Stochastic Hartree NLS in 3d coming from a Many-Body Quantum System with White Noise Potential
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912357820661760 |
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| author | De Vecchi, Francesco Carlo Ji, Xiaohao Zachhuber, Immanuel |
| author_facet | De Vecchi, Francesco Carlo Ji, Xiaohao Zachhuber, Immanuel |
| contents | In this paper, we consider the defocusing Hartree NLS with white noise external potential on T^3 i.e. the Hartree NLS whose linear part is given by the Anderson Hamiltonian. A Strichartz-type estimate is established for the Anderson Hamiltonian using perturbative arguments and the local and global well-posedness of the NLS is considered with initial data in the domain and form-domain of the Anderson Hamiltonian under different regularity assumptions on the Hartree interaction. Furthermore, we establish the Anderson Hartree NLS as an effective equation describing many-body Bosonic systems and, in particular, we prove the convergence of the linear Schrödinger equation for the many body system to the BBGKY hierarchy for the Coulomb interaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Hartree NLS in 3d coming from a Many-Body Quantum System with White Noise Potential De Vecchi, Francesco Carlo Ji, Xiaohao Zachhuber, Immanuel Analysis of PDEs Mathematical Physics Probability 35Q55, 81V70, 60H17 In this paper, we consider the defocusing Hartree NLS with white noise external potential on T^3 i.e. the Hartree NLS whose linear part is given by the Anderson Hamiltonian. A Strichartz-type estimate is established for the Anderson Hamiltonian using perturbative arguments and the local and global well-posedness of the NLS is considered with initial data in the domain and form-domain of the Anderson Hamiltonian under different regularity assumptions on the Hartree interaction. Furthermore, we establish the Anderson Hartree NLS as an effective equation describing many-body Bosonic systems and, in particular, we prove the convergence of the linear Schrödinger equation for the many body system to the BBGKY hierarchy for the Coulomb interaction. |
| title | Stochastic Hartree NLS in 3d coming from a Many-Body Quantum System with White Noise Potential |
| topic | Analysis of PDEs Mathematical Physics Probability 35Q55, 81V70, 60H17 |
| url | https://arxiv.org/abs/2505.01157 |