Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems
Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems
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DOI：
10.1007/s10955-021-02700-w
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发表时间：
2019-10
影响因子：
1.6
通讯作者：
Li Chen;Jinyeop Lee;Matthew Liew
中科院分区：
文献类型：
--
作者：
Li Chen;Jinyeop Lee;Matthew Liew
研究了三维半经典尺度下大型无自旋费米子的含时薛定谔方程。利用相干态定义的Husimi测度，我们将薛定谔方程改写为k粒子Husimi测度的BBGKY型谱系。进一步得到了Husimi测度的弱紧性的估计，并得到了族中剩余项的一致估计，从而证明了在半经典情形下Husimi测度的弱极限正是Vlasov方程的解.
We study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scalein three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for thekparticle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.