TITLE:
Quantum Statistical Derivation of a Ginzburg-Landau Equation
AUTHORS:
Shigeji Fujita, Akira Suzuki
KEYWORDS:
Ginzburg-Landau Equation, Complex-Order Parameter, Coherent Length, Cooper Pair (Pairon), Pairon Density Operator, T-Dependent Pairon Energy Gap
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.16,
October
20,
2014
ABSTRACT: The pairon field operator ψ(r,t) evolves, following Heisenberg’s equation of motion. If the
Hamiltonian H contains a condensation
energy α0(, ,
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 Tc, where εg(T) is the T-dependent pairon energy gap. Its solution yields the condensed
pairon density .
The T-dependence of the expansion
parameters near Tc obtained by GL: constant is confirmed.