Quantitative Derivation of the Euler-Poisson Equation from Quantum Many-Body Dynamics  

作　　者：Xuwen Chen Shunlin Shen Zhifei Zhang 

机构地区：[1]Department of Mathematics,University of Rochester,Rochester,NY 14627,USA [2]School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Peking Mathematical Journal》2024年第2期643-711,共69页北京数学杂志（英文）

基　　金：X.Chen was supported in part by NSF grant DMS-2005469 and a Simons fellowship numbered 916862;S.Shen was supported in part by the Postdoctoral Science Foundation of China under Grant 2022M720263;Z.Zhang was supported in part by NSF of China under Grant 12171010 and 12288101.

摘　　要：We study the three dimensional quantum many-body dynamics with repulsive Coulomb interaction in the mean-field setting.The Euler-Poisson equation is its limit as the particle number tends to infinity and Planck’s constant tends to zero.By a new scheme combining the hierarchy method and the modulated energy method,we establish strong and quantitative microscopic to macroscopic convergence of mass and momentum densities as well as kinetic and potential energies before the 1st blow up time of the limiting Euler-Poisson equation.

关 键 词：Euler-Poissonequation BBGKY hierarchy Quantum many-body dynamics Modulated energy 

分 类 号：O41[理学—理论物理]