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

• Authors: M. Agop , P. Nica , A. Harabagiu
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

05.45.Df; 47.53.+n; 03.65.-w

Discipline

• 05.45.Df: Fractals(see also 47.53.+n Fractals in fluid dynamics; 61.43.Hv Fractals; macroscopic aggregates in structure of solids)
• 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]
• 47.53.+n: Fractals in fluid dynamics(see also 05.45.Df Fractals in Statistical physics, thermodynamics, and nonlinear dynamical systems)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2008
• Volume: 113
• Issue: 6
• Pages: 1571-1588

Dates

published

2008-06

received

2008-01-16

(unknown)

2008-02-21

Contributors

author

M. Agop

• Department of Physics, University of Athens, Athens 15771, Greece
• Department of Physics, Technical "Gh. Asachi" University, Blvd. Mangeron No. 64, Iasi 700029, Romania

author

P. Nica

• Department of Physics, Technical "Gh. Asachi" University, Blvd. Mangeron No. 64, Iasi 700029, Romania

author

A. Harabagiu

• Faculty of Physics, "Al.I.Cuza" University, Blvd. Carol I, No. 11, Iasi 700506, Romania

References

• 1. E. Madelung, Z. Phys. 40, 322 (1926)
• 2. T. Takabayasi, Prog. Theor. Phys. 8, 143 (1952)
• 3. T. Takabayasi, Prog. Theor. Phys. 9, 187 (1953)
• 4. T. Takabayasi, Prog. Theor. Phys. 14, 283 (1955)
• 5. T. Takabayasi, Prog. Theor. Phys. 70, 1 (1983)
• 6. D. Bohm, R. Schiller, J. Tiomno, Suppl. Nuovo Cimento 1, 48 (1955)
• 7. D. Bohm, R. Schiller, Suppl. Nuovo Cimento 1, 67 (1955)
• 8. L. Janossy, M. Ziegler-Naray, Acta Phys. Hung. 20, 23 (1965)
• 9. T. Takabayasi, Nuovo Cimento 3, 233 (1956)
• 10. I. Bialynicki-Birula, Acta Phys. Pol. B 26, 1201 (1995)
• 11. I. Bialynicki-Birula, in: Nonlinear, Chaotic, and Complex Systems, Eds. E. Infeld, R. Zelazny, A. Galkowski, Cambridge U. Press, Cambridge 1997
• 12. L. Nottale, J. Schneider, J. Math. Phys. 25, 1296 (1984)
• 13. G.N. Ord, J. Phys. A, Math. Gen. 16, 1869 (1983)
• 14. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York 1965
• 15. L.F. Abbott, M.B. Wise, Am. J. Phys. 49, 37 (1981)
• 16. E. Campesino-Romeo, J.C. D'Olivo, M. Socolovsky, Phys. Lett. 89A, 321 (1982)
• 17. A.D. Allen, Speculations Sci. Tech. 6, 165 (1983)
• 18. S.S. Schweber, Rev. Mod. Phys. 58, 449 (1986)
• 19. L. Nottale, Int. J. Mod. Phys. A 4, 5047 (1989)
• 20. L. Nottale, Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity, World Scientific, London 1993
• 21. B. Mandelbrot, Les Objets Fractals, Flammarion, Paris 1975;B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco 1982
• 22. E. Nelson, Phys. Rev. 150, 1079 (1966)
• 23. E. Nelson, Quantum Fluctuations, Princeton Univ. Press, Princeton 1985
• 24. L. Nottale, Chaos, Solitons Fractals 7, 877 (1996)
• 25. M. Agop, P. Nica, P.D. Ioannou, Olga Malandraki, I. Gavanas-Pahomi, Chaos, Solitons Fractals 34, 1704 (2007)
• 26. M. Agop, L. Chicos, M. Girtu, Acta Phys. Pol. A 112, 3 (2007)
• 27. M. Agop, P. Nica, M. Girtu, Gen. Relativ. Gravit. 40, 35 (2008)
• 28. L. Nottale, M.N. Célérier, T. Lehner, J. Math. Phys. 47, 032303 (2006)
• 29. L. Nottale, Marie-Nöelle Célérier, J. Phys. A, Math. Theor. 40, 14471 (2007)
• 30. L. Nottale, Chaos, Solitons Fractals 25, 797 (2005)
• 31. L. Nottale, Prog. Phys. 1, 12 (2005)
• 32. J. Cresson, J. Math. Phys. 44, 4907 (2003)
• 33. J. Cresson, J. Math. Anal. Appl. 307, 48 (2005)
• 34. D.K. Ferry, S.M. Goodnick, Transport in Nanostructures, Cambridge Univ. Press, Cambridge 1997
• 35. Y. Imry, Introduction to Mesoscopic Physics, Oxford Univ. Press, Oxford 2002
• 36. V. Chiroiu, P. Stiuca, L. Munteanu, S. Donescu, Introduction to Nanomechanics, Roumanian Academy Publishing House, Bucharest 2005
• 37. E.A. Jackson, Perspectives in Nonlinear Dynamics, Vols. I and II, Cambridge University Press, Cambridge 1991
• 38. F. Bowman, Introduction to Elliptic Function with Applications, English University Press, London 1955
• 39. A. Mejias, L. Sogalotti, Di G. Sira, F.E. De Felice, Chaos, Solitons Fractals 19, 773 (2004)
• 40. J. Argyris, C. Ciubotariu, Chaos, Solitons Fractals 8, 743 (1997)
• 41. M.S. El Naschie, Int. J. Nonlin. Sci. Num. Simulat. 6, 331 (2005)
• 42. M. Chaichian, N.F. Nelipa, Introduction to Gauge Field Theories, Springer-Verlag, Berlin 1984
• 43. C.P Poole, H.A. Farach, R.J. Geswich, Superconductivity, Academic Press, San Diego 1995
• 44. D. Bohm, Phys. Rev. 85, 166 (1951)

Identifiers

DOI

10.12693/APhysPolA.113.1571