2009, Senf, F., Altrock, P.M., Behn, U.

A finite array of N globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling, there is a clear separation of timescales of centre of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the centre of mass coordinate. We compute analytically the stationary probability distribution and the moments of the centre of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter ac(N) is determined. We identify a crossover from linear to square root scaling with increasing distance from ac. The crossover point approaches ac in the limit N →∞ which reproduces previous results for infinite arrays. Our results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on N and is determined by the scaling behaviour near a fixed point of the stochastic flow. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

2022, Wang, Jiawei, Valligatla, Sreeramulu, Yin, Yin, Schwarz, Lukas, Medina-Sánchez, Mariana, Baunack, Stefan, Lee, Ching Hua, Thomale, Ronny, Li, Shilong, Fomin, Vladimir M., Ma, Libo, Schmidt, Oliver G.

The Möbius strip, a fascinating loop structure with one-sided topology, provides a rich playground for manipulating the non-trivial topological behaviour of spinning particles, such as electrons, polaritons and photons, in both real and parameter spaces. For photons resonating in a Möbius-strip cavity, the occurrence of an extra phase—known as the Berry phase—with purely topological origin is expected due to its non-trivial evolution in parameter space. However, despite numerous theoretical investigations, characterizing the optical Berry phase in a Möbius-strip cavity has remained elusive. Here we report the experimental observation of the Berry phase generated in optical Möbius-strip microcavities. In contrast to theoretical predictions in optical, electronic and magnetic Möbius-topology systems where only Berry phase π occurs, we demonstrate that a variable Berry phase smaller than π can be acquired by generating elliptical polarization of resonating light. Möbius-strip microcavities as integrable and Berry-phase-programmable optical systems are of great interest in topological physics and emerging classical or quantum photonic applications.