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Derivation of Vlasov equations for multi-species fermions

Year: 2025
Type: article
Abstract: We explore a system of two-species fermions with N particles. Through this exploration, we establish a two-species Husimi measure and construct a two-species Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy hierarchy with error terms. We provide proofs of the smallness of these errors in the semiclassical and mean-field limits, fixing ℏ = N−1/3. After that, we rigorously establish the uniqueness of this hierarchy. This allows us to conclude that the two-species Husimi measure from the solution of N-particle Schrödinger equation approximates the solution of the Vlasov equation for two-species systems.
DOI: 10.1063/5.0228404
Language: English
Open Access status: hybrid
Funders: National Science Foundation, National Centres of Competence in Research SwissMAP, National Center of Competence in Research AntiResist, National Research Foundation, Deutsche Forschungsgemeinschaft, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, National Research Foundation of Korea, European Research Council, HORIZON EUROPE European Research Council
Awards: G2223384380, G2664982278, Rigorous Approximations for Many-Body Quantum Systems, G5141357660, G6409808771, TRR 352: Mathematik der VielteilchenQuantensysteme und ihrer kollektiven Phänomene, From Newton and Schrödinger many-body dynamics to the Boltzmann equation
OpenAlex ID: W4407119033
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Cites: 41
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Related to: 10