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Quasiclassical Theory of Spin Dynamics in Superfluid \(^3\)He: Kinetic Equations in the Bulk and Spin Response of Surface Majorana States

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Abstract

We develop a theory based on the formalism of quasiclassical Green’s functions to study the spin dynamics in superfluid \(^3\)He. First, we derive kinetic equations for the spin-dependent distribution function in the bulk superfluid reproducing the results obtained earlier without quasiclassical approximation. Then, we consider spin dynamics near the surface of fully gapped \(^3\)He-B-phase taking into account spin relaxation due to the transitions in the spectrum of localized fermionic states. The lifetimes of longitudinal and transverse spin waves are calculated taking into account the Fermi-liquid corrections which lead to a crucial modification of fermionic spectrum and spin responses.

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Acknowledgements

We thank V. El’tsov and G. Volovik for stimulating discussions. This work was supported by the Academy of Finland.

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Authors and Affiliations

  1. Department of Physics and Nanoscience Center, University of Jyväskylä, P.O. Box 35 (YFL), 40014, Jyväskylä, Finland

    M. A. Silaev

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  1. M. A. Silaev
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Correspondence to M. A. Silaev.

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Silaev, M.A. Quasiclassical Theory of Spin Dynamics in Superfluid \(^3\)He: Kinetic Equations in the Bulk and Spin Response of Surface Majorana States. J Low Temp Phys 191, 393–407 (2018). https://doi.org/10.1007/s10909-018-1864-9

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  • DOI: https://doi.org/10.1007/s10909-018-1864-9

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