M. C. Firpo | Searcharxiv

arXiv1998

Analytic estimation of Lyapunov exponent in a mean-field model undergoing a phase transition

The parametric instability contribution to the largest Lyapunov exponent (LLE) is derived for a mean-field Hamiltonian model, with attractive long-range interactions. This uses a recent Riemannian approach to describe Hamiltonian chaos with a large number N of degrees of freedom. Through microcanonical estimates of suitable geometrical observables, the mean-field behavior of the LLE is analytically computed and related to the second order phase transition undergone by the system. It predicts that chaoticity drops to zero at the critical temperature and remains vanishing above it, with the LLE scaling as N^-1/3 to the leading order in N.

chao-dyn↗

arXiv1997

Kinetic limit of N-body description of wave-particle self- consistent interaction

A system of N particles eN=(x1,v1,...,xN,vN) interacting self-consistently with M waves Zn=An*exp(iTn) is considered. Hamiltonian dynamics transports initial data (eN(0),Zn(0)) to (eN(t),Zn(t)). In the limit of an infinite number of particles, a Vlasov-like kinetic equation is generated for the distribution function f(x,v,t), coupled to envelope equations for the M waves. Any initial data (f(0),Z(0)) with finite energy is transported to a unique (f(t),Z(t)). Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution fN(0)-->f(O) weakly and with Zn(0)-->Z(O) as N tends to infinity, the states generated by the Hamiltonian dynamics at all time 0<t<T are such that (eN(t),Zn(t)) converges weakly to (f(t),Z(t)). Comments: Kinetic theory, Plasma physics.

physics.plasm-ph↗