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.Comment: 22 page

Non equilibrium stationary state for the SEP with births and deaths

We consider the symmetric simple exclusion process in the interval \La_N:=[-N,N]\cap\mathbb Z with births and deaths taking place respectively on suitable boundary intervals $I_+$ and $I_-$, as introduced in De Masi et al. (J. Stat. Phys. 2011). We study the stationary measure density profile in the limit $N\to\infty

Symmetric simple exclusion process with free boundaries

We consider the one dimensional symmetric simple exclusion process (SSEP) with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle. At a fixed rate birth of particles occur at the position of the leftmost hole and at the same rate, independently, the rightmost particle dies. We prove convergence to a hydrodynamic limit and discuss its relation with a free boundary problem.Comment: 29 pages, 4 figure

Optimal strategy for polarization modulation in the LSPE-SWIPE experiment

Context. Cosmic microwave background (CMB) B-mode experiments are required to control systematic effects with an unprecedented level of accuracy. Polarization modulation by a half wave plate (HWP) is a powerful technique able to mitigate a large number of the instrumental systematics. Aims. Our goal is to optimize the polarization modulation strategy of the upcoming LSPE-SWIPE balloon-borne experiment, devoted to the accurate measurement of CMB polarization at large angular scales. Methods. We departed from the nominal LSPE-SWIPE modulation strategy (HWP stepped every 60 s with a telescope scanning at around 12 deg/s) and performed a thorough investigation of a wide range of possible HWP schemes (either in stepped or continuously spinning mode and at different azimuth telescope scan-speeds) in the frequency, map and angular power spectrum domain. In addition, we probed the effect of high-pass and band-pass filters of the data stream and explored the HWP response in the minimal case of one detector for one operation day (critical for the single-detector calibration process). We finally tested the modulation performance against typical HWP-induced systematics. Results. Our analysis shows that some stepped HWP schemes, either slowly rotating or combined with slow telescope modulations, represent poor choices. Moreover, our results point out that the nominal configuration may not be the most convenient choice. While a large class of spinning designs provides comparable results in terms of pixel angle coverage, map-making residuals and BB power spectrum standard deviations with respect to the nominal strategy, we find that some specific configurations (e.g., a rapidly spinning HWP with a slow gondola modulation) allow a more efficient polarization recovery in more general real-case situations. Conclusions. Although our simulations are specific to the LSPE-SWIPE mission, the general outcomes of our analysis can be easily generalized to other CMB polarization experiments

Slow motion and metastability for a non local evolution equation

In this paper we consider a non local evolution mean field equation proving the existence of an invariant, unstable, one dimensional manifold connecting the critical droplet with the stable and the metastable phases. We prove that the points on the manifold are droplets longer or shorter than the critical one, and that their motion is very slow in agreement with the theory of metastable patterns

Duality and exact correlations for a model of heat conduction

We study a model of heat conduction with stochastic diffusion of energy. We obtain a dual particle process which describes the evolution of all the correlation functions. An exact expression for the covariance of the energy exhibits long-range correlations in the presence of a current. We discuss the formal connection of this model with the simple symmetric exclusion process.Comment: 19 page

Large deviations for the macroscopic motion of an interface

We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac interaction evolving in time according to Glauber (non-conservative) dynamics. Such interfaces separate two stable phases of a ferromagnetic system and in the macroscopic scale are represented by sharp transitions. We derive quantitative estimates for the upper and the lower bound of the cost functional that penalizes all possible deviations and obtain explicit error terms which are valid also in the macroscopic scale. Furthermore, using the result of a companion paper about the minimizers of this cost functional for the macroscopic motion of the interface in a fixed time, we prove that the probability of such events can concentrate on nucleations should the transition happen fast enough