Weak Chaos and the "Melting Transition" in a Confined Microplasma System

Date
Authors
Antonopoulos, Chris
Basios, Vasileios
Bountis, Tassos
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long--range Coulomb interactions. In its lower energy regime, we first detect macroscopically, the transition from a "crystalline--like" to a "liquid--like" behavior, which we call the "melting transition". We then proceed to study this transition using a microscopic chaos indicator called the \emph{Smaller Alignment Index} (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasi--periodic) orbits, while it decays exponentially to zero for chaotic orbits as $\exp(-(\lambda_{1}-\lambda_{2})t)$, where $\lambda_{1}>\lambda_{2}>0$ are the two largest Lyapunov exponents. During the "melting phase", SALI exhibits a peculiar, stair--like decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the $\Delta\lambda=\lambda_{1}-\lambda_{2}$ variations in that regime and helps us identify the energy range over which "melting" occurs as a multi--stage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the $GALI_{k}$ indices, which generalize SALI (=$GALI_{2}$) to the case of $k>2$ deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.
Comment: 21 pages, 7 figures, submitted at PRE
Keywords
Nonlinear Sciences - Chaotic Dynamics
Citation
Collections