Collisional relaxation and dynamical scaling in multiparticle collisions dynamics

TL;DR

This paper introduces a Multi-Particle-Collision (MPC) simulation method for low-dimensional systems, demonstrating its ability to model collisional relaxation and anomalous dynamical scaling, with results aligning with KPZ universality.

Contribution

The paper develops and applies an MPC approach to a 1D gas model, revealing long-lived suprathermal particles and confirming KPZ universality in dynamical scaling.

Findings

Existence of long-lived suprathermal particles propagating ballistically.

Simulation results agree with nonlinear fluctuating hydrodynamics predictions.

Model exhibits KPZ universality class behavior.

Abstract

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.