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math.AP2022
On the Cauchy problem for the Hartree approximation in quantum dynamics
Rémi Carles, Clotilde Fermanian Kammerer, Caroline Lasser
We prove existence and uniqueness results for the time-dependent Hartree approximation arising in quantum dynamics. The Hartree equations of motion form a coupled system of nonline…
math.AP2020
Effective mass theorems with Bloch modes crossings
Victor Chabu, Clotilde Fermanian Kammerer, Fabricio Macià
We study a Schr{ö}dinger equation modeling the dynamics of an electron in a crystal in the asymptotic regime of small wavelength comparable to the characteristic scale of the cryst…