A random cloud model for the Wigner equation
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 60J25 81Q05
- Wigner equation, probabilistic representation, stochastic particle model, piecewise deterministic Markov process
A probabilistic model for the Wigner equation is studied. The model is based on a particle system with the time evolution of a piecewise deterministic Markov process. Each particle is characterized by a real-valued weight, a position and a wave-vector. The particle position changes continuously, according to the velocity determined by the wave-vector. New particles are created randomly and added to the system. The main result is that appropriate functionals of the process satisfy a weak form of the Wigner equation.
- Kinet. Relat. Models, 9 (2016) pp. 217--235.