Phase mixing for the Hartree equation and Landau damping in the semiclassical limit
Abstract
The asymptotic behaviour of the Hartree equation is studied near translation-invariant steady states. For short-range interaction kernels satisfying a uniform Penrose stability condition, including the screened Coulomb interaction, phase-mixing estimates in finite regularity are established. These demonstrate density decay and scattering of solutions in weighted quantum Sobolev spaces, providing a quantum analogue of Landau damping in classical plasma physics. The results hold uniformly in the semiclassical limit, thereby bridging the quantum and classical regimes.
Fields of Study & Subjects
Quantum chaos and dynamical systems
Laser-Matter Interactions and Applications
Cold Atom Physics and Bose-Einstein Condensates
Publication details
- Journal / source
- Journal de l’École polytechnique — Mathématiques
- Volume
- 13
- Pages
- 1483–1546
- Publication date
- 24 September 2026
- Language
- EN