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The Boltzmann–Langevin approach: A simple quantum-mechanical derivation

Institution:	1. Institute of Physics, National Academy of Sciences of Ukraine, 03680 Kyiv, Ukraine;2. Research Physico-Technical Institute, State University of Nizhni Novgorod, 603950 Nizhni Novgorod, Russia;1. Institut de Physique et de Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France;2. Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität, Albertstr. 19, D-79104 Freiburg, Germany;1. Centro de Física de Materiales, Centro Mixto CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, E-20018 Donostia-San Sebastián, Spain;2. Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 Donostia-San Sebastián, Spain;3. IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain;4. Departamento de Química-Física, UPV/EHU, Apartado 644, 48080 Bilbao, Spain;5. Department of Physics, Shanghai University, 200444 Shanghai, People''s Republic of China

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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