Abstract

A FEYNMAN PATH INTEGRAL FORMULATION OF LANDAU-GINZSBURG THEORY OF SUPERCONDUCTING SYSTEM

Ephraim P. Inyang, Uza T. Isaac* and Etido P. Inyang

ABSTRACT

In this paper, we derive the Feynman‟s path integral expression of the Landau-Ginzburg free energy functional of superconducting system in terms of the magnetic system or a bar magnet.Ginsburg-Landau theory of superconducting system forms a phenomenological model which analyses the materials that have zero resistance to electric current in the vicinity or close to their critical temperature on an infinitesimal or microscopic measurement. In spite of being a very successful physical model, it has also a good idea of mathematics that has been studied. Microscopically, superconductivity occurs as a result attraction between electrons, making them to transform into quantum wedded electrons. We look at certain regions of the magnet that are average and associate such areas with magnetization (M) as a function of position (). The local magnetization is used to obtain the Feynman‟s path integral expression of the Landau-Ginzburg free energy functional of superconducting system using field theoretical methods. In this system (the bar magnet), we look at the possibility of position () to describe the system in N-dimensions and characterized it by different configuration and assigned it with a rate of probability of different realization (𝘞). The probability rate of finding a sub-system with energy being in a particular micro-state of the medium of energy () is evaluated. An analytical expansion of the sub-divisions of the magnetization give rise to the partition function as a function of temperature and the zero field in the vicinity or close to the critical temperature as the free energy functional of the superconducting system. The results we obtained in this paper are in agreements with the results of Landau-Ginzburg free energy functional of superconducting system obtained by Gorkov in 1959 and it is also in agreement with the results of Landau-Ginzburg free energy functional of superconducting system.

Keywords: Magnetic system, superconducting system, Landau-Ginzburg theory and partition function.