Phase mixing for the Hartree equation and Landau damping in the semiclassical limit

2024/12/19 by Smith, Marnie · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.14842

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.

Cited by

• Semi-classical limit of quantum scattering states for the nonlinear Hartree equation
• Large Time Behavior of the Klein-Gordon-Schrödinger system

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