We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such ...fields have been studied in systems with a single species, the multi-species setting is much less understood. Among other results, we show that when the system starts from stationary states with a particular property, the scaling limits of the multi-species fluctuation fields, seen in a characteristic traveling frame, solve a coupled Burgers SPDE, which is a formal spatial gradient of a coupled KPZ equation.
We prove the hydrodynamic limit for the symmetric exclusion process with long jumps given by a mean zero probability transition rate with infinite variance and in contact with infinitely many ...reservoirs with density
α
at the left of the system and
β
at the right of the system. The strength of the reservoirs is ruled by
κ
N
-
θ
>
0
. Here
N
is the size of the system,
κ
>
0
and
θ
∈
R
. Our results are valid for
θ
≤
0
. For
θ
=
0
, we obtain a collection of fractional reaction–diffusion equations indexed by the parameter
κ
and with Dirichlet boundary conditions. Their solutions also depend on
κ
. For
θ
<
0
, the hydrodynamic equation corresponds to a reaction equation with Dirichlet boundary conditions. The case
θ
>
0
is still open. For that reason we also analyze the convergence of the unique weak solution of the equation in the case
θ
=
0
when we send the parameter
κ
to zero. Indeed, we conjecture that the limiting profile when
κ
→
0
is the one that we should obtain when taking small values of
θ
>
0
.
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic ...conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31–45,
2010
). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.
We consider extended slow-fast systems of
N
interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean–Vlasov equation depending on
ε
, the scaling ...parameter separating the time scale of the slow variable from the time scale of the fast variable. Its atypical behavior is encapsulated in a large
N
Large Deviation Principle with a rate functional
I
ε
. We study the
Γ
-convergence of
I
ε
as
ε
→
0
and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory for diffusive systems.
Harmonic Systems with Bulk Noises Bernardin, C.; Kannan, V.; Lebowitz, J. L. ...
Journal of statistical physics,
02/2012, Letnik:
146, Številka:
4
Journal Article
Recenzirano
Odprti dostop
We consider a harmonic chain in contact with thermal reservoirs at different temperatures and subject to bulk noises of different types: velocity flips or self-consistent reservoirs. While both ...systems have the same covariances in the non-equilibrium stationary state (NESS) the measures are very different. We study hydrodynamical scaling, large deviations, fluctuations, and long range correlations in both systems. Some of our results extend to higher dimensions.
We consider a chain composed of
N
coupled harmonic oscillators in contact with heat baths at temperature
T
ℓ
and
T
r
at sites 1 and
N
respectively. The oscillators are also subjected to non-momentum ...conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier’s law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.
We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on Formula omitted, the ...scaling parameter separating the time scale of the slow variable from the time scale of the fast variable. Its atypical behavior is encapsulated in a large N Large Deviation Principle with a rate functional Formula omitted. We study the Formula omitted-convergence of Formula omitted as Formula omitted and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory for diffusive systems.
PDF
