  We present the Multi-Particle-Collision (MPC) dynamics approach to simulate
properties of low-dimensional systems. In particular, we illustrate the method
for a simple model: a one-dimensional gas of point particles interacting
through stochastic collisions and admitting three conservation laws (density,
momentum and energy). Motivated from problems in fusion plasma physics, we
consider an energy-dependent collision rate that accounts for the lower
collisionality of high-energy particles. We study two problems: (i) the
collisional relaxation to equilibrium starting from an off-equilibrium state
and (ii) the anomalous dynamical scaling of equilibrium time-dependent
correlation functions. For problem (i), we demonstrate the existence of
long-lived population of suprathermal particles that propagate ballistically
over a quasi-thermalized background. For (ii) we compare simulations with the
predictions of nonlinear fluctuating hydrodynamics for the structure factors of
density fluctuations. Scaling analysis confirms the prediction that such model
belong to the Kardar-Parisi-Zhang universality class.
