Quantum Statistical Derivation of a Ginzburg-Landau Equation

Shigeji Fujita¹, Akira Suzuki^2*

¹Department of Physics, University at Buffalo, State University of New York, Buffalo, USA.
²Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo, Japan.

DOI: 10.4236/jmp.2014.516157                

Abstract

The pairon field operator ψ(r,t) evolves, following Heisenberg’s equation of motion. If the Hamiltonian H contains a condensation energy α₀(<0) and a repulsive point-like interparticle interaction , , the evolution equation for ψ is non-linear, from which we derive the Ginzburg-Landau (GL) equation: for the GL wave function where σdenotes the state of the condensed Cooper pairs (pairons), and n the pairon density operator (u and are kind of square root density operators). The GL equation with holds for all temperatures (T) below the critical temperature T_c, where ε_g(T) is the T-dependent pairon energy gap. Its solution yields the condensed pairon density . The T-dependence of the expansion parameters near T_c obtained by GL: constant is confirmed.

Keywords

Ginzburg-Landau Equation, Complex-Order Parameter, Coherent Length, Cooper Pair (Pairon), Pairon Density Operator, T-Dependent Pairon Energy Gap

Conflicts of Interest

The authors declare no conflicts of interest.

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