Wigner Monte Carlo simulation without discretization error of the tunneling rectangular barrier

Abstract

The Wigner transport equation can be solved stochastically by Monte Carlo techniques based on the theory of piecewise deterministic Markov processes. A new stochastic algorithm, without time discretization error, has been implemented and studied in the case of the quantum transport through a rectangular potential barrier.

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

“…Generation of new particles is dictated by Eq. (16). The probability that a particle will survive without generation during a ballistic flight of duration Δt is:…”

“…Recently this method has also been be understood in terms of the Markov jump process theory [12,17], producing a class of new stochastic algorithms. Algorithms that belong to this class are a standard time-splitting algorithm and a new no-splitting algorithm that avoids errors due to time-discretization [13,16,18]. The goal of this paper is twofold: i) to write, for the sake of clarity and dissemination purposes, a simplified set of rules for the splitting and no-splitting algorithms to help a potential user; ii) to perform, from a mathematical point of view, numerical experiments to compare the standard timesplitting algorithm with the the new no-splitting algorithm, for a simplified GaAS Resonant Tunneling Diode (RTD) structure.…”