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Is there a simple derivation of Ginzburg-Landau theory of superconductivity, with emphasis on simple, from the BCS theory?
Fred Wright said:I think that you are asking for the impossible unless you consider quantum field theory simple. The following is an historical overview of the process of developing the BCS microscopic theory from the Landau-Ginzberg free energy model by its original author, Lev Gor'kov: Gor'kov paper (LG to BCS)
Quantum field theory, or second quantization, is simple in my view. But the way how it is used, for instance, in the book by Abrikosov, Gorkov and Dzyaloshinskii is not simple. On the other hand, the book by Mattuck is much simpler. An even simpler book on QFT is the one by Lancaster and Blundell (QFT for the Gifted Amateur), which in fact does give a rough simple idea of how to get GL from BCS and something more complete on that level would be very desirable. I hope it helps to get a picture of what do I mean by "simple".Fred Wright said:I think that you are asking for the impossible unless you consider quantum field theory simple.
That's the original Gorkov's derivation, which is anything but simple.dRic2 said:This is above my current understanding, so I don't really know if that's what you are looking for.
The simplest explanation of BBGKY I am aware is presented in Tong's lectures:MathematicalPhysicist said:I find BBGKY difficult, tried to understand it from Kardar's textbook; for the life of me this is difficult.
It appears to be available on arxiv.vanhees71 said:A. Schmitt, Introduction to Superfluidity, Springer 2015
The Ginzburg-Landau theory is a mathematical model used to describe the behavior of superconductors at temperatures close to their critical temperature. It is based on the BCS theory, which explains the phenomenon of superconductivity.
The Ginzburg-Landau theory is derived from the BCS theory by making simplifying assumptions about the behavior of the superconducting order parameter and the electron-phonon interaction. This allows for a simpler mathematical description of the superconductor's properties near the critical temperature.
The simplified approach assumes that the superconducting order parameter is constant throughout the material and that the electron-phonon interaction is weak. It also neglects the effects of impurities and external magnetic fields.
The Ginzburg-Landau theory predicts that the superconducting transition is second-order, meaning that there is no latent heat involved. It also predicts the existence of a critical magnetic field and critical current density, as well as the behavior of the order parameter near the critical temperature.
The Ginzburg-Landau theory is used to understand and predict the behavior of superconductors in various applications, such as in superconducting magnets for MRI machines and in superconducting wires for power transmission. It also provides a framework for studying and designing new superconducting materials with desired properties.