Quantum Statistics and the Many-Body Problem pp 155-162 | Cite as

# Free Energy Functionals for Superfluid ^{3}He

## Abstract

From the first suggestions in the early 1960’s of the possibility of pairing in ^{3}He, until well after the discovery of the A and B phases in 1972, theoretical investigations of the properties of ^{3}He with pairing took as a working assumption that this system would be well described by the simplest possible combination of BCS pairing theory and Landau’s Fermi liquid theory. The Fermi liquid theory provides an exact account of normal ^{3}He just above T_{c} in terms of interacting quasi-particles, and corrections to BCS pairing theory for these quasi-particles were expected to be of order (k_{F}ξ_{O})^{-1} ~ (T_{c}/T_{F}) ~ 3 × 10^{-3}. However, experiments on the A and B phases soon showed this assumption to be incorrect.^{1} In particular, the experiments imply that both new phases have odd-ℓ, spin-triplet pairing; that ℓ is the same in both phases; and that ^{3}He-A is an equal-spin pairing state, while ^{3}He-B is not. BCS pairing theory, on the other hand, predicts that the equilibrium state for triplet pairing is never an equal-spin pairing state.^{2} Furthermore, in simple BCS theories ΔC/C_{N}, the ratio of the specific heat discontinuity at T_{c} to the specific heat in the normal phase just above T_{c}, is always ≤ 1.43, while experiments at melting pressure give ΔC/C_{N} ≅ 2.0.

## Keywords

Free Energy Vertex Function Melting Pressure Fermi Liquid Theory Exact Account## Preview

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## References

- (1).Further details and original references on the experimental picture of superfluid He can be found in J. C. Wheatley, Rev. Mod. Phys. 47, 415 (.1975).ADSCrossRefGoogle Scholar
- (2).R. Balian and N. R. Werthamer, Phys. Rev. 131, 1553 (1963).ADSCrossRefGoogle Scholar
- (3).A. J. Leggett, Ann. Phys. (N.Y.) 85, 11 (1974).ADSCrossRefGoogle Scholar
- (4).N. D. Mermin and G. Stare, Phys. Rev. Lett. 30, 1135 (1973); G. Stare, 1974, Thesis, Cornell University, unpublished.ADSCrossRefGoogle Scholar
- (5).V. Ambegaokar, P. G. de Gennes, and D. Rainer, Phys. Rev. A 9, 1676 (1974).ADSCrossRefGoogle Scholar
- (6).W. F. Brinkman, J. W. Serene, and P. W. Anderson, Phys. Rev. A 10, 1386 (1974).ADSGoogle Scholar
- (7).J. M. Luttinger and J. C. Ward, Phys. Rev. 118, 1417 (1960).MathSciNetADSMATHCrossRefGoogle Scholar
- (8).C. DeDominicis and P. C. Martin, J. Math. Phys. 5, 31 (1964).MathSciNetADSCrossRefGoogle Scholar
- (9).K. S. Dy and C. J. Pethick, Phys. Rev. 185, 373 (1969).ADSCrossRefGoogle Scholar
- (10).C. J. Pethick, H. Smith, and P. Bhattacharyya, Phys. Rev. Lett. 34, 643 (1975).ADSCrossRefGoogle Scholar