Generalized entropy and temperature in nuclear multifragmentation

In the framework of a 2D Vlasov model, we study the time evolution of the "coarse-grained" Generalized Entropy (GE) in a nuclear system which undergoes a multifragmentation (MF) phase transition. We investigate the GE both for the gas and the fragments (surface and bulk part respectively). We find that the formation of the surface causes the growth of the GE during the process of fragmentation. This quantity then characterizes the MF and confirms the crucial role of deterministic chaos in filling the new available phase-space: at variance with the exact time evolution, no entropy change is found when the linear response is applied. Numerical simulations were used also to extract information about final temperatures of the fragments. From a fitting of the momentum distribution with a Fermi-Dirac function we extract the temperature of the fragments at the end of the process. We calculate also the gas temperature by averaging over the available phase space. The latter is a few times larger than the former, indicating a gas not in equilibrium. Though the model is very schematic, this fact seems to be very general and could explain the discrepancy found in experimental data when using the slope of light particles spectra instead of the double ratio of isotope yields method in order to extract the nuclear caloric curve.Comment: 26 pages, 9 postscript figures included, Revtex, some figures and part of text changed, version accepted for publication in PR

Multifragmentation of charge asymmetric nuclear systems

The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of the growth of density fluctuations in unstable expanding nuclear matter. The statistical model makes a choice of the final multifragment configuration according to its statistical weight at a global thermal equilibrium. Similarities and differences in the predictions of the two models on the isotopic composition of the produced fragments are presented and the most sensitive observable characteristics are discussed.Comment: 15 pages, 8 figure

Chaos vs. Linear Instability in the Vlasov Equation: A Fractal Analysis Characterization

In this work we discuss the most recent results concerning the Vlasov dynamics inside the spinodal region. The chaotic behaviour which follows an initial regular evolution is characterized through the calculation of the fractal dimension of the distribution of the final modes excited. The ambiguous role of the largest Lyapunov exponent for unstable systems is also critically reviewed.Comment: 10 pages, RevTeX, 4 figures not included but available upon reques

Chaos and Statistical Mechanics in the Hamiltonian Mean Field Model

We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which shows a second order phase transition. The canonical thermodynamical solution is briefly recalled and its predictions are tested numerically at finite $N$. The Vlasov stationary solution is shown to give the same consistency equation of the canonical solution and its predictions for rotator angle and momenta distribution functions agree very well with numerical simulations. A link is established between the behavior of the maximal Lyapunov exponent and that of thermodynamical fluctuations, expressed by kinetic energy fluctuations or specific heat. The extensivity of chaos in the $N \to \infty$ limit is tested through the scaling properties of Lyapunov spectra and of the Kolmogorov-Sinai entropy. Chaotic dynamics provides the mixing property in phase space necessary for obtaining equilibration; however, the relaxation time to equilibrium grows with $N$, at least near the critical point. Our results constitute an interesting bridge between Hamiltonian chaos in many degrees of freedom systems and equilibrium thermodynamics.Comment: 19 pages, 10 postscript figures included, Latex, Elsevier macros included. Invited talk at the conference ``Classical Chaos and its quantum manifestations'' in honour of Boris Chirikov, Sputnik conference of STATPHYS 20 - Toulouse, France - July 16-18, 1998. Revised version (added refs, changed part of the text and some figures) accepted for publication in Physica

One-body dissipation and chaotic dynamics in a classical simulation of a nuclear gas

In order to understand the origin of one-body dissipation in nuclei, we analyze the behavior of a gas of classical particles moving in a two-dimensional cavity with nuclear dimensions. This "nuclear" billiard has multipole-deformed walls which undergo periodic shape oscillations. We demonstrate that a single particle Hamiltonian containing coupling terms between the particles' motion and the collective coordinate induces a chaotic dynamics for any multipolarity, independently on the geometry of the billiard. If the coupling terms are switched off the "wall formula" predictions are recovered. We discuss the dissipative behavior of the wall motion and its relation with the order-to-chaos transition in the dynamics of the microscopic degrees of freedom.Comment: 16 pages, 12 postscript figures included, revtex, new version completely revised accepted by Physical Review C and scheduled to appear in the issue of november 199

Proposal for an MRPC system with high-precision timing in the LVD structure

The purpose of this paper is to present a project in order to verify -without the need of knowing the distance CERN-Gran Sasso- the discovery made by the OPERA Collaboration concerning the speed of the CERN neutrinos. The project consists of two parts. A simple one and a less simple one. Both have the great advantage of being totally independent of the knowledge of the distance, ≃ 732 km, between the two Labs, CERN and LNGS, where the neutrinos are produced and detected, respectively. The "simple" version of this project is based on the high-energy horizontal cosmic muons, which traverse LVD and OPERA detectors, thus allowing to cross-calibrate the timing systems of both experiments in a way which is totally independent of the TOF measurements of CNGS. This component of the project is being studied in collaboration with the OPERA group, as the time stabilities of both experiments are needed. In fact it is since a long time that the two groups are engaged with this problem. In this paper we will present and discuss the "less simple" part which allows to establish, at the highest possible level of accuracy, if (v > c) effects really exist. © Società Italiana di Fisica/Springer-Verlag 2012

Proposal for an MRPC system with high-precision timing in the LVD structure

The purpose of this paper is to present a project in order to verify -without the need of knowing the distance CERN-Gran Sasso- the discovery made by the OPERA Collaboration concerning the speed of the CERN neutrinos. The project consists of two parts. A simple one and a less simple one. Both have the great advantage of being totally independent of the knowledge of the distance, ≃ 732 km, between the two Labs, CERN and LNGS, where the neutrinos are produced and detected, respectively. The "simple" version of this project is based on the high-energy horizontal cosmic muons, which traverse LVD and OPERA detectors, thus allowing to cross-calibrate the timing systems of both experiments in a way which is totally independent of the TOF measurements of CNGS. This component of the project is being studied in collaboration with the OPERA group, as the time stabilities of both experiments are needed. In fact it is since a long time that the two groups are engaged with this problem. In this paper we will present and discuss the "less simple" part which allows to establish, at the highest possible level of accuracy, if (v > c) effects really exist