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General Equilibrium Condition and Hydrodynamics of Superfluid 3He-A

  • Chia-Ren Hu

Abstract

It is now generally accepted that the order parameter of superfluid 3He-A is a complex tensor \({A_{\mu i}} = {\Delta _0}{\hat d_\mu }({\hat m_i} + i{\hat n_i})\), where \(\hat d\), \(\hat m\) and \(\hat n\)(m) are three real unit vectors. A “texture” of 3He-A refers to a slow spatial variation of the “orbital or anisotropy axis” \(\ell \equiv \hat m \times \hat n\), and the “spin axis” \(\hat d\), possibly accompanied by a nonvanishing “superfluid velocity” \({\vec \nabla ^{(s)}} \equiv (h/2M){m_j}\vec \nabla {n_j}\) (where M is the mass of a 3He atom), while the magnitude parameter Δ0 is usually fixed at the constant equilibrium value. Such textures are all quasi-degenerate in energy because the 3He-A order parameter has spontaneously broken the gauge symmetry and the rotational symmetries in. orbital and spin spaces. From the above definitions of \({\vec \nabla ^{(s)}}\) and \(\hat \ell\), one may verify a relation first obtained by Mermin and Ho:2
$${\partial _i}{V_j}^{(s)} - {\partial _j}{V_i}^{(s)} = (\hbar /2M)\hat \ell \bullet {\partial _i}\hat \ell \times {\partial _j}\hat \ell$$
(1)
which implies
$$ \partial {V^{(s)}}_i = - (\hbar /2M)\hat \ell \bullet ({\partial _i}\hat \ell ) \times \delta \hat \ell + (\hbar /2M){\partial _i}(\delta \phi ) $$
(2)
.

Keywords

Gauge Symmetry Spin Axis Spin Space Anisotropy Axis Galilean Invariance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • Chia-Ren Hu
    • 1
  1. 1.Department of PhysicsTexas A&M UniversityCollege StationUSA

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