JMP  Vol.5 No.16 , October 2014
Quantum Statistical Derivation of a Ginzburg-Landau Equation
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 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.

Cite this paper
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.
References
[1]   Ginzburg, V.L. and Landau, L.D. (1950) Journal of Experimental and Theoretical Physics (USSR), 20, 1064.

[2]   Landau, L.D. and Lifshitz, E.M. (1980) Statistical Physics, Part I. 3rd Edition, Pergamon Press, Oxford, 171-174.

[3]   Cooper, L.N. (1956) Physical Review, 104, 1189.
http://dx.doi.org/10.1103/PhysRev.104.1189

[4]   Bardeen, J., Cooper, L.N. and Schrieffer, J.R. (1957) Physical Review, 108, 1175.
http://dx.doi.org/10.1103/PhysRev.108.1175

[5]   Fujita, S., Ito, K. and Godoy, S. (2009) Quantum Theory of Conducting Matter: Superconductivity. Springer, New York, 77-79, 133-138.
http://dx.doi.org/10.1007/978-0-387-88211-6

[6]   Schrieffer, J.R. (1964) Theory of Superconductivity. Benjamin, New York.

[7]   Dirac, P.A.M. (1958) Principle of Quantum Mechanics. 4th Edition, Oxford University Press, London, 136-138.

[8]   File, J. and Mills, R.G. (1963) Physical Review Letters, 10, 93.
http://dx.doi.org/10.1103/PhysRevLett.10.93

[9]   Gorkov, I. (1958) Soviet Physics—JETP, 7, 505.

[10]   Gorkov, I. (1959) Soviet Physics—JETP, 9, 1364.

[11]   Gorkov, I. (1960) Soviet Physics—JETP, 10, 998.

[12]   Glaever, I. (1960) Physical Review Letters, 5, 147.
http://dx.doi.org/10.1103/PhysRevLett.5.147

[13]   Glaever, I. (1960) Physical Review Letters, 5, 464.
http://dx.doi.org/10.1103/PhysRevLett.5.464

[14]   Glaever, I. and Megerle, K. (1961) Physical Review, 122, 1101.
http://dx.doi.org/10.1103/PhysRev.122.1101

[15]   Glover III, R.E. and Tinkham, M. (1957) Physical Review, 108, 243.
http://dx.doi.org/10.1103/PhysRev.108.243

[16]   Biondi, M.A. and Garfunkel, M. (1959) Physical Review, 116, 853.
http://dx.doi.org/10.1103/PhysRev.116.853

[17]   Abrikosov, A.A. (1957) Soviet Physics—JETP, 5, 1174.

[18]   Josephson, B.D. (1962) Physics Letters, 1, 251-253.
http://dx.doi.org/10.1016/0031-9163(62)91369-0

[19]   Josephson, B.D. (1964) Reviews of Modern Physics, 36, 216.
http://dx.doi.org/10.1103/RevModPhys.36.216

 
 
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