinite dimensional dynamical system with random
initial condition (the disorder). It is defined through a recurrence relation
for the law of a random variable {R_n}_{n=1,2,...}, which in absence of
disorder (i.e., when the initial condition is degenerate) reduces to a
particular case of the well-known Logistic Map. The large-n limit of the
sequence of random variables 2^{-n} log R_n, a non-random quantity which is
naturally interpreted as a free energy, plays a central role in our analysis.
The model depends on a parameter alpha>0, related to the geometry of the
hierarchical lattice, and has a phase transition in the sense that the free
energy is positive if the expectation of R_0 is larger than a certain threshold
value, and it is zero otherwise. It was conjectured by Derrida et al. (1992)
that disorder is relevant (respectively, irrelevant or marginally relevant) if
1/2<alpha<1 (respectively, alpha<1/2 or alpha=1/2), in the sense that an
arbitrarily small amount of randomness in the initial condition modifies the
critical point with respect to that of the pure (i.e., non-disordered) model if
alpha is larger or equal to 1/2, but not if alpha is smaller than 1/2. Our main
result is a proof of these conjectures for the case alpha different from 1/2.
We emphasize that for alpha>1/2 we find the correct scaling form (for weak
disorder) of the critical point shift.Comment: 26 pages, 2 figures. v3: Theorem 1.6 improved. To appear on Probab.
Theory Rel. Field
Effective Constraints and Physical Coherent States in Quantum Cosmology: A Numerical Comparison
A cosmological model with a cyclic interpretation is introduced, which is
subject to quantum back-reaction and yet can be treated rather completely by
physical coherent state as well as effective constraint techniques. By this
comparison, the role of quantum back-reaction in quantum cosmology is
unambiguously demonstrated. Also the complementary nature of strengths and
weaknesses of the two procedures is illustrated. Finally, effective constraint
techniques are applied to a more realistic model filled with radiation, where
physical coherent states are not available.Comment: 32 pages, 25 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
On the study of jamming percolation
We investigate kinetically constrained models of glassy transitions, and
determine which model characteristics are crucial in allowing a rigorous proof
that such models have discontinuous transitions with faster than power law
diverging length and time scales. The models we investigate have constraints
similar to that of the knights model, introduced by Toninelli, Biroli, and
Fisher (TBF), but differing neighbor relations. We find that such knights-like
models, otherwise known as models of jamming percolation, need a ``No Parallel
Crossing'' rule for the TBF proof of a glassy transition to be valid.
Furthermore, most knight-like models fail a ``No Perpendicular Crossing''
requirement, and thus need modification to be made rigorous. We also show how
the ``No Parallel Crossing'' requirement can be used to evaluate the provable
glassiness of other correlated percolation models, by looking at models with
more stable directions than the knights model. Finally, we show that the TBF
proof does not generalize in any straightforward fashion for three-dimensional
versions of the knights-like models.Comment: 13 pages, 18 figures; Spiral model does satisfy property
Relaxation times of kinetically constrained spin models with glassy dynamics
We analyze the density and size dependence of the relaxation time for
kinetically constrained spin systems. These have been proposed as models for
strong or fragile glasses and for systems undergoing jamming transitions. For
the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any
density and for the Knight model below the critical density at which
the glass transition occurs, we show that the persistence and the spin-spin
time auto-correlation functions decay exponentially. This excludes the
stretched exponential relaxation which was derived by numerical simulations.
For FA2f in , we also prove a super-Arrhenius scaling of the form
. For FA1f in = we
rigorously prove the power law scalings recently derived in \cite{JMS} while in
we obtain upper and lower bounds consistent with findings therein.
Our results are based on a novel multi-scale approach which allows to analyze
in presence of kinetic constraints and to connect time-scales and
dynamical heterogeneities. The techniques are flexible enough to allow a
variety of constraints and can also be applied to conservative stochastic
lattice gases in presence of kinetic constraints.Comment: 4 page
The free energy in the Derrida--Retaux recursive model
We are interested in a simple max-type recursive model studied by Derrida and
Retaux (2014) in the context of a physics problem, and find a wide range for
the exponent in the free energy in the nearly supercritical regime
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
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