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Article Dans Une Revue Journal of Physics A: Mathematical and General (1975 - 2006) Année : 2009

Generalized quantum potentials

Résumé

We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (depending on a constant which may be different from the standard quantum constant planck) is equivalent to a generalized Schrödinger equation for a 'wavefunction' whose modulus squared yields the fluid density. Then we show that even in the case of the presence of vorticity, it is also possible to obtain a nonlinear Schrödinger-like equation (now of the vectorial field type) from the continuity and Euler equations including a quantum potential. The same kind of transformation also applies to a classical charged fluid subjected to an electromagnetic field and to an additional potential having the form of a quantum potential. Such a fluid can therefore be described by an equation of the Ginzburg-Landau type, and is expected to show some superconducting-like properties. Moreover, a Schrödinger form can be obtained for a fluctuating rotational motion of a solid. In this case the mass is replaced by the tensor of inertia, and a generalized form of the quantum potential is derived. We finally reconsider the case of a standard diffusion process, and we show that, after a change of variable, the diffusion equation can also be given the form of a continuity and Euler system including an additional potential energy. Since this potential is exactly the opposite of a quantum potential, the quantum behavior may be considered, in this context, as an anti-diffusion.

Dates et versions

hal-03732429 , version 1 (21-07-2022)

Identifiants

Citer

Laurent Nottale. Generalized quantum potentials. Journal of Physics A: Mathematical and General (1975 - 2006), 2009, 42, pp.5306. ⟨10.1088/1751-8113/42/27/275306⟩. ⟨hal-03732429⟩
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