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Optimized Particle Regeneration Scheme for the Wigner Monte Carlo Method

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8962)

Abstract

The signed-particle Monte Carlo method for solving the Wigner equation has made multi-dimensional solutions numerically feasible. The latter is attributable to the concept of annihilation of independent indistinguishable particles, which counteracts the exponential growth in the number of particles due to generation. After the annihilation step, the particles regenerated within each cell of the phase-space should replicate the same information as before the annihilation, albeit with a lesser number of particles. Since the semi-discrete Wigner equation allows only discrete momentum values, this information can be retained with regeneration, however, the position of the regenerated particles in the cell must be chosen wisely. A simple uniform distribution over the spatial domain represented by the cell introduces a ‘numerical diffusion’ which artificially propagates particles simply through the process of regeneration. An optimized regeneration scheme is proposed, which counteracts this effect of ‘numerical diffusion’ in an efficient manner.

Keywords

  • Wigner Function
  • Monte Carlo Approach
  • Particle Generation
  • Numerical Diffusion
  • Discrete Momentum

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Akhiezer, N.: The Classical Moment Problem: And Some Related Questions in Analysis. University Mathematical Monographs, Oliver & Boyd, London (1965)

    MATH  Google Scholar 

  2. Ellinghaus, P., Nedjalkov, M., Selberherr, S.: Implications of the coherence length on the discrete wigner potential. In: Abstracts of the 16th International Workshop on Computational Electronics (IWCE), pp. 155–156 (2014)

    Google Scholar 

  3. Karian, Z., Dudewicz, E.: Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods. Taylor & Francis, New York (2010)

    CrossRef  Google Scholar 

  4. Nedjalkov, M., Schwaha, P., Selberherr, S., Sellier, J.M., Vasileska, D.: Wigner quasi-particle attributes - an asymptotic perspective. Appl. Phys. Lett. 102(16), 163113 (2013)

    CrossRef  Google Scholar 

  5. Nedjalkov, M., Vasileska, D.: Semi-discrete 2D wigner-particle approach. J. Comput. Electron. 7(3), 222–225 (2008)

    CrossRef  Google Scholar 

  6. Shohat, J.A., Tamarkin, J.D., Society, A.M.: The Problem of Moments. Mathematical Surveys and Monographs. American Mathematical Society, Providence (1943)

    CrossRef  MATH  Google Scholar 

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Acknowledgement

This research has been supported by the Austrian Science Fund through the project WigBoltz (FWF-P21685-N22).

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Correspondence to Paul Ellinghaus .

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Ellinghaus, P., Nedjalkov, M., Selberherr, S. (2015). Optimized Particle Regeneration Scheme for the Wigner Monte Carlo Method. In: Dimov, I., Fidanova, S., Lirkov, I. (eds) Numerical Methods and Applications. NMA 2014. Lecture Notes in Computer Science(), vol 8962. Springer, Cham. https://doi.org/10.1007/978-3-319-15585-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-15585-2_3

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-15585-2

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