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The Role of Annihilation in a Wigner Monte Carlo Approach

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8353)

Abstract

The Wigner equation provides an interesting mathematical limit, which recovers the constant field, ballistic Boltzmann equation. The peculiarities of a recently proposed Monte Carlo approach for solving the transient Wigner problem, based on generation and annihilation of particles are summarized. The annihilation process can be implemented at consecutive time steps to improve the Monte Carlo resolution. We analyze theoretically and numerically this process applied to the simulation of important quantum phenomena, such as time-dependent tunneling of a wave packet through potential barriers.

Keywords

  • Monte Carlo Resolution
  • Wigner Equation
  • Time-dependent Tunneling
  • Renormalization Technique
  • Initial Wave Vector

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. Querlioz, D., Dollfus, P.: The Wigner Monte Carlo Method for Nanoelectronic Devices - A Particle Description of Quantum Transport and Decoherence. ISTE-Wiley, London (2010)

    MATH  Google Scholar 

  2. Nedjalkov, M., Kosina, H., Selberherr, S., Ringhofer, C., Ferry, D.K.: Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices. Phys. Rev. B 70, 115319 (2004)

    CrossRef  Google Scholar 

  3. Sellier, J.M.: www.gnu.org/software/archimedes

  4. Sellier, J.M.: Archimedes, the Free Monte Carlo simulator ( 2012). http://arxiv.org/abs/1207.6575arXiv:1207.6575

  5. Sellier, J.M.: www.nano-archimedes.com

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Acknowledgment

This work has been supported by the the project EC AComIn (FP7-REGPOT-2012-2013-1), and Bulgarian NSF Grants DTK 02/44/2009 and Austrian Science Fund Project FWF-P21685-N22.

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Correspondence to Ivan Dimov .

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Sellier, J.M., Nedjalkov, M., Dimov, I., Selberherr, S. (2014). The Role of Annihilation in a Wigner Monte Carlo Approach. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_20

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  • DOI: https://doi.org/10.1007/978-3-662-43880-0_20

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  • Publisher Name: Springer, Berlin, Heidelberg

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  • Online ISBN: 978-3-662-43880-0

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