General Equilibrium Condition and Hydrodynamics of Superfluid 3He-A

  • Chia-Ren Hu


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
$${\partial _i}{V_j}^{(s)} - {\partial _j}{V_i}^{(s)} = (\hbar /2M)\hat \ell \bullet {\partial _i}\hat \ell \times {\partial _j}\hat \ell$$
which implies
$$ \partial {V^{(s)}}_i = - (\hbar /2M)\hat \ell \bullet ({\partial _i}\hat \ell ) \times \delta \hat \ell + (\hbar /2M){\partial _i}(\delta \phi ) $$


Gauge Symmetry Spin Axis Spin Space Anisotropy Axis Galilean Invariance 
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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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