A Hybrid Monte Carlo Method for Simulation of Quantum Transport

  • Todor Gurov
  • Emanouil Atanassov
  • Sofiya Ivanovska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4310)


In this work we propose a hybrid Monte Carlo method for solving the Levinson equation. This equation describes the electron-phonon interaction on a quantum-kinetic level in a wire. The evolution problem becomes inhomogeneous due to the spatial dependence of the initial condition. The properties of the presented algorithm, such as computational complexity and accuracy, are investigated on the Grid by mixing quasi-random numbers and pseudo-random numbers. The numerical results are obtain for a physical model with GaAs material parameters in the case of zero electrical field.


Monte Carlo Wigner Function Quantum Transport 120fs 242m5 Quantum Kinetic Equation 
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  1. 1.
    Levinson, I.: Translational invariance in uniform fields and the equation for the density matrix in the Wigner representation. Sov. Phys. JETP 30, 362–367 (1970)MathSciNetGoogle Scholar
  2. 2.
    Herbst, M., et al.: Electron-phonon quantum kinetics for spatially inhomogeneous excitations. Physical Review B 67, 195305, 1–18 (2003)Google Scholar
  3. 3.
    Gurov, T.V., Whitlock, P.A.: An efficient backward Monte Carlo estimator for solving of a quantum kinetic equation with memory kernel. Mathematics and Computers in Simulation 60(1-2), 85–105 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Niederreiter, H.: Random Number Generations and Quasi-Monte Carlo Methods. SIAM, Philadelphia (1992)Google Scholar
  5. 5.
    Nedjalkov, M., et al.: Femtosecond Evolution of Spatially Inhomogeneous Carrier Excitatons - Part I: Kinetic Approach. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2005. LNCS, vol. 3743, pp. 149–155. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Atanassov, E.: A New Efficient Algorithm for Generating the Scrambled Sobol Sequence. In: Dimov, I.T., et al. (eds.) NMA 2002. LNCS, vol. 2542, pp. 83–90. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Gurov, T.V., Dimov, I.T.: A Parallel Monte Carlo Method For Electron Quantum Kinetic Equation. In: Lirkov, I., et al. (eds.) LSSC 2003. LNCS, vol. 2907, pp. 151–161. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Mascagni, M.: SPRNG: A Scalable Library for Pseudorandom Number Generation. In: Iliev, O., et al. (eds.) Recent Advances in Numerical Methods and Applications II, Proceeding of NMA 1998, pp. 284–295. World Scientific, Singapore (1999)Google Scholar
  9. 9.
    Nedjalkov, M., et al.: Unified Particle Approach to Wigner-Boltzmann Transport in Small Semiconductor Devices. Phys. Rev. B 70, 115319–115335 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Todor Gurov
    • 1
  • Emanouil Atanassov
    • 1
  • Sofiya Ivanovska
    • 1
  1. 1.Institute for Parallel Processing - Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl.25A, 1113 SofiaBulgaria

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