Spontaneous symmetry breaking

My first venture during my PhD went into the statistical physics of optomechanical arrays as their nonlinear dynamics offers a rich variety of behaviour. I found out in (Pelka et al., 2020) that two identical arrays can encounter so-called spontaneous symmetry breaking upon coupling them weakly together. Here, the broken symmetry is the \(\mathbb{Z}_2\)-exchange symmetry of the arrays while the order parameter is given by the complex synchronisation-parameter \(\frac{1}{N}\sum\limits_{j=1}^{N}\exp(i\phi_j)\) of each array. The control parameter is the mechanical coupling which can lead the system to attain synchronisation in only one of the arrays whilst the other cannot synchronise anymore.

This animation shows the behaviour of a two arrays in the Chimera phase under slight variation of the initial condition. The upper line shows the evolutino of some initial condition of the first array (upper left picture) and the second array (upper right picture) which shows that the second array synchronises under the weak mechanical coupling. The second row shows that only changing this inital condition slightly as indicated in the red circles characterising the deviation in initial condition hinders the first array (lower left picture) to synchronise whilst the second array (lower right picture) perfectly synchronises now. This behaviour depends only on the initial condition, as caused by a thermal fluctuation for instance, and has been coined Chimera state reflecting the two different behaviours that each system shows.