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- W3123927048 abstract "Abstract We study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $$hbar = N^{-1/3}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>ħ</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>N</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle 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." @default.
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- W3123927048 date "2021-01-25" @default.
- W3123927048 modified "2023-10-15" @default.
- W3123927048 title "Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems" @default.
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- W3123927048 doi "https://doi.org/10.1007/s10955-021-02700-w" @default.
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