Quantum Statistical Derivation of a Ginzburg-Landau Equation - Journal of Modern Physics

JMP > Vol.5 No.16, October 2014

Quantum Statistical Derivation of a Ginzburg-Landau Equation ()

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DOI: 10.4236/jmp.2014.516157 5,498 Downloads 6,910 Views

Author(s)

Shigeji Fujita¹, Akira Suzuki^2*

Affiliation(s)

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.

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

Share and Cite:

Fujita, S. and Suzuki, A. (2014) Quantum Statistical Derivation of a Ginzburg-Landau Equation. Journal of Modern Physics, 5, 1560-1568. doi: 10.4236/jmp.2014.516157.

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