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Semiclassical limit of Husimi function

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  • We will show that Liouville and quantum Liouville operators $L$ and $L_\hbar$ generate two $C_0$-groups $e^{tL}$ and $e^{tL_h}$ of isometries in $L^2(\mathbb{R}^{2n})$ and $e^{tL_h}$ converges ultraweakly to $e^{tL}$. As a consequence we show that the Gaussian mollifier of the Wigner function, called Husimi function, converges in $L^1(\mathbb{R}^{2n})$ to the solution of the Liouville equation.
    Mathematics Subject Classification: 81Q20, 47C05.


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