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Magnetic type “charge” for superfluid velocity νs in 3He-A and 3He-B

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  • Galasiewicz, Z.M.

Abstract

The equations of motion for the averaged order parameter operator in superfluid 3He, which is proportional to a 3 × 3 matrix Aij, are derived. The normalization condition (AijAij∗ = 1) leads to the restriction for Adotij (representing equations of motion), of the form AdotijAij∗ + AijAdotij∗ = 0. This condition is however not fulfilled identically but forces a relation for superfluid velocity of the form div νs = Q [with Q(t) → − Q(−t)]. A general expression for Q is worked out on the basis of an equation of motion approach. From this it follows that a nonvanishing Q can arise as a consequence of correlations in the expectation values of field operators (in the mean-field situation Q will vanish). The consequence of the term with Q will be discussed for the A and B phases, in relation to the simple phenomenological approaches to spin dynamics. For the A and B-phases Q(t) is a linear combination built from spin density components [ms(t) → −ms(−t)] with coefficients being even functions of time. This preserves the proper behaviour of Q(t) under time reflection.

Suggested Citation

  • Galasiewicz, Z.M., 1989. "Magnetic type “charge” for superfluid velocity νs in 3He-A and 3He-B," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 159(2), pages 301-317.
    • Handle: RePEc:eee:phsmap:v:159:y:1989:i:2:p:301-317
    DOI: 10.1016/0378-4371(89)90572-4
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