Stable and unstable trajectories in a dipolar chain

Dynamics of a pair of magnetic dipoles with nonreciprocal interactions due to a moving conductor

“…These phenomena may be related to notions in dynamical systems such as chaos [37]. Furthermore, we have also argued, that many of this effects could well be observable in experiments, for example in setups as in [12][13][14]. The results on statistical physics of non-reciprocal systems [7,9] motivate the experimental and theoretical study of the described system as well as possible future studies of many-body systems with non-reciprocal magnetic interactions.…”

“…In various experimental setups [12-14, 31, 32], two-dimensional magnetic moments (XY rotors) can be realized. Especially, given that the scales in the setup of [12][13][14] could be suitable to observe the effects of non-reciprocity, as discussed in Appendix F, we will look into this type of setup more closely in the following. The main features are rigid body dipoles (rods in the experiment) i.e.…”

“…and the dynamical equation for a rigid body [33] rotating around the z−axis with the moment of inertia I and the angle ϕ representing the orientation of the dipole relative to the x−axis. Introducing a further friction term appearing in the experiments [12][13][14], the EOM reads…”

“…In the experiments [12][13][14] cylindrical magnetic Neodymium rods constrained to move in the xy−plane act as magnetic dipoles. The parameters vary across the cited works, with the ones in [12] seeming most favorable for our setup, therefore we will use these here.…”

“…In Sec. IV, the main part of the article, we analyze the dynamics of a pair of rigid XY dipoles motivated by the experimental setup in [12][13][14]. We derive the equations of motion, which turn out to be a system of coupled non-linear equations, and solve these numerically.…”