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Background: The mercury isotopes around $N=104$ are a well-known example of nuclei exhibiting shape coexistence. Mixing of configurations can be studied by measuring the monopole strength $\rho^2(E0)$, however, currently the experimental information is scarce and lacks precision, especially for the $I^\pi \rightarrow I^\pi$ ($I \neq 0$) transitions. Purpose: The goals of this study were to increase the precision of the known branching ratios and internal conversion coefficients, to increase the amount of available information regarding excited states in $^{182,184,186}$Hg and to interpret the results in the framework of shape coexistence using different models. Method: The low-energy structures in $^{182,184,186}$Hg were populated in the $\beta$ decay of $^{182,184,186}$Tl, produced at ISOLDE and purified by laser ionization and mass separation. The $\gamma$-ray and internal conversion electron events were detected by five germanium clover detectors and a segmented silicon detector, respectively, and correlated in time to build decay schemes. Results: In total, 193, 178 and 156 transitions, including 144, 140 and 108 observed for the first time in a $\beta$-decay experiment, were assigned to $^{182,184,186}$Hg, respectively. Internal conversion coefficients were determined for 23 transitions, out of which 12 had an $E0$ component. Extracted branching ratios allowed the sign of the interference term in $^{182}$Hg as well as $\rho^2(E0;0^+_2\rightarrow 0^+_1)$ and $B(E2;0^+_2\rightarrow 2^+_1)$ in $^{184}$Hg to be determined. By means of electron-electron coincidences, the $0^+_3$ state was identified in $^{184}$Hg. The experimental results were qualitatively reproduced by five theoretical approaches, the IBM with configuration mixing with two different parametrizations, the General Bohr Hamiltonian, the BMF model and the SCCM model. However, a quantitative description is lacking., Comment: 21 pages, 30 figures, accepted for publication in Physical Review C

The N/Z dependence of projectile fragmentation at relativistic energies has been studied with the ALADIN forward spectrometer at the GSI Schwerionen Synchrotron (SIS). Stable and radioactive Sn and La beams with an incident energy of 600 MeV per nucleon have been used in order to explore a wide range of isotopic compositions. For the interpretation of the data, calculations with the statistical multifragmentation model for a properly chosen ensemble of excited sources were performed. The parameters of the ensemble, representing the variety of excited spectator nuclei expected in a participant-spectator scenario, are determined empirically by searching for an optimum reproduction of the measured fragment-charge distributions and correlations. An overall very good agreement is obtained. The possible modification of the liquid-drop parameters of the fragment description in the hot freeze-out environment is studied, and a significant reduction of the symmetry-term coefficient is found necessary to reproduce the mean neutron-to-proton ratios /Z and the isoscaling parameters of Z<=10 fragments. The calculations are, furthermore, used to address open questions regarding the modification of the surface-term coefficient at freeze-out, the N/Z dependence of the nuclear caloric curve, and the isotopic evolution of the spectator system between its formation during the initial cascade stage of the reaction and its subsequent breakup., Comment: 23 pages, 29 figures, published in Physical Review C

A phase transition signature associated with cumulants of the largest fragment size distribution has been identified in statistical multifragmentation models and examined in analysis of the ALADIN S254 data on fragmentation of neutron-poor and neutron-rich projectiles. Characteristics of the transition point indicated by this signature are weakly dependent on the A/Z ratio of the fragmenting spectator source. In particular, chemical freeze-out temperatures are estimated within the range 5.9 to 6.5 MeV. The experimental results are well reproduced by the SMM model., Comment: 7 pages, 3 figures, Proceedings of the International Workshop on Multifragmentation and Related Topics (IWM2009), Catania, Italy, November 2009.

We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection between the two models, which can be considered as limiting cases (dissipative and conservative, respectively) of a more general dynamical system of damped-driven coupled pendula. We also show that, in the Kuramoto model, the shape of the phase transition and the largest Lyapunov exponent behavior are strongly dependent on the distribution of the natural frequencies., Comment: 6 pages, 6 figures. Fig.2,3,5 corrected for the Lyapunov exponents of the Kuramoto model, minor changes in the text

We give a closer look at the Central Limit Theorem (CLT) behavior in quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. The frequency of occurrence of each class depends on the size of the system. The different microsocopic nature of the QSS leads to different dynamical correlations and therefore to different results for the observed CLT behavior., Comment: 11 pages, 8 figures. Text and figures added, Physica A in press

In this paper we discuss the nonergodic behavior for a class of long-standing quasi-stationary states in a paradigmatic model of long-range interacting systems, i.e. the HMF model. We show that ensemble averages and time averages for velocities probability density functions (pdfs) do not coincide and in particular the latter exhibit a tendency to converge towards a q-Gaussian attractor instead of the usual Gaussian one predicted by the Central Limit Theorem, when ergodicity applies., Comment: 7 pages, 5 figures, paper presented at the International SPIE Conference on Complex Systems, 5-7 December 2007, Canberra, Australia, http://spie.org/x12360.xml

We explore the quasistationary regime of the Hamiltonian Mean Field Model (HMF) showing that at least three different classes of events exist, with a different diffusive behavior and with a relative frequency which depends on the size of the system. Along the same line of a recent work \cite{epl}, these results indicate that one must be very careful in exchanging time averages with ensemble averages during the non-ergodic metastable regime and at the same time they emphasize the role of finite size effects in the evaluation of the diffusive properties of the system., Comment: 8 pages, Paper presented at the intern. conf. CTNEXT07, satellite of STAPHYS23, 1-5 july 2007, Catania, Italy http://www.ct.infn.it/ctnext07 Available online at http://proceedings.aip.org/proceedings/confproceed/965.jsp

We present a molecular dynamics test of the Central Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime (specifically, at thermal equilibrium), ergodicity is essentially verified, and the Pdfs of the sums appear to be Gaussians, consistently with the standard CLT. When the system is, instead, only weakly chaotic (specifically, along longstanding metastable Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time averages) is observed, and robust $q$-Gaussian attractors emerge, consistently with recently proved generalizations of the CLT., Comment: 6 pages 7 figures. Improved version accepted for publication on Europhysics Letters

We investigate the Coulomb excitation of low-lying states of unstable nuclei in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/nucleon). It is shown that the cross sections for the $E1$ and $E2$ transitions are larger at lower energies, much less than 10 MeV/nucleon. Retardation effects and Coulomb distortion are found to be both relevant for energies as low as 10 MeV/nucleon and as high as 500 MeV/nucleon. Implications for studies at radioactive beam facilities are discussed., Comment: 12 pages, 2 figures, accepted for publication in Phys. Lett. B

We discuss the non-Boltzmannian nature of quasi-stationary states in the Hamiltonian Mean Field (HMF) model, a paradigmatic model for long-range interacting classical many-body systems. We present a theorem excluding the Boltzmann-Gibbs exponential weight in Gibbs $\Gamma$-space of microscopic configurations, and comment a paper recently published by Baldovin and Orlandini (2006). On the basis of the points here discussed, the ongoing debate on the possible application, within appropriate limits, of the generalized $q$-statistics to long-range Hamiltonian systems remains open., Comment: 8 pages, 4 figures. New version accepted for publication in Physica A

In a recent letter (PRL 95, 190601 (2005)), T.M. Rocha Filho and coworkers address the very interesting issue of the entropic form to be used for Hamiltonians with long-range interactions. In our opinion the letter misses several points quite debated in the recent literature which are of fundamental importance for a complete discussion of this problem. Moreover it contains several statements which are not true or not corroborated by any evidence. In this comment we discuss these arguments and severely question the generality of the conclusions of this letter., Comment: 1 page, no figures. Revised version, refs added

We discuss the role of the initial conditions for the dynamical anomalies observed in the quasi-stationary states of the Hamiltonian Mean Field (HMF) model., Comment: 8 pages, 5 figures, submitted to Physica A for the proceedings of the conference Frontier Science 2003 Pavia, Italy, 8-12 September 2003

We study the relaxation dynamics of a Hamiltonian system of N fully-coupled XY spins. The thermodynamics of the system predicts a ferromagnetic and a paramagnetic phase. Starting from out-of-equilibrium initial conditions, the dynamics at constant energy drives the system into quasi-stationary states (QSS) characterized by dynamical frustration. We introduce the spin polarization as a new order parameter which allows to interpret the dynamically generated QSS regime as a glassy phase of the model., Comment: Revtex4, 4 pages, 3 figures. New revised and improved version. Analogy with spin-glasses relativised, refs added, fig3 improved

We study the microscopic dynamics of the metastable Quasi-Stationary States (QSS) in the Hamiltonian Mean Field (HMF) model, a Hamiltonian system of N classical inertial spins with infinite-range interactions which shows a second order phase transition. In order to understand the origin of metastability, which appears in an energy region below the critical point, we consider two different classes of out-of-equilibrium initial conditions, both leading to QSS, and having respectively initial magnetization equal to one (M1 IC) and equal to zero (M0 IC). We compare the corresponding $\mu$-space, the resulting velocity pdfs and correlations, and the eventual aging features of the microscopic dynamics. In both cases the model exhibits non-gaussian pdfs, though anomalous correlations are present only when the system is started with an initial magnetization equal to one. In the M0 IC case the relaxation to equilibrium is almost exponential, while,for M1 IC, when correlations and aging are found, the decay is a power-law and the overall behavior can be very well reproduced by a Tsallis q-exponential function. These results contribute to clarify the overall scenario, which is more complex than previously expected and stress the importance of the dynamics in the relaxation process. The nonextensive statistical mechanics formalism proposed by Tsallis seems to be valid, in the out-of-equilibrium phase, when correlations and strong long-term memory effects emerge. This regime becomes stable if the $N\to \infty $ limit is performed before the $t\to \infty $ limit., Comment: 15 pages, 10 figs. Revised version: fig.2 improved, conclusions expanded refs. updated. Invited talk at the Los Alamos int. conf. on "Anomalous distributions..." held in Santa Fe 6-9 Nov. 2002. Physica D (2003) in press. The paper contains a partial reply to the manuscript by Zanette and Montemurro [cond-mat/0209640]. Contact the authors for figures of better quality

We present a brief pedagogical guided tour of the most recent applications of nextensive statistical mechanics to well defined nonlinear dynamical systems, ranging from one-dimensional dissipative maps to many-body Hamiltonian systems., Comment: 24 pages,14 figures. Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/)

We discuss the occurrence of negative specific heat in a nonextensive system which has an equilibrium second-order phase transition.The specific heat is negative only in a transient regime before equilibration, in correspondence to long-lasting metastable states. For these states standard equilibrium Bolzmann-Gibbs thermodynamics does not apply and the system shows non-Gaussian velocity distributions, anomalous diffusion and correlation in phase space. Similar results have recently been found also in several other nonextensive systems, supporting the general validity of this scenario. These models seem also to support the conjecture that a nonexstensive statistical formalism, like the one proposed by Tsallis, should be applied in such cases. The theoretical scenario is not completely clear yet, but there are already many strong theoretical indications suggesting that, it can be wrong to consider the observation of an experimental negative specific heat as an unique and unambiguous signature of a standard equilibrium first-order phase transition., Comment: ReVteX, 7 pages, 4 ps figures, talk presented at IWM 2001. A few typos corrected

Schmidt et al (Phys Rev Lett 86, 1191 (2001)) observe and analyze a negative specific heat in Na clusters. The analysis is done within the framework of Boltzmann-Gibbs equilibrium statistical mechanics. We argue that this is not the only physical possibility to be taken into account. A possible connection with nonextensive statistical mechanics is considered as well., Comment: 7 pages including one figure

We study the dynamics of a Hamiltonian system of N classical spins with infinite-range interaction. We present numerical results which confirm the existence of metaequilibrium Quasi Stationary States (QSS), characterized by non-Gaussian velocity distributions, anomalous diffusion, L\'evy walks and dynamical correlation in phase-space. We show that the Thermodynamic Limit (TL) and the Infinite-Time Limit (ITL) do not commute. Moreover, if the TL is taken before the ITL the system does not relax to the Boltzmann-Gibbs equilibrium, but remains in this new equilibrium state where nonextensive thermodynamics seems to apply., Comment: ReVteX, 10 pages, 5 ps figures, talk presented by V. Latora at NEXT 2001. Revised version with improved figs and updated refs. To be published in Physica A

We study the dynamics of a system of N classical spins with infinite-range interaction. We show that, when the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions and dynamical power-law correlation in phase-space., Comment: ReVteX, 6 pages, 3 ps figures, revised version, figures modified more arguments and refs added, typos corrected

We present for the first time to the nuclear physics community the Hamiltonian Mean Field (HMF) model. The model can be solved analytically in the canonical ensemble and shows a second-order phase transition in the thermodynamic limit. Numerical microcanonical simulations show interesting features in the out-of-equilibrium regime: in particular the model has a negative specific heat. The potential relevance for nuclear multifragmentation is discussed., Comment: 9 pages, Latex, 4 figures included, invited talk to the Int. Conf. CRIS2000 on "Phase transitions in strong interactions: status and perspectives", Acicastello (Italy) May 22-26 2000, submitted to Nucl Phys. A

The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the critical point. In particular, when the particles are prepared in a ``water bag'' initial state, the relaxation to equilibrium is very slow. In the transient time the system lives in a dynamical quasi-stationary state and exhibits anomalous (enhanced) diffusion and L\'evy walks. In this paper we study temperature and velocity distribution of the quasi-stationary state and we show that the lifetime of such a state increases with N. In particular when the $N\to \infty$ limit is taken before the $t \to \infty$ limit, the results obtained are different from the expected canonical predictions. This scenario seems to confirm a recent conjecture proposed by C.Tsallis., Comment: 7 pages, Latex, 4 eps figures included, talk presented at the Intern. Workshop "Classical and quantum complexity and nonextensive thermodynamics", held in Denton, Texas, April 3-6 2000

We study chaos in the Hamiltonian Mean Field model (HMF), a system with many degrees of freedom in which $N$ classical rotators are fully coupled. We review the most important results on the dynamics and the thermodynamics of the HMF, and in particular we focus on the chaotic properties.We study the Lyapunov exponents and the Kolmogorov--Sinai entropy, namely their dependence on the number of degrees of freedom and on energy density, both for the ferromagnetic and the antiferromagnetic case., Comment: 10 pages, Latex, 4 figures included, invited talk to the Int. school/Conf. on "Let's face Chaos Through Nonlinear Dynamics" Maribor (Slovenia) 27 june - 11 july 1999, submitted to Prog. Theor. Physics suppl

Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This connection is here generalized to a simple dissipative system, the logistic map, and especially to the chaos threshold of the latter, the edge of chaos. It is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon entropy is not appropriate. Instead, the non-extensive entropy $S_q\equiv \frac{1-\sum_{i=1}^W p_i^q}{q-1}$, must be used. The latter contains a parameter q, the entropic index which must be given a special value $q^*\ne 1$ (for q=1 one recovers the usual entropy) characteristic of the edge-of-chaos under consideration. The same q^* enters also in the description of the sensitivity to initial conditions, as well as in that of the multifractal spectrum of the attractor., Comment: 6 pages, Latex, 4 figures included, final version accepted for publication in Physics Letters A

We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous diffusion is observed only in a transient out-of-equilibrium regime and for a small range of energy, below the critical one. Superdiffusion is due to L\'evy walks of single particles and is checked independently through the second moment of the distribution, power spectra, trapping and walking time probabilities. Diffusion becomes normal at equilibrium, after a relaxation time which diverges with N., Comment: 5 pages, 4 postscript figures included, revtex, revised version refs. and a few sentences added, fig.3 revised, typos corrected. Accepted for publication in Phys. Rev. Lett., september (1999)

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 PRC

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 D

We study the largest Lyapunov exponent $\lambda$ and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $\lambda$ shows a peak which persists for very large N-values (N=20000). We show, both numerically and analytically, that chaoticity is strongly related to kinetic energy fluctuations. In the limit of small energy, $\lambda$ goes to zero with a N-independent power law: $\lambda \sim \sqrt{U}$. In the continuum limit the system is integrable in the whole high temperature phase. More precisely, the behavior $\lambda \sim N^{-1/3}$ is found numerically for $U > U_c$ and justified on the basis of a random matrix approximation., Comment: 5 pages, Revtex, 3 figures included. Both text and figures have been changed. New Version accepted for publication in Physical Review Letters

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 1998

We discuss the presence of both dynamical chaos and signals of a second--order phase transition in numerical Vlasov simulations of nuclear multifragmentation. We find that chaoticity and criticality are strongly related and play a crucial role in the process of fragments formation. This connection is not limited to our model and seems a rather general feature., Comment: 15 pages, LaTeX, 8 figures available upon request, to be published in the proccedings of the XXXIV Winter Meeting on Nuclear Physics, Bormio (Italy) 22-27 January 1996, ed. I. Iori

We analyze the behavior of a gas of classical particles moving in a two-dimensional "nuclear" billiard whose multipole-deformed walls 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. The absence of coupling terms allows us to recover qualitatively the "wall formula" predictions. We also 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: LateX, 11 pages, 7 figures available on request, to appear in the Proceedings of XXXIV Winter Meeting on Nuclear Physics, Bormio 22-27 January, 1996

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 request

We study the motion of classical particles confined in a two-dimensional "nuclear" billiard whose walls undergo periodic shape oscillations according to a fixed multipolarity. The presence of a coupling term in the single particle Hamiltonian between the particle motion and the collective coordinate generates a fully selfconsistent dynamics. We consider in particular monopole oscillations and demonstrate that self-consistency is essential in order to induce chaotic single-particle motion. We also discuss the dissipative behaviour of the wall motion and its relation with the order-to-chaos transition in the dynamics of the microscopic degrees of freedom. Analogous considerations can be extended to higher multipolarities., Comment: LateX, 10 pages, 3 figures available on request

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic $^4He$ Equation Of State respectively near the critical point for liquid-gas phase transition. We find the largest fluctuations for an initial "critical temperature". The largest Lyapunov exponents $\lambda$ are always positive and can be very well fitted near this "critical temperature" with a functional form $\lambda\propto |T-T_c|^{-\omega}$, where the exponent $\omega=0.15$ is independent of the system and mass number. At smaller temperatures we find that $\lambda\propto T~ ^{0.4498}$, a universal behavior characteristic of an order to chaos transition., Comment: 11 pages, RevTeX, 3 figures not included available upon request

The Vlasov-Nordheim equation is solved numerically on a lattice for nuclear matter in two dimensions. We discuss the reliability of the model at normal density and then study the response of the system to small perturbations. We find deterministic chaos inside the spinodal zone where fragment formation occurs. We discuss in detail the dynamical features of this phenomenon in order to clarify the mechanisms leading to nuclear disassembly in heavy--ion collisions., Comment: 33 pages (16 figures not included but available upon request). RevTEX, Phys. Rev. C submitted, CT-Univ. preprint No.94/04

In the framework of the time-dependent mean field theory, we solve the Vlasov-Nordheim equation and study the sensitive dependence of this highly non-linear equation on the initial conditions. We find that, when nuclear matter is inside the spinodal region, initially small differences between similar trajectories grow exponentially and produce strongly divergent paths resulting in a chaotic evolution. We focus on the fact that chaos spontaneously arises without putting any additional noise. We calculate the largest Lyapunov exponent for various initial densities. This analysis is performed for nuclear matter in two dimensions. It is argued that the mean field chaoticity can cause nuclear multifragmentation observed in intermediate energy heavy-ion reactions., Comment: 7 pages, 7 postscript figures available upon request to A. Rapisarda. Latex version 3.1. Catania University preprint no.93/37

We discuss the relevance of chaotic scattering in heavy--ion reactions at energies around the Coulomb barrier. A model in two and three dimensions which takes into account rotational degrees of freedom is discussed both classically and quantum-mechanically. The typical chaotic features found in this description of heavy-ion collisions are connected with the anomalous behaviour of several experimental data., Comment: 35 pages in RevTex (version 3.0) plus 27 PostScript figures obtainable by anonymous ftp from VAXFCT.CT.INFN.IT in directory kaos. Fig. 1 upon request to the authors. To be published in the October Focus issue on chaotic scattering of CHAOS

We demonstrate, by numerical simulations, that the dynamics of nuclear matter mean field inside the spinodal region is chaotic. Spontaneous symmetry-breaking - no explicit fluctuating term is considered - occurs leading to wild unpredictable density fluctuations. A proper recipe to calculate an average Lyapunov exponent in this multidimensional phase space is introduced. The latter is calculated for different values of the density in order to characterize in a quantitative way the chaotic and regular regions. It is argued that the mean field chaoticity can be the main mechanism of the nuclear multifragmentation occurring in the intermediate energy reactions., Comment: 11 pages (3 figures not included but available upon request). In RevTex (version 3.0). Catania University preprint no.93/20

The distortion on the intermittency signal, due to detection efficiency and to the presence of pre--equilibrium emitted particles, is studied in a schematic model of nuclear multi- fragmentation. The source of the intermittency signal is modeled with a percolating system. The efficiency is schematized by a simple function of the fragment size, and the presence of pre--equilibrium particles is simulated by an additional non--critical fragment source. No selection on the events is considered, and therefore all events are used to calculate the moments. It is found that, despite the absence of event selection, the intermittency signal is quite resistant to the distortion due to the apparatus efficiency, while the inclusion of pre--equilibrium particles in the moment calculation can substantially reduce the strength of the signal. Pre--equilibrium particles should be therefore carefully separated from the rest of the detected fragments, before the intermittency analysis on experimental charge or mass distributions is carried out., Comment: 12 pages, 3 postscript figures included at the end of the manuscript. Plain TeX (version 3.0). Catania University Preprint N.93/01

Cross section fluctuations in nuclear scattering are briefly reviewed in order to show the main important features. Then chaotic scattering is introduced by means of a very simple model. It is shown that chaoticity produces the same kind of irregular fluctuations observed in light heavy--ion collisions. The transition from order to chaos allows a new general framework for a deeper understanding of reaction mechanisms., Comment: 12 pages (8 figures not included but available upon request). In plain Tex (version 3.0). Talk presented at the First Joint Italian-Japanese meeting, "Perspectives in Heavy-Ion Physics", LNS, Catania (Italy), September 29-October 2 1992