Convergency of the Monte Carlo algorithm for the solution of the Wigner quantum-transport equation. (English) Zbl 0860.65144
This paper discusses the convergence of the Monte Carlo algorithm for the solution of the Wigner quantum-transport equation. Essentially there is a convergence problem at the boundaries \(+\infty\) and \(-\infty\) for the momentum \(p\). This is discussed in detail and it is shown that the approximation tends to the Wigner function uniformly as the domain of the simulation domain for \(p\) tends to \(-\infty < p < \infty\).
Reviewer: B.Burrows (Stafford)
MSC:
| 65R20 | Numerical methods for integral equations |
| 81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
| 65C05 | Monte Carlo methods |
| 45K05 | Integro-partial differential equations |
References:
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| [4] | Vitanov, P.; Nedjalkov, M.; Jacoboni, C.; Rossi, F.; Abramo, A., Unified Monte Carlo approach to the Boltzmann and Wigner equations, (Dimov, I.; Tonev, O., Advances in Parallel Algorithms (1994), IOS Press: IOS Press Amsterdam), 117 |
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