Abstract

In this study, a 4th-order Ginzburg-Landau differential equation is obtained based on the generalization of the Heisenberg's uncertainty relation recently introduced in literature. This equation is similar to the Fisher-Kolmogorov equation which occurs in many physical models. The Lagrangian and the Hamiltonian of the 4th-prder Ginzburg-Landau equation were constructed and it was observed that the energy is a conserved quantity along its corresponding orbits. Two applications were discussed mainly the occurrence of superconductivity in a bulk superconductor through an external magnetic field and the microscopic formulation of BCS superconductivity. Several properties were discussed accordingly.

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