2016 International Symposium on Nanofluid Heat and Mass Transfer in Textile Engineering and 5th International Symposium on Nonlinear Dynamics


Journal: Nonlinear Science Letters A
(ISSN 2519-9072(Online), ISSN 2076-2275 (Print))          Vol. 1 No. 2
Time Dependent Ginzburg-Landau Equation in Fractal Space-time
C. Gh. Buzea 1, I. Rusu 2, V. Bulancea 2 , Gh. Bădărău 2, V.P. Păun 3 and M. Agop 4
1. National Institute of Research and Development for Technical Physics , D. Mangeron 47, 700050 - Iasi, Romania; E-mail: calinb2003@yahoo.com
2. Material and Engineering Science, Technical “Gh. Asachi” University, D. Mangeron 67, 700050 - Iasi, Romania
3. Faculty of Applied Sciences, Politechnical University of Bucharest, Department of Physics, Splaiul Independentei 313, 060042 - Bucharest, Romania
4. Department of Physics, Technical “Gh. Asachi” University, D. Mangeron 67, 700050 - Iasi, Romania

Abstract: We use the hydrodynamic formulation of Scale Relativity Theory to analyze the time-dependent Ginzburg-Landau equation. As a result, London equations come naturally from the system, when equating to zero the real velocity, the imaginary one turns real, the superconducting fluid acts as a subquantum medium energy accumulator, the vector potential, the real and the imaginary velocities are all written in terms of the elliptic function. When solving the resulted system by means of WKBJ method, we get tunneling and quantization. In other words, scale transformation laws produce effects which are analogous to those of a ”macroscopic quantum mechanics”.

Keywords: Time dependent Ginzburg-Landau equations, scale relativity, WKBJ method, fractal space-time, non-differentiability

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