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M Pettini

Publications and source records attributed to M Pettini.

At least 19 recordsLinked to original sources
PubMed2000

Topology and phase transitions: paradigmatic evidence

We report upon the numerical computation of the Euler characteristic chi (a topologic invariant) of the equipotential hypersurfaces Sigma(v) of the configuration space of the two-dimensional lattice varphi(4) model. The pattern chi(Sigma(v)) versus v (potential energy) reveals that a major topology change in the family Sigma(v)(vinR) is at the origin of the phase transition in the model considered. The direct evidence given here-of the relevance of topology for phase transitions-is obtained through a general method that can be applied to any other model.

Journal Article↗
PubMed2000

Hamiltonian dynamics and geometry of phase transitions in classical XY models

The Hamiltonian dynamics associated with classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. In addition to the conventional signatures of phase transitions, here obtained through time averages of thermodynamical observables in place of ensemble averages, qualitatively different information is derived from the temperature dependence of Lyapunov exponents. A Riemannian geometrization of Newtonian dynamics suggests consideration of other observables of geometric meaning tightly related to the largest Lyapunov exponent. The numerical computation of these observables--unusual in the study of phase transitions--sheds light on the microscopic dynamical counterpart of thermodynamics, also pointing to the existence of some major change in the geometry of the mechanical manifolds at the thermodynamical transition. Through the microcanonical definition of the entropy, a relationship between thermodynamics and the extrinsic geometry of the constant energy surfaces sigma E of phase space can be naturally established. In this framework, an approximate formula is worked out determining a highly nontrivial relationship between temperature and topology of sigma E. From this it can be understood that the appearance of a phase transition must be tightly related to a suitable major topology change of sigma E. This contributes to the understanding of the origin of phase transitions in the microcanonical ensemble.

Journal Article↗
PubMed2000

Analytic lyapunov exponents in a classical nonlinear field equation

It is shown that the nonlinear wave equation partial differential(2)(t)straight phi- partial differential2xstraight phi-&mgr;(0) partial differential(x)( partial differential(x)straight phi)(3)=0, which is the continuum limit of the Fermi-Pasta-Ulam beta model, has a positive Lyapunov exponent lambda(1), whose analytic energy dependence is given. The result (a first example for field equations) is achieved by evaluating the lattice-spacing dependence of lambda(1) for the FPU model within the framework of a Riemannian description of Hamiltonian chaos. We also discuss a difficulty of the statistical mechanical treatment of this classical field system, which is absent in the dynamical description.

Journal Article↗
PubMed2000

Phase space geometry and stochasticity thresholds in hamiltonian dynamics

Results of numerical computations of the largest Lyapunov exponent lambda(1)(varepsilon,N) as a function of the energy density varepsilon and the number of particles N are here reported for a Fermi-Pasta-Ulam alpha+beta model. These results show the coexistence at large N of two thresholds: a stochasticity threshold, found before for the alpha model alone, and a strong stochasticity threshold (SST), found before for the beta model alone. Although this coexistence may seem at first sight plausible, it is not obvious a priori that the alpha+beta model superimposes properties of the alpha and beta models independently. The main point of this paper, however, is a geometric characterization of the SST via the mean curvature of the constant energy hypersurfaces in the phase space of the model and the characteristic decay time of its time autocorrelation function tau(c)(varepsilon,N), which correlates with that of lambda(1)(varepsilon,N) for fixed N. This appears to provide important information on the very complicated geometry of the phase space of this simple solidlike model.

Journal Article↗
PubMed1999

Topological aspects of geometrical signatures of phase transitions.

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical phi(4) models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart to a phase transition.

Journal Article↗
PubMed1994

[An outpatient regimen for dental improvements in patients with valvular cardiopathies and oral anticoagulant therapy (a preliminary note)].

The purpose of this paper is to verify the level of confidence of a new approach to the management of patients with cardiovalvular prosthetic and oral treatment with anticoagulants during high level risk oral surgery procedures. The new protocol includes: interrupted oral anticoagulant treatment; ambulatory regimen instead of hospital regimen; special dentistry management. No hemorrhagic complications occurred in the study sample. This paper concludes with a review of the role of Quick test in the management of patients with cardiac prostheses.

Administration, Oral↗