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

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arxiv 2412.14842 v2 pith:MQPXNSWK submitted 2024-12-19 math.AP

Marnie Smith This is my paper · ORCID
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keywords quantumclassicaldampingequationhartreeinteractionlandaulimit
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Semi-classical limit of quantum scattering states for the nonlinear Hartree equation

    math.AP 2025-07 conditional novelty 8.0 of 10

    Quantum scattering states for the nonlinear Hartree equation converge, via Wigner transforms, to classical Vlasov scattering states in the semiclassical limit, with new uniform-in-Planck-constant dispersion estimates ...

  2. The semiclassical limit from Hartree to Vlasov at positive density: strong uniform-in-time convergence and scattering

    math.AP 2026-07 accept novelty 7.0 of 10

    Strong, quantitative convergence from Hartree to Vlasov is shown near Penrose-stable steady states, with uniform-in-time control of Wigner transforms and scattering profiles.

  3. Uniform dispersive estimates for the semi-classical Hartree equation with long-range interaction

    math.AP 2025-07 reject novelty 7.0 of 10

    Small-data solutions of the semiclassical Hartree equation with long-range interaction satisfy the uniform-in-hbar optimal density decay ||rho(t)||_{L∞} ≲ <t>^{-3}.

  4. Large Time Behavior of the Klein-Gordon-Schr\"{o}dinger system

    math.AP 2025-06 conditional novelty 7.0 of 10

    Small localized data in H^4000 for the 3D Klein-Gordon-Schrödinger system produce global solutions that decay and scatter to free waves.

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