Spatial dynamics in homogeneous systems governed by known rate equations

Sung Po Chao^1*, Ding Hong Chen¹

¹Physics, National Kaohsiung normal university, Kaohsiung, Taiwan

* Presenter:Sung Po Chao, email:spchao@mail.nknu.edu.tw

The rate equations are widely used in describing the time evolution of events such as chemical reactions, nuclear interactions, coalescence of colloids, evolution of epidemics, just to name a few. Using the equation of motion in Heisenberg picture, we connect the rate equation with its model Hamiltonian, assuming nearest neighbors’ interaction. We then apply classical Monte Carlo simulations to show the spatial dynamics of the events. We illustrate this concept using Ising model in 2D magnetic system, and Susceptible-Iinfected (SI) model in epidemics.

Keywords: classical Monte Carlo simulation, Ising model, SI model