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arXiv · 1903.06001

Semiclassical limit to the Vlasov equation with inverse power law potentials

Chiara Saffirio
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Abstract

We consider mixed quasi-free states describing $N$ fermions in the mean-field limit. In this regime, the time evolution is governed by the nonlinear Hartree equation. In the large $N$ limit, we study the convergence towards the classical Vlasov equation. Under integrability and regularity assumptions on the initial state, we prove strong convergence in trace and Hilbert-Schmidt norm and provide explicit bounds on the convergence rate for a class of singular potentials of the form $V(x)=|x|^{-\alpha}$, for $\alpha\in(0,1/2)$.

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Chiara Saffirio. 2019-03-14. Semiclassical limit to the Vlasov equation with inverse power law potentials. https://doi.org/10.1007/s00220-019-03397-5

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