Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode

A Monte Carlo technique for the solution of the Wigner transport equation has been developed, based on the generation and annihilation of signed particles (Nedjalkov et al. in Phys Rev B 70:115319, 2004). A stochastic algorithm without time discretization error has been recently introduced (Muscato and Wagner in Kinet Relat Models 12(1):59–77, 2019). Its derivation is based on the theory of piecewise deterministic Markov processes. Numerical experiments are performed in the case of a GaAs resonant tunneling diode. Convergence of the time-splitting scheme to the no-splitting algorithm is demonstrated. The no-splitting algorithm is shown to be more efficient in terms of computational effort.