Perturbation Expansion for a Fermi Superfluid. : I.Basic Formalism and Angular Momentum

概要

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A theory of a Fermi superfluid is fortnulated based on the condensate wave ftmnction of theconfiguration space. First, two basic ingredients are extracted frona the wave function, i.e, theeffective condensate wave ftrnction v(xr, rr) and the quasiparticle field 'y(r) wnth x denoting thespace and spin coordinates 7'c). After transforrning a Hamiltonian into a normal-ordered productof '7, a perturbation expansion with respect to the quasiparticle interaction is formulated forboth the thermodynarnic potential Q and the one-particle density matrix p. The thertuuodynamicpotential thus ol*tained includes the normal-state expression of Luttin er and Ward as the limit ofv -: 0, The density matrix is written as a surn of the coherent part p' and the quasiparticle partp"", where p"' is expressed only with respect to 'u(rj, xc). It is shown that v and y are responsiblefor the coherent and thermodynarnic properties respectively. Thvrs the present formalism gxvesa microscopic foundation for the two-fluid rnodel. Connections with the Gor'kov equations andthe Bogoliubov-de Gennes equations are also clarified. It is found that the one-particle densityrnatrices of those forrnalisms are not eqttivalent to p of the present formalism. The origun of theangular momentum paradox of 'He-,4 is traced to this difference.
社団法人日本物理学会の論文
1996-05-15