# Dynamics of particle moving in one dimensional Lorentz lattice gas

## TL;DR

This paper investigates the complex dynamics of a particle in a one-dimensional Lorentz lattice-gas, revealing how different parameters influence ballistic motion, diffusion, and confinement, with a focus on deterministic and probabilistic regimes.

## Contribution

It introduces a detailed analysis of particle dynamics in a Lorentz lattice-gas with random scatterers, highlighting the transition from deterministic to probabilistic behavior and characterizing the resulting diffusion regimes.

## Key findings

- Deterministic case shows propagation or confinement.
- Probabilistic case exhibits anomalous and normal diffusion.
- Phase diagram maps asymptotic behaviors across parameters.

## Abstract

We study the dynamics of a particle moving in one-dimensional Lorentz lattice-gas where particle performs mainly three different kinds of motion {\it viz} ballistic motion, diffusion and confinement. There are two different types of scatterers, {\it viz} reflector and transmitters, randomly placed in the lattice. Reflectors are such that they reverse the particle's velocity direction and transmitters let it pass through. Scatterers also change their character with flipping probability $1-\alpha$, once the particle interacts with a scatterer. Hence the system is defined by two sets of parameters, $r$, which is the initial density of reflector/transmitter and $\alpha$. For $\alpha=0$ and $\alpha=1$ dynamics of the particle is purely deterministic else it is probabilistic. In the pure deterministic case dynamics of the particle is either propagation in one direction or confined between two near-by reflectors present. For the probabilistic case $\alpha \ne 1$ and $\ne 0$, although the dynamics of particle shows anomalous diffusion where dynamics is faster, slower and comparable to normal diffusion on the variation of system parameters $(\alpha, r)$, but the asymptotic behaviour of the particle is normal diffusion. We plot the phase diagram for the asymptotic behaviour, in the plane of $\alpha$ and $r$.