2003/07/15 by D. A. Garanin, R. Schilling · 2 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Materials Science · Physics and Astronomy · #Advanced NMR Techniques and Applications #Electron Spin Resonance Studies #Magnetism in coordination complexes #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.69.104412
published as Phys. Rev. B 69, 104412 (2004) · 4 Phys. Rev. pages 2 Figs
arxiv created 2003/07/15 · openalex publication_date 2004/03/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present a method, the dynamical cumulant expansion, that allows us to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum spin model \ifmmode H\else \H\fi=\ensuremath-Hz(t)Sz+V(S) with Hz(\ifmmode±\else\textpm\fi\ensuremath∞)=\ifmmode±\else\textpm\fi\ensuremath∞ and \ensuremathΨ(\ensuremath-\ensuremath∞)=|\ensuremath-S〉 to find P(t)=(1\ensuremath-〈Sz〉t/S)/2. The case V(S)=\ensuremath-HxSx corresponds with the standard Landau-Zener-Stueckelberg model of tunneling at avoided level crossings for N=2S independent particles mapped onto a single-spin-S problem, P(t) being the staying probability. Here the solution does not depend on S and it follows, e.g., from the classical Landau-Lifshitz equation. A term \ensuremath-DSz2 accounts for the particle interaction and it makes the model nonlinear and essentially quantum mechanical. The 1/S corrections obtained with our method are in good accord with a full quantum-mechanical solution if the classical motion is regular, as for D>0. If the classical motion shows special points, as is the case for D<0 for particular values of the sweep rate, or is irregular (the biaxial-anisotropy model with field along the hard axis) the cumulant expansion fails.