Quantum--Fluid Correspondence for Systems of Nonrelativistic Spin-$\frac{1}{2}$ Particles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910232468258816 |
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| author | Sato, Naoki Yamada, Michio |
| author_facet | Sato, Naoki Yamada, Michio |
| contents | We show that a charged fluid endowed with an internal spin degree of freedom naturally satisfies the Pauli equation for a nonrelativistic spin-1/2 particle, and that a collection of n such interacting fluids can be reformulated as an Euler flow in 3n dimensions, thereby providing a natural representation of a system of n Pauli particles. These results provide a fluid-mechanical derivation of the Pauli equation and extend the Madelung, or quantum-hydrodynamic, picture to many-particle quantum systems. In particular, they imply that an n-qubit quantum computer can, at least in principle, be realized as a suitable combination of n fluids, or equivalently as a 3n-dimensional Euler flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum--Fluid Correspondence for Systems of Nonrelativistic Spin-$\frac{1}{2}$ Particles Sato, Naoki Yamada, Michio Quantum Physics Mathematical Physics We show that a charged fluid endowed with an internal spin degree of freedom naturally satisfies the Pauli equation for a nonrelativistic spin-1/2 particle, and that a collection of n such interacting fluids can be reformulated as an Euler flow in 3n dimensions, thereby providing a natural representation of a system of n Pauli particles. These results provide a fluid-mechanical derivation of the Pauli equation and extend the Madelung, or quantum-hydrodynamic, picture to many-particle quantum systems. In particular, they imply that an n-qubit quantum computer can, at least in principle, be realized as a suitable combination of n fluids, or equivalently as a 3n-dimensional Euler flow. |
| title | Quantum--Fluid Correspondence for Systems of Nonrelativistic Spin-$\frac{1}{2}$ Particles |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2605.18247 |