A deterministic solver for the Langevin Boltzmann equation including the Pauli principle

Christoph Jungemann

doi:10.1117/12.724514

8 June 2007 A deterministic solver for the Langevin Boltzmann equation including the Pauli principle

Christoph Jungemann

Proceedings Volume 6600, Noise and Fluctuations in Circuits, Devices, and Materials; 660007 (2007) https://doi.org/10.1117/12.724514
Event: SPIE Fourth International Symposium on Fluctuations and Noise, 2007, Florence, Italy

Abstract

A deterministic solver for the Langevin Boltzmann equation including the Pauli principle is presented based on a spherical harmonics expansion. The solver can handle rare events, slow processes and low frequencies without problems and without an increase in CPU time in contrast to the Monte Carlo method. This is demonstrated for strongly degenerate systems and deep traps. Although the two electron sub-ensembles for the different spin directions are correlated due to the deep traps, the spin variable can be eliminated without any approximations resulting in a reduction of the number of unknowns by two. Approximations for the inclusion of the Pauli principle are investigated and found to be so bad that it is better to neglect the Pauli principle than to use those approximations.

Citation Download Citation

Christoph Jungemann "A deterministic solver for the Langevin Boltzmann equation including the Pauli principle", Proc. SPIE 6600, Noise and Fluctuations in Circuits, Devices, and Materials, 660007 (8 June 2007); https://doi.org/10.1117/12.724514

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