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

TL;DR

This paper investigates the melting transition in a confined microplasma system by analyzing its collective dynamics and chaos indicators, revealing a multi-stage diffusion process characterized by weak chaos and sticky orbits.

Contribution

It introduces the use of the SALI and GALI indices to identify the melting transition and characterize the chaotic behavior in a microplasma with long-range interactions.

Findings

Detection of a melting transition from crystalline to liquid-like behavior.

Identification of a multi-stage diffusion process during melting.

Observation of stair-like SALI decay indicating sticky orbits.

Abstract

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.