Padé approximations for the magnetic susceptibilities of Heisenberg antiferromagnetic spin chains for various spin values.

The temperature dependence of the spin susceptibilities of S = 1, 3/2, 2, 5/2 and 7/2 Heisenberg antiferromagnetic 1D spins chains with nearest-neighbor coupling was simulated via quantum Monte Carlo calculations, within the reduced temperature range of 0.005 ≤ T* ≤ 100, and fitted to a Padé approximation with deviations between the simulated and fitted data of the same order of magnitude as or smaller than the quantum Monte Carlo simulation error. To demonstrate the practicality of our theoretical findings, we compare these results with the susceptibility of the well known 1D chain compound TMMC ([(CH(3))(4)N[MnCl(3)]], d(5), S = 5/2) and find that different intra-chain spin-exchange parameters result if we consider the data above and below the structural phase transition reported for TMMC at ~126 K. The structural phase transition, which gives rise to an anomaly in the magnetic susceptibility, is independent of the magnetic field up to magnetic fields of 7 T. Additionally, we show that the S = 1 system NiTa(2)O(6) with tri-rutile crystal structure can be very well described as a Heisenberg S = 1 spin chain.

Delayed feedback control of dynamical systems at a subcritical Hopf bifurcation.

We consider the delayed feedback control of a torsion-free unstable periodic orbit originated in a dynamical system at a subcritical Hopf bifurcation. Close to the bifurcation point the problem is treated analytically using the method of averaging. We discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a nonlinear coupling between the controlled system and controller. To demonstrate our analytical approach the specific example of a nonlinear electronic circuit is taken as a model of a subcritical Hopf bifurcation.

Influence of stable Floquet exponents on time-delayed feedback control

The performance of time-delayed feedback control is studied by linear stability analysis. Analytical approximations for the resulting eigenvalue spectrum are proposed. Our investigations demonstrate that eigenbranches that develop from the stable Lyapunov exponents of the free system also have a strong influence on the control properties, either by hybridization or by a crossing of branches which interchanges the role of the leading eigenvalue. Our findings are confirmed by numerical analysis of two particular examples, the Toda and the Rossler models. More important is the verification by actual electronic circuit experiments. Here, the observed reduction of control domains can be attributed to these additional eigenvalue branches. The investigations lead to a thorough analytical understanding of the stability properties in time-delayed feedback systems.