Simplified (Coarse-Grained) Description of Magnon Transport Kinetics along a Ferromagnetic Chain

Using a coarse-grained description of the kinetic process – based on the hierarchy of transition rates in a quantum system – the kinetics of the establishment of a steady-state magnon flow from a magnon source to a magnon receiver has been investigated. It is shown that if the characteristic hopping rate of magnons between adjacent chain units significantly exceeds their decay rate, the final stage of the establishment of a steady-state regime of magnon transport along the chain can exhibit a double-exponential or even single-exponential character. Analytical expressions have been obtained for magnon transport rates and the steady-state magnon flow. It is shown that increasing the magnon lifetime significantly improves the transport properties of the chain.