Monte Carlo framework for noncontinuous interactions between particles and classical fields

Particles and fields are standard components in numerical calculations like transport simulations in nuclear physics and have well-understood dynamics. Still, a common problem is the interaction between particles and fields due to their different formal description. Particle interactions are discrete, pointlike events while field dynamics is described with continuous partial-differential equations of motion. A workaround is the use of effective theories like the Langevin equation with the drawback of energy conservation violation. We present a method, which allows us to model noncontinuous interactions between particles and scalar fields, allowing us to simulate scattering-like interactions which exchange discrete "quanta" of energy and momentum between fields and particles while obeying energy and momentum conservation and allowing control over interaction strengths and times. In this paper we apply this method to different model systems, starting with a simple harmonic oscillator, which is damped by losing discrete energy quanta. The second and third system consists of an oscillator and a one-dimensional field, which are damped via discrete energy loss and are coupled to a stochastic force, leading to equilibrium states which correspond to statistical Langevin-like systems. The last example is a scalar field in (1 + 3) space-time dimensions, which is coupled to a microcanonical ensemble of particles by incorporating particle production and annihilation processes. Obeying the detailed-balance principle, the system equilibrates to thermal and chemical equilibrium with dynamical fluctuations on the fields, generated dynamically by the discrete interactions.