Dynamical phase transitions at many body exceptional points

Spontaneous synchronization is at the coreof many natural phenomena. Your heartbeat is maintained because cells contractin a synchronous wave; some bird species synchronize their motion into flocks;quantum synchronization is responsible for laser action and superconductivity.The transition to synchrony, or between states of different patterns ofsynchrony, is a dynamical phase transition that has much in common withconventional phase transitions of state – for example solid to liquid, ormagnetism – but the striking feature of driven dynamical systems is that thecomponents are “active”. Consequently quantum systems with dissipation anddecay are described by non-Hermitian Hamiltonians, and active matter canabandon Newton’s third law and have non-reciprocal interactions. Thissubstantially changes the character of many-degree-of-freedom dynamical phasetransitions, and the critical phenomena in their vicinity, since the criticalpoint is an “exceptional point” where eigenvalues coalesce. We will illustrate this in two verydifferent systems – a Bose-Einstein condensate of polaritons, and models ofmulticomponent active matter such as flocks of birds.