Comparison of deterministic and stochastic methods for time-dependent Wigner simulations
| Autor: | Jean Michel D. Sellier, Sihong Shao |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Quantum Monte Carlo Monte Carlo method Computer Science Applications Hybrid Monte Carlo Computational Mathematics Modeling and Simulation Dynamic Monte Carlo method Monte Carlo integration Statistical physics Kinetic Monte Carlo Quasi-Monte Carlo method Mathematics Monte Carlo molecular modeling |
| Zdroj: | Journal of Computational Physics. 300:167-185 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2015.08.002 |
| Popis: | Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution of a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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