Asymptotic stability of a wide class of stationary solutions for the Hartree and Schrödinger equations for infinitely many particles
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917196644483072 |
|---|---|
| author | Hadama, Sonae |
| author_facet | Hadama, Sonae |
| contents | We consider the Hartree and Schrödinger equations describing the time evolution of wave functions of infinitely many interacting fermions in three-dimensional space. These equations can be formulated using density operators, and they have infinitely many stationary solutions. In this paper, we prove the asymptotic stability of a wide class of stationary solutions. We emphasize that our result includes Fermi gas at zero temperature. This is one of the most important steady states from the physics point of view; however, its asymptotic stability has been left open after Lewin and Sabin first formulated this stability problem and gave significant results in their seminal work [arXiv:1310.0604]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15929 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic stability of a wide class of stationary solutions for the Hartree and Schrödinger equations for infinitely many particles Hadama, Sonae Analysis of PDEs Mathematical Physics Primary, 35Q40. Secondary, 35B35, 35B40 We consider the Hartree and Schrödinger equations describing the time evolution of wave functions of infinitely many interacting fermions in three-dimensional space. These equations can be formulated using density operators, and they have infinitely many stationary solutions. In this paper, we prove the asymptotic stability of a wide class of stationary solutions. We emphasize that our result includes Fermi gas at zero temperature. This is one of the most important steady states from the physics point of view; however, its asymptotic stability has been left open after Lewin and Sabin first formulated this stability problem and gave significant results in their seminal work [arXiv:1310.0604]. |
| title | Asymptotic stability of a wide class of stationary solutions for the Hartree and Schrödinger equations for infinitely many particles |
| topic | Analysis of PDEs Mathematical Physics Primary, 35Q40. Secondary, 35B35, 35B40 |
| url | https://arxiv.org/abs/2308.15929 |