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Spin and wave function as attributes of ideal fluid. (English) Zbl 0946.76104

Summary: We consider an ideal fluid whose internal energy depends on density, density gradient, and entropy. Dynamic equations are integrated, and a description is given in terms of hydrodynamic (Clebsch) potentials. We show that all essential information about the fluid flow (including initial and boundary conditions) is contained in dynamic equations for hydrodynamic potentials. Information about initial values of the fluid flow is contained in arbitrary integration functions. Initial and boundary conditions for potentials contain only nonessential information concerning the fluid particle labeling. We show further that the description in terms of \(n\)-component complex wave function is a particular case of description in terms of hydrodynamic potentials. Spin determined by the irreducible number \(n_m\) of the wave function components appears to be an attribute of the fluid flow, and the classification of fluid flows by the spin is connected with invariant subspaces of the relabeling group.

MSC:

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
82D15 Statistical mechanics of liquids
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