Time Dependent Ginzburg-Landau Equation in Fractal Space-time
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The hydrodynamic formulation of Scale Relativity theory is used to analyze the Time Dependent Ginzburg-Landau (TDGL) 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 act as a sub-quantum medium energy accumulator, the vector potential, the real and the imaginary velocity are all written in terms of the elliptic function. When solving the resulted system by means of WKBJ method, one gets tunneling and quantization. In other words, scale transformation laws produce, on the moti...
The hydrodynamic formulation of Scale Relativity theory is used to analyze the Time Dependent Ginzburg-Landau (TDGL) 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 act as a sub-quantum medium energy accumulator, the vector potential, the real and the imaginary velocity are all written in terms of the elliptic function. When solving the resulted system by means of WKBJ method, one gets tunneling and quantization. In other words, scale transformation laws produce, on the motion equation of particles governed by the TDGL equation, under some peculiar assumptions, effects which are analogous to those of a macroscopic quantum mechanics .
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