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Relation between BCS Hamiltonian and Ginzburg–Landau equation
Author(s) -
Aono Shigeyuki
Publication year - 1998
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1998)69:6<693::aid-qua1>3.0.co;2-q
Subject(s) - hamiltonian (control theory) , physics , boson , path integral formulation , mathematical physics , ginzburg–landau theory , quantum mechanics , superconductivity , fermion , electron , quantum electrodynamics , mathematics , quantum , mathematical optimization
It is intended to derive the Ginzburg–Landau (GL) equation directly from the Bardeen–Cooper–Schrieffer (BCS) Hamiltonian. By the use of the Hubbard–Stratonovitch transformation, the electron–electron interaction composed of four fermion operators is eliminated to yield an auxiliary boson field. This is an effective field in which electrons behave as if they were free. In applying the path integral method, the electron field is integrated out to remain the Lagrangian for this boson field. The symmetry breaking and the phase transition of the system described by this field are discussed, and it is shown that this boson field turns out to be the GL order parameter. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 693–703, 1998