IFM learns deterministic tangent velocity fields on CP^{d-1} via Pancharatnam phase-aligned paths, recovering marginal transport with endpoint and stability guarantees while showing empirical gains over Euclidean flow matching on quantum benchmarks.
Bohmian mechanics versus Madelung quantum hydrodynamics
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abstract
It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic interpretation of quantum mechanics is proposed, which is the background of the Madelung quantum hydrodynamics. Its relation to the complex mechanics is also explored. A new complex hydrodynamics is proposed, which eliminates completely the Bohm quantum potential. It describes the quantum evolution of the probability density by a convective diffusion with imaginary transport coefficients.
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Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport
IFM learns deterministic tangent velocity fields on CP^{d-1} via Pancharatnam phase-aligned paths, recovering marginal transport with endpoint and stability guarantees while showing empirical gains over Euclidean flow matching on quantum benchmarks.