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Abstracts
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.
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)
Journal
Year
Volume
Issue
Pages
1571-1588
Physical description
Dates
published
2008-06
received
2008-01-16
(unknown)
2008-02-21
Contributors
author
- Department of Physics, University of Athens, Athens 15771, Greece
- Department of Physics, Technical "Gh. Asachi" University, Blvd. Mangeron No. 64, Iasi 700029, Romania
author
- Department of Physics, Technical "Gh. Asachi" University, Blvd. Mangeron No. 64, Iasi 700029, Romania
author
- 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)
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Publication order reference
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YADDA identifier
bwmeta1.element.bwnjournal-article-appv113n602kz