arXiv subjects

Gioia Carinci

Publications and source records attributed to Gioia Carinci.

23 records · Page 2Linked to original sources

arXiv2013

Super-hydrodynamic limit in interacting particle systems

This paper is a follow-up of the work initiated in [3], where it has been investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two further results: first we characterize the stationary states on the hydrodynamic time scale and show that they are given by a family of linear macroscopic profiles whose parameters are determined by the current reservoirs and the system mass. Then we prove the existence of a super-hyrdrodynamic time scale, beyond the hydrodynamic one. On this larger time scale the system mass fluctuates and correspondingly the macroscopic profile of the system randomly moves within the family of linear profiles, with the randomness of a Brownian motion.

math.PR↗

arXiv2013

Random Hysteresis Loops

Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order $N^{2/3}$, with $N$ the size of the system, the "critical" hysteresis loop becomes random.

math.PR↗

arXiv2013

Hydrodynamic limit in a particle system with topological interactions

We study a system of particles in the interval $[0,ε^{-1}] \cap \mathbb Z$, $ε^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new particles are injected at site 0 at rate $jε$ ($j>0$) and removed at same rate from the rightmost occupied site. The removal mechanism is therefore of topological rather than metric nature. The determination of the rightmost occupied site requires a knowledge of the entire configuration and prevents from using correlation functions techniques. We prove using stochastic inequalities that the system has a hydrodynamic limit, namely that under suitable assumptions on the initial configurations, the law of the density fields $ε\sum ϕ(εx) ξ_{ε^{-2}t}(x)$ ($ϕ$ a test function, $ξ_t(x)$ the number of particles at site $x$ at time $t$) concentrates in the limit $ε\to 0$ on the deterministic value $\int ϕρ_t$, $ρ_t$ interpreted as the limit density at time $t$. We characterize the limit $ρ_t$ as a weak solution in terms of barriers of a limit free boundary problem.

math.PR↗

arXiv2013

Langevin dynamics with a tilted periodic potential

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $γ$ and subject to a further external field $α$. For a suitable choice of the parameters $α$ and $γ$ the related deterministic dynamics yields heteroclinic orbits. In such a regime, in absence of stochastic noise both confined and unbounded orbits coexist. We prove that, with the inclusion of an arbitrarly small noise only the confined orbits survive in a sub-exponential time scale.

math-ph↗

arXiv2013

Duality for stochastic models of transport

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particles densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites. The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Long-range correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.

math-ph↗