Stochastic description of the dynamics of the random-exchange Heisenberg chain

Abstract

We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta }$, 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 $\beta$, 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.

arXiv comment6 pages, 4 figures

References in corpus (17)

• Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
• Experimental evidence of delocalized states in random dimer superlattices
• Experimental observation of the mobility edge in a waveguide with correlated disorder
• Observation of Fluctuation-Dissipation-Theorem Violations in a Structural Glass
• Mobility Edge in Aperiodic Kronig-Penney Potentials with Correlated Disorder: Perturbative Approach
• Delocalization in harmonic chains with long-range correlated random masses
• Violation of the fluctuation-dissipation theorem for fast superdiffusion
• Roundoff-induced Coalescence of Chaotic Trajectories
• Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange
• Absence of localization and large dc conductance in random superlattices with correlated disorder
• Delocalization in Continuous Disordered Systems
• Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics
• Enhanced suppresion of localization in a continuous Random-Dimer Model
• Two time scales and FDT violation in a Finite Dimensional Model for Structural Glasses
• Glassy dynamics, metastability limit and crystal growth in a lattice spin model
• Three-dimensional effects on extended states in disordered models of polymers
• Extended States in a One-dimensional Generalized Dimer Model

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• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Spatio-temporal conjecture for diffusion
• A geometrical interpretation of critical exponents
• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model
• Mixing, Ergodicity and the Fluctuation-Dissipation Theorem in complex systems