By Zygmunt M. Galasiewicz (Auth.)

ISBN-10: 0080130895

ISBN-13: 9780080130897

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2 fufl + Y*(fuh) [F(fl9f2)-F*(f29fù]· fufz For the Lagrange multipliers λ, μ, α, γ we have the following relations : A(/i,/2) = A*(/2,/i), «(A,/*) = -«*σ 2 ,/ι). Α*σι,/2) = /*ί/2,/ι), r(/i>/2) = 7(Λ,/0, which follow from the properties of F, Φ. We now treat the variations OF, δΦ, OF*, <5Φ* as independent. 19) the coefficients of these variations must vanish. 21a) f -^(f9f1)0{f29f) f + f ^^(f9fùF*(f9f^ - ] [ y ( / , / 2 ) F * ( / , / i ) = 0. 21a,b). Now we wish to eliminate the Lagrange multipliers λ and μ.

25) is equivalent to the H-F principle. We see that the new variational principle should describe more correlations among particles and its solutions should contain more physical content. /2' IW/O+^tf/')] IW/2;/i,/i) - U(fl ,/ 2 ;ft 9fu\F*(fi 9f[)F(f2 ,f2). 18a) the form ^F(fl9f)F(f9f2)^F(fl9f2) = 0. 18a,b) and eqns. 29)), different from the H-F solution, for which bW is equal to zero. Whether this solution actually corresponds to a minimum of o is a question to be solved after we examine the sign of 62W.

5b,c) Those diagrams were introduced by Hugenholtz (quoted here after Bogoliubov (1958a, b)). Straight lines denote particles and wavy lines phonons. At point 1 (Fig. 5b) HA x contributes ~ uk,vk(oc£,+ ai k _ A + octk+(x^_)bq and at point 2, H2 contributes ~ b+(ukuk,a£+ afc,+ —#fcSVai / a_ ) On the other hand at point 1 (Fig 5c) H , . fc + fc+ . )bq. The same terms come from the processes in Fig. 5b and 5c. 53) œ(k—k') ^(ul-vl), œ(k-k') + el(k) + ei(k') k' El(k) = (E(k)-X)(ul-vî). a ko b) a kö a k,-o FIG.

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Superconductivity and Quantum Fluids by Zygmunt M. Galasiewicz (Auth.)


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