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

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Antonopoulos, Chris

Basios, Vasileios

Bountis, Tassos

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##### 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

Comment: 21 pages, 7 figures, submitted at PRE

##### Keywords

Nonlinear Sciences - Chaotic Dynamics