Wigner Monte Carlo Simulation of a Double Potential Barrier

Muscato, Orazio

doi:10.1007/978-3-030-44101-2_15

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Muscato

2021

J Comput Electron

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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.

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