Nonlinear Landau damping and asymptotic stability are established for translation-invariant Hartree-Fock equilibria with off-diagonal exchange in R^d for d at least 3.
Global well-posedness of th e nonlinear Hartree equation for infinitely many particles with singular interaction
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Proves phase mixing estimates for densities in the nonlinear Hartree equation around stable equilibria via nonlinear iteration and provides a Penrose-Lindhard stability criterion based on the equilibrium marginal.
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Asymptotic Stability of Hartree--Fock Homogenous Equilibria in $\mathbb{R}^d$
Nonlinear Landau damping and asymptotic stability are established for translation-invariant Hartree-Fock equilibria with off-diagonal exchange in R^d for d at least 3.
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Phase mixing estimates for the nonlinear Hartree equation of infinite rank
Proves phase mixing estimates for densities in the nonlinear Hartree equation around stable equilibria via nonlinear iteration and provides a Penrose-Lindhard stability criterion based on the equilibrium marginal.