Nonlinear behavior of a many-body one-dimensional plasma sheet model and its transport phenomena

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A one-dimenslonal plasma sheet model, which consists of negatively charged sheets in a uniformly distributed positive charges, is equivalent to a system of harmonic oscillators around equilibrium positions equally separated from each other, neighboring oscillators colliding elastically. Therefore, if the motion of each sheet is described in terms of action and angle variables, the action variables are constants of motion and the motion is regular until collision of oscillators occurs. When collisionof neighboring pair of oscillators, their action variables undergo discontinuous jumps due to exchange of momenta between neighboring pair. Numerical calculation can be done by connecting analytical solutions before and after each collision. First, we investigated thermal conductivity of this system by imposing boundary condition of heat baths of different temperatures and calculate energyflow from one boundary to the other. The size dependence of the conductivity coefficient is normal as long as the system is at low temperature. However, at higher temperature, there is size-dependence of the coefficient, which is due to ballistic motion of sheets as observed in the phase space. Namely there are ballistic sheets(free particle motion) and trapped sheets in potential wells. The tendencyto Maxwell distribution of velocities is quick at lower temperature, where orbital instability is enhanced due to chaos. We succeeded to explain these behavior by the usage of escape rate formalism which implies that Green-Kubo formula works at least at low temperature. In order to under stand these observations, we are now developing a kinetic theory based up on action and angle variables for the evolution of distribution function of angle variables. We have also investigated effect of particle transport (diffusion) on non-linear chemical reaction, which may create spatial correlation under nonequilibrium conditions,