735 research outputs found
A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model
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 pres
On the non-Boltzmannian nature of quasi-stationary states in long-range interacting systems
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 -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
-statistics to long-range Hamiltonian systems remains open.Comment: 8 pages, 4 figures. New version accepted for publication in Physica
Dynamical anomalies and the role of initial conditions in the HMF model
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 200
Dynamics and Thermodynamics of a model with long-range interactions
The dynamics and the thermodynamics of particles/spins interacting via
long-range forces display several unusual features with respect to systems with
short-range interactions. The Hamiltonian Mean Field (HMF) model, a Hamiltonian
system of N classical inertial spins with infinite-range interactions
represents a paradigmatic example of this class of systems. The equilibrium
properties of the model can be derived analytically in the canonical ensemble:
in particular the model shows a second order phase transition from a
ferromagnetic to a paramagnetic phase. Strong anomalies are observed in the
process of relaxation towards equilibrium for a particular class of
out-of-equilibrium initial conditions. In fact the numerical simulations show
the presence of quasi-stationary state (QSS), i.e. metastable states which
become stable if the thermodynamic limit is taken before the infinite time
limit. The QSS differ strongly from
Boltzmann-Gibbs equilibrium states: they exhibit negative specific heat,
vanishing Lyapunov exponents and weak mixing, non-Gaussian velocity
distributions and anomalous diffusion, slowly-decaying correlations and aging.
Such a scenario provides strong hints for the possible application of Tsallis
generalized thermostatistics. The QSS have been recently interpreted as a
spin-glass phase of the model. This link indicates another promising line of
research, which is not alternative to the previous one.Comment: 12 pages, 5 figures. Recent review paper for Continuum Mechanics and
Thermodynamic
Microscopic dynamics of a phase transition: equilibrium vs out-of-equilibrium regime
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.
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 in the thermodynamic limit
We study chaos in the Hamiltonian Mean Field model (HMF), a system with many
degrees of freedom in which 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 supp
Lyapunov instability and finite size effects in a system with long-range forces
We study the largest Lyapunov exponent 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 ,
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, goes to zero with
a N-independent power law: . In the continuum limit the
system is integrable in the whole high temperature phase. More precisely, the
behavior is found numerically for 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 Letter
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