116 research outputs found
Fractional-filling Mott domains in two dimensional optical superlattices
Ultracold bosons in optical superlattices are expected to exhibit
fractional-filling insulating phases for sufficiently large repulsive
interactions. On strictly 1D systems, the exact mapping between hard-core
bosons and free spinless fermions shows that any periodic modulation in the
lattice parameters causes the presence of fractional-filling insulator domains.
Here, we focus on two recently proposed realistic 2D structures where such
mapping does not hold, i.e. the two-leg ladder and the trimerized kagome'
lattice. Based on a cell strong-coupling perturbation technique, we provide
quantitatively satisfactory phase diagrams for these structures, and give
estimates for the occurrence of the fractional-filling insulator domains in
terms of the inter-cell/intra-cell hopping amplitude ratio.Comment: 4 pages, 3 figure
Topological regulation of activation barriers on fractal substrates
We study phase-ordering dynamics of a ferromagnetic system with a scalar
order-parameter on fractal graphs. We propose a scaling approach, inspired by
renormalization group ideas, where a crossover between distinct dynamical
behaviors is induced by the presence of a length associated to the
topological properties of the graph. The transition between the early and the
asymptotic stage is observed when the typical size of the growing
ordered domains reaches the crossover length . We consider two
classes of inhomogeneous substrates, with different activated processes, where
the effects of the free energy barriers can be analytically controlled during
the evolution. On finitely ramified graphs the free energy barriers encountered
by domains walls grow logarithmically with while they increase as a
power-law on all the other structures. This produces different asymptotic
growth laws (power-laws vs logarithmic) and different dependence of the
crossover length on the model parameters. Our theoretical picture
agrees very well with extensive numerical simulations.Comment: 13 pages, 4 figure
Superdiffusion and Transport in 2d-systems with L\'evy Like Quenched Disorder
We present an extensive analysis of transport properties in superdiffusive
two dimensional quenched random media, obtained by packing disks with radii
distributed according to a L\'evy law. We consider transport and scaling
properties in samples packed with two different procedures, at fixed filling
fraction and at self-similar packing, and we clarify the role of the two
procedures in the superdiffusive effects. Using the behavior of the filling
fraction in finite size systems as the main geometrical parameter, we define an
effective L\'evy exponents that correctly estimate the finite size effects. The
effective L\'evy exponent rules the dynamical scaling of the main transport
properties and identify the region where superdiffusive effects can be
detected.Comment: 12 pages, 19 figure
On a class of rational matrices and interpolating polynomials related to the discrete Laplace operator
Let \dlap be the discrete Laplace operator acting on functions (or rational
matrices) , where is the two
dimensional lattice of size embedded in . Consider a rational
matrix , whose inner entries
satisfy \dlap\mathcal{H}_{ij}=0. The matrix is thus the
classical finite difference five-points approximation of the Laplace operator
in two variables. We give a constructive proof that is the
restriction to of a discrete harmonic polynomial in two
variables for any . This result proves a conjecture formulated in the
context of deterministic fixed-energy sandpile models in statistical mechanics.Comment: 18 pag, submitted to "Note di Matematica
Anomalous transmission and drifts in one-dimensional Levy structures
We study the transmission of random walkers through a finite-size
inhomogeneous material with a quenched, long-range correlated distribution of
scatterers. We focus on a finite one-dimensional structure where walkers
undergo random collisions with a subset of sites distributed on deterministic
(Cantor-like) or random positions, with L\'evy spaced distances. Using scaling
arguments, we consider stationary and time-dependent transmission and we
provide predictions on the scaling behaviour of particle current as a function
of the sample size. We show that, even in absence of bias, for each single
realization a non-zero drift can be present, due to the intrinsic asymmetry of
each specific arrangement of the scattering sites. For finite systems, this
average drift is particularly important for characterizing the transmission
properties of individual samples. The predictions are tested against the
numerical solution of the associated master equation. A comparison of different
boundary conditions is given.Comment: Submitted to Chaos, Solitons and Fractal
Fast rare events in exit times distributions of jump processes
Rare events in the first-passage distributions of jump processes are capable
of triggering anomalous reactions or series of events. Estimating their
probability is particularly important when the jump probabilities have
broad-tailed distributions, and rare events are therefore not so rare. We study
three jump processes that are used to model a wide class of stochastic
processes ranging from biology to transport in disordered systems, ecology and
finance. We consider discrete time random-walks, continuous time random-walks
and the L\'evy-Lorentz gas and determine the exact form of the scaling function
for the probability distribution of fast rare events, in which the jump process
exits in a very short time at a large distance opposite to the starting point.
For this estimation we use the so called big jump principle, and we show that
in the regime of fast rare events the exit time distributions are not
exponentially suppressed, even in the case of normal diffusion. This implies
that fast rare events are actually much less rare than predicted by the usual
estimates of large deviations and can occur on timescales orders of magnitude
shorter than expected. Our results are confirmed by extensive numerical
simulations.Comment: 6 pages, 4 figure
Phase ordering in disordered and inhomogeneous systems
We study numerically the coarsening dynamics of the Ising model on a regular
lattice with random bonds and on deterministic fractal substrates. We propose a
unifying interpretation of the phase-ordering processes based on two classes of
dynamical behaviors characterized by different growth-laws of the ordered
domains size - logarithmic or power-law respectively. It is conjectured that
the interplay between these dynamical classes is regulated by the same
topological feature which governs the presence or the absence of a
finite-temperature phase-transition.Comment: 15 pages, 7 figures. To appear on Physical Review E (2015
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