On the asymmetric zero-range in the rarefaction fan

We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial condition and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps we derive the Law of Large Numbers for the position of a second class particle under the initial configuration in which all the positive sites are empty, all the negative sites are occupied with infinitely many first class particles and with a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle, this particle chooses randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation through some sort of renormalization function. By coupling the zero-range with the exclusion process we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic

Speedy motions of a body immersed in an infinitely extended medium

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Psi. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound "runaway effect". Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a heuristic level the case in which Psi(r) diverges at short distances like g r^{-a}, g,a>0, by showing that the runaway effect still occurs if a<2.Comment: 15 page

Forecasts for the detection of the magnetised cosmic web from cosmological simulations

The cosmic web contains a large fraction of the total gas mass in the universe but is difficult to detect at most wavelengths. Synchrotron emission from shock-accelerated electrons may offer the chance of imaging the cosmic web at radio wavelengths. In this work we use 3D cosmological ENZO-MHD simulations (combined with a post-processing renormalisation of the magnetic field to bracket for missing physical ingredients and resolution effects) to produce models of the radio emission from the cosmic web. In post-processing we study the capabilities of 13 large radio surveys to detect this emission. We find that surveys by LOFAR, SKA1-LOW and MWA have a chance of detecting the cosmic web, provided that the magnetisation level of the tenuous medium in filaments is of the order of 1% of the thermal gas energy.Comment: 19 pages, 18 figures. A&A accepted, in press. The public repository of radio maps for the full volumes studied in this work is available at http://www.hs.uni-hamburg.de/DE/Ins/Per/Vazza/projects/Public_data.htm

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure

Exclusion and zero-range in the rarefaction fan

In these notes we briefly review asymptotic results for the totally asymmetric simple exclusion process and the totally asymmetric constant-rate zero-range process, in the presence of particles with different priorities. We review the Law of Large Numbers for a second class particle added to those systems and we present the proof of crossing probabilities for a second and a third class particles. This is done, for the exclusion process, by means of a particle-hole symmetry argument, while for the zero-range process it is a consequence of a coupling argument.FC

Atmospheric neutrinos in a Large Liquid Argon detector

In view of the evaluation of the physics goals of a large Liquid Argon TPC, evolving from the ICARUS technology, we have studied the possibility of performing precision measurements on atmospheric neutrinos. For this purpose we have improved existing Monte Carlo neutrino event generators based on FLUKA and NUX by including the 3-flavor oscillation formalism and the numerical treatment of Earth matter effects. By means of these tools we have studied the sensitivity in the measurement of Theta(23) through the accurate measurement of electron neutrinos. The updated values for Delta m^2(23) from Super-Kamiokande and the mixing parameters as obtained by solar and KamLand experiments have been used as reference input, while different values of Theta(13) have been considered. An exposure larger than 500 kton yr seems necessary in order to achieve a significant result, provided that the present knowledge of systematic uncertainties is largely improved.Comment: Talk given at the worksgop "Cryogenic Liquid Detectors for Future Particle Physics", LNGS (Italy) March 13th-14th, 200

From interacting particle systems to random matrices

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.