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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.14842 |
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| _version_ | 1866912434731614208 |
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| author | Smith, Marnie |
| author_facet | Smith, Marnie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase mixing for the Hartree equation and Landau damping in the semiclassical limit Smith, Marnie Analysis of PDEs 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. |
| title | Phase mixing for the Hartree equation and Landau damping in the semiclassical limit |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.14842 |