Learning Coulomb Potentials and Beyond with Free Fermions in Continuous Space
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912986036174848 |
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| author | Bluhm, Andreas Lemm, Marius Möbus, Tim Siebert, Oliver |
| author_facet | Bluhm, Andreas Lemm, Marius Möbus, Tim Siebert, Oliver |
| contents | The first-principles formulation of quantum mechanics relevant for quantum chemistry and trapped quantum gases involves particles in the continuous space $\mathbb R^d$. We present a unified framework and modular algorithm for learning external potentials $V$ with free-fermion models in the continuum. Compared to the lattice-based approaches, the continuum presents new mathematical challenges: the state space is infinite-dimensional and the Hamiltonian contains the Laplacian, which is unbounded in the continuum and produces an unbounded speed of information propagation. We address these through novel optimization methods and information-propagation bounds in combination with a priori regularity assumptions on the external potential. The resulting algorithm provides a unified and robust approach to learn parametric interactions (e.g., Coulomb potentials or periodic potentials) and general smooth functions. Our results lay the foundation for a scalable and generalizable toolkit to learn Hamiltonians in continuous space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08471 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Coulomb Potentials and Beyond with Free Fermions in Continuous Space Bluhm, Andreas Lemm, Marius Möbus, Tim Siebert, Oliver Quantum Physics Mathematical Physics The first-principles formulation of quantum mechanics relevant for quantum chemistry and trapped quantum gases involves particles in the continuous space $\mathbb R^d$. We present a unified framework and modular algorithm for learning external potentials $V$ with free-fermion models in the continuum. Compared to the lattice-based approaches, the continuum presents new mathematical challenges: the state space is infinite-dimensional and the Hamiltonian contains the Laplacian, which is unbounded in the continuum and produces an unbounded speed of information propagation. We address these through novel optimization methods and information-propagation bounds in combination with a priori regularity assumptions on the external potential. The resulting algorithm provides a unified and robust approach to learn parametric interactions (e.g., Coulomb potentials or periodic potentials) and general smooth functions. Our results lay the foundation for a scalable and generalizable toolkit to learn Hamiltonians in continuous space. |
| title | Learning Coulomb Potentials and Beyond with Free Fermions in Continuous Space |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2510.08471 |