A Monte Carlo framework for noncontinuous interactions between particles and classical fields

Abstract

Particles and fields are standard components in numerical simulations like transport simulations in nuclear physics and have very well understood dynamics. Still, a common problem is the interaction between particles and fields due to their different formal description. Particle interactions are discrete, point-like events while fields have purely continuous 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 new method, which allows to model non-continuous interactions between particles and scalar fields, allowing us to simulate scattering-like interactions which exchange energy and momentum quanta between fields and particles obeying full energy and momentum conservation and control over interaction strengths and times. In this paper we apply this method to different model systems, starting with a simple scalar harmonic oscillator which is damped by losing discrete energy quanta. The second and third system is a scalar oscillator and a one dimensional field which are both damped by discrete energy loss and which 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 3D 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.

28 pages, 11 figures

References in corpus (16)

• Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
• Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations
• Quantum dynamics and thermalization for out-of-equilibrium phi^4-theory
• Thermalization of fermionic quantum fields
• Nonequilibrium time evolution of the spectral function in quantum field theory
• Nonequilibrium chiral fluid dynamics including dissipation and noise
• Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid
• Resonance Transport and Kinetic Entropy
• Self-Consistent Approximations to Non-Equilibrium Many-Body Theory
• Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes
• Chiral fluid dynamics with explicit propagation of the Polyakov loop
• Forming Disoriented Chiral Condensates through Fluctuations
• Equilibration and relaxation times at the chiral phase transition including reheating
• Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution
• Stochastic treatment of Disoriented Chiral Condensates within a Langevin description
• Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect

Cited by in corpus (6)

• Classical model for diffusion and thermalization of heavy quarks in a hot medium: memory and out-of-equilibrium effects
• Kinetic approach to a relativistic Bose-Einstein condensate
• Kinetics of the chiral phase transition in a linear $\sigma$ model
• Dynamical scheme for hadronization with first-order phase transition
• Monte-Carlo approach to particle-field interactions and the kinetics of the chiral phase transition
• Kinetics of the chiral phase transition in a quark-meson $\sigma$-model