Three-dimensional classical and quantum stable structures of dissipative systems

Discontinuous spirals of stability in an optically injected semiconductor laser

We report a new kind of discontinuous spiral with stable periodic orbits in the parameter space of an optically injected semiconductor laser model, which is a combination of the intercalation of fish-like and cuspidal-like structures (the two normal forms of complex cubic dynamics). The spiral has a tridimensional structure that rolls up in at least three directions. A turn of approximately 2π radians along the spiral and toward the center increases the number of peaks in the laser intensity by one, which does not occur when traversing the discontinuities. We show that as we vary the linewidth enhancement factor (α), discontinuities are created (destroyed) through disaggregation (collapses) from (into) the so-called shrimp-like structures. Future experimental verification and applications, as well as theoretical studies to explain its origin and relation with homoclinic spirals that exist in its neighborhood, are needed.

Classical stochastic discrete time crystals

We describe a general and simple paradigm for discrete time crystals (DTCs), systems with a stable subharmonic response to an external driving field, in a classical thermal setting. We consider, specifically, an Ising model in two dimensions, as a prototypical system with a phase transition into stable phases distinguished by a local order parameter, driven by thermal dynamics and periodically kicked with a noisy protocol. By means of extensive numerical simulations for large sizes-allowed by the classical nature of our model-we show that the system features a true disorder-DTC order phase transition as a function of the noise strength, with a robust DTC phase extending over a wide parameter range. We demonstrate that, when the dynamics is observed stroboscopically, the phase transition to the DTC state appears to be in the equilibrium two-dimensional Ising universality class. However, we explicitly show that the DTC is a genuine nonequilibrium state. More generally, we speculate that systems with thermal phase transitions to multiple competing phases can give rise to DTCs when appropriately driven.