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Illg, Christian, Haag, Michael, Teeny, Nicolas, Wirth, Jens, Fähnle, Manfred. (1394). Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing. , 10(1), 1-6. doi: 10.1007/s40094-015-0193-5
Christian Illg; Michael Haag; Nicolas Teeny; Jens Wirth; Manfred Fähnle. "Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing". , 10, 1, 1394, 1-6. doi: 10.1007/s40094-015-0193-5
Illg, Christian, Haag, Michael, Teeny, Nicolas, Wirth, Jens, Fähnle, Manfred. (1394). 'Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing', , 10(1), pp. 1-6. doi: 10.1007/s40094-015-0193-5
Illg, Christian, Haag, Michael, Teeny, Nicolas, Wirth, Jens, Fähnle, Manfred. Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing. , 1394; 10(1): 1-6. doi: 10.1007/s40094-015-0193-5

Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing

Journal of Theoretical and Applied Physics
مقاله 1، دوره 10، شماره 1، خرداد 2016، صفحه 1-6  XML اصل مقاله (427.91 K)
شناسه دیجیتال (DOI): 10.1007/s40094-015-0193-5
نویسندگان
Christian Illg1؛ Michael Haag1؛ Nicolas Teeny2؛ Jens Wirth3؛ Manfred Fähnle email 1
1Max Planck Institute for Intelligent Systems
2Max Planck Institute for Nuclear Physics
3Institut für Analysis, Dynamik und Modellierung, Universität Stuttgart
چکیده
AbstractScatterings of electrons at quasiparticles or photons are very important for many topics in solid-state physics, e.g., spintronics, magnonics or photonics, and therefore a correct numerical treatment of these scatterings is very important. For a quantum-mechanical description of these scatterings, Fermi’s golden rule is used to calculate the transition rate from an initial state to a final state in a first-order time-dependent perturbation theory. One can calculate the total transition rate from all initial states to all final states with Boltzmann rate equations involving Brillouin zone integrations. The numerical treatment of these integrations on a finite grid is often done via a replacement of the Dirac delta distribution by a Gaussian. The Dirac delta distribution appears in Fermi’s golden rule where it describes the energy conservation among the interacting particles. Since the Dirac delta distribution is a not a function it is not clear from a mathematical point of view that this procedure is justified. We show with physical and mathematical arguments that this numerical procedure is in general correct, and we comment on critical points.
کلیدواژه‌ها
Electron scattering؛ Boltzmann rate equations؛ Brillouin zone integration؛ Treatment of Diracs delta distribution
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