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Wave-Particle Duality through a Hydrodynamic Model of the Fractal Space-Time Theory

100%

Agop M., Nica P., Harabagiu A.

Acta Physica Polonica A

2008

vol. 113

issue 6

1571-1588

Considering that the microparticle movements take place on fractal curves, the wave-particle duality is studied in the fractal space-time theory (scale relativity theory). The Nottale model was extended by assuming arbitrary fractal dimension, D_F, of the fractal curves and third-order terms in the equation of motion of a complex speed field. It results that, in a fractal fluid, the convection, dissipation, and dispersion are reciprocally compensating at any scale (differentiable or non-differentiable), whereas a generalized Schrödinger equation is obtained for an irrotational movement of the fractal fluid. The absence of the dispersion implies a generalized Navier-Stokes type equation and the usual Schrödinger equation results for the irrotational movement in D_F=2 of the fractal fluid. The absence of dissipation implies a generalized Korteweg-de Vries type equation. In such conjecture, the duality is analyzed through a hydrodynamic formulation. At the differentiable scale, the duality is achieved by the flowing regimes of the fractal fluid, while at the non-differentiable scale, a fractal potential controls, through the coherence, the duality.

Fractal Transport Phenomena through the Scale Relativity Model

76%

Colotin M., Pompilian G., Nica P., Gurlui S., Paun V., Agop M.

Acta Physica Polonica A

2009

vol. 116

issue 2

157-164

A correspondence between Nottale's scale relativity model and Cresson's mathematical procedures is analyzed. It results that the "synchronization" of the movements at different scales (fractal scale, differential scale etc.) gives conductive type properties to the fractal fluid, while the absence of "synchronization" is inducing properties of convective type. The behavior of a conductive fractal fluid is illustrated through the numerical simulation of plasma diffusion that is generated by laser ablation. Rotational and irrotational convective behaviors of a fractal fluid are established. Particularly, at Compton spatial and temporal scales, the irrotational behavior implies the standard Schrödinger equation.

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2 Acta Physica Polonica A

1 2009

1 2008

2 Agop M.

2 Nica P.

1 Colotin M.

1 Gurlui S.

1 Harabagiu A.

1 Paun V.

1 Pompilian G.

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Wave-Particle Duality through a Hydrodynamic Model of the Fractal Space-Time Theory

Fractal Transport Phenomena through the Scale Relativity Model