Quasiclassical theory of spin dynamics in superfluid ${}^3$He: kinetic equations in the bulk and spin response of surface Majorana states

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 a 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 lifetime of longitudinal and transverse spin waves is calculate taking into account the Fermi-liquid corrections which lead to the crucial modification of fermionic spectrum and spin responses.

Submitted to proceedings of QTC2017. In the new version several typos are corrected and the discussion of interaction between the spin waves and Majorana states is extended

References in corpus (6)

• Long-range spin and charge accumulation in mesoscopic superconductors with Zeeman splitting
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Superfluid 3He in a restricted geometry with a perpendicular magnetic field
• Long-range spin imbalance in mesoscopic superconductors under a Zeeman splitting
• Measurements of anisotropic mass of magnons confined in a harmonic trap in superfluid ${}^3$He-B
• Locally gauge-invariant spin response of ${}^3$He-$B$ films with Majorana surface states

Cited by in corpus (2)

• Magnon Bose-Einstein condensates: from time crystals and quantum chromodynamics to vortex sensing and cosmology
• NMR-like effect on Anisotropic Magnetic Moment of Surface Bound States in Topological Superfluid ${}^3$He-B