We derive the flow of discrete NLS equations by the mean field asymptotics of a many body quantum model for $N$ interacting particles as $N$ becomes large. This is obtained through $L^2$ - estimates on Wick symbols with respect to a class of flow invariant measures. Furthermore, we show weighted Hilbert-Schmidt norm estimates for Wick operators evolved in the Heisenberg picture. This leads to an Egorov type result for Wick symbols, global in time and with quantitative estimates.
Mean field asymptotics and invariant measures for the flow of dNLS
Lorenzo Zanelli
In corso di stampa
Abstract
We derive the flow of discrete NLS equations by the mean field asymptotics of a many body quantum model for $N$ interacting particles as $N$ becomes large. This is obtained through $L^2$ - estimates on Wick symbols with respect to a class of flow invariant measures. Furthermore, we show weighted Hilbert-Schmidt norm estimates for Wick operators evolved in the Heisenberg picture. This leads to an Egorov type result for Wick symbols, global in time and with quantitative estimates.File in questo prodotto:
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