Volta

Quantum–fluid correspondence for systems of nonrelativistic spin- 1 2 particles

Abstract 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 3 n 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 3 n -dimensional Euler flow.

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