Stochastic description of the dynamics of the random-exchange Heisenberg chain
M. H. Vainstein, R. Morgado, F. A. Oliveira, F. A. B. F. de Moura, M. D. Coutinho-Filho
Abstract
We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as k-β, using a stochastic description. It establishes a direct connection between the fluctuation in the spin-wave density of states and the noise density of states. For continuous ranges of the exponent β, we find superdiffusive and ballistic spin-wave motions. Both diffusion exponents predicted by the stochastic procedure agree with the ones calculated using the Hamiltonian dynamics.
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