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Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation
Institution:1. NEST, Scuola Normale Superiore, and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy;2. MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand;3. NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy;1. Univ. Grenoble Alpes, INAC-SPSMS, F-38000 Grenoble, France;2. CEA, INAC-SPSMS, F-38000 Grenoble, France;3. Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA;4. Kavli Institute of NanoScience, Delft University of Technology, Lorentzweg 1, NL-2628 CJ, Delft, The Netherlands;1. Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy;2. Nano-Bio Spectroscopy Group, Departamento de Fìsica de Materiales, Universidad del Paìs Vasco UPV/EHU, E-20018 San Sebastiàn, Spain;1. Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany;2. Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany;1. Université de Nice Sophia-Antipolis, INLN, CNRS, 06560 Valbonne, France;2. Institut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands;3. Aix Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France;4. Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France
Abstract:We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann–Langevin equation. The specific case of electron–phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.
Keywords:Boltzmann equation  Nonequilibrium electrical noise  Electron–phonon scattering
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