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Global-in-time semiclassical regularity for the Hartree-Fock equation

Jacky J. Chong, Laurent Lafleche, Chiara Saffirio

28/2/22 Published in : arXiv:2202.13998

For arbitrarily large times T>0, we prove the uniform in \hbar propagation of semiclassical regularity for the solutions to the Hartree-Fock equation with singular interactions of the form V(x)=\pm\,|x|^{-a} with a\in(0,\frac12). As a byproduct of this result, we extend to arbitrarily long times the derivation of the Hartree-Fock and the Vlasov equations from the many-body dynamics provided in [J. Chong, L. Lafleche, C. Saffirio: arXiv:2103.10946 (2021)].

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Security of quantum key distribution from generalised entropy accumulation

Propagation of moments for large data and semiclassical limit to the relativistic Vlasov equation

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