Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Nonlinear Dynamics, Synchronization and Chaos

DY 31.5: Talk

Wednesday, April 3, 2019, 11:00–11:15, H20

Harmonic Oscillator Interacting with Random Ising Spins — •Paul Zech and Günter Radons — Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany

Hysteresis phenomena can be found in very different research fields, such as magnetic materials, porous materials, shape memory alloys, etc. One of the most prominent model of hysteresis is the zero-temperature Random Field Ising Model (RFIM). While the hysteretic behavior of the RFIM has been investigated in detail, not much is known about scenarios which arise if the RFIM is coupled dynamically to its environment, especially as the number of spins goes to infinity (thermodynamic limit). In this talk, we want to investigate the dynamical properties of a harmonic oscillator coupled to Ising spins in quenched random local fields. By applying established methods of dynamical systems and piecewise-smooth system theory to this hybrid system we show, how chaos emerges for two different spin set-ups. We first treat independent spins and secondly we introduce hysteretic behavior by a pairwise coupling of the spins, which results in an ensemble of spin dimers. We will show, that the approach to the thermodynamic limit results in an asymptotic nonlinearity in form of a error function and a hysteretic play operator, respectively. For an increasing number of spins we will also demonstrate, that the fractal dimensions of the chaotic attractors of the piecewise-smooth system approach those of the system in the thermodynamic limit and that both fractal dimensions are self-averaging quantities, in contrast to the time-averaged magnetization.