We discuss the emergence of non-stationarity in open quantum manybody systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent, time-periodic oscillations induced by noisy contact with an environment. We use the Loschmidt echo and local observables to indicate the presence of a dissipative time crystal. Starting from the closed Hubbard model we then provide examples of dissipation mechanisms that yield experimentally observable quantum limit cycles and allow analysis of the emergence of dissipative time crystals. For a disordered Hubbard model including two-particle loss and gain we find a dark Hamiltonian driving oscillations between GHZ states in the long-time limit. Finally, we discuss how the presented examples could be experimentally realized.

We develop a Bethe ansatz based approach to study dissipative systems experiencing loss. The method allows us to exactly calculate the spectra of interacting, many-body Liouvillians. We discuss how the dissipative Bethe ansatz opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.

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The genomes of a large number of highly diverse novel circular DNA viruses from a wide range of sources have been characterised in recent years, including circular single-stranded DNA (ssDNA) viruses that share similarities with plant-infecting ssDNA viruses of the family Geminiviridae. Here, we describe six novel circular DNA viral genomes that encode replication-associated (Rep) proteins that are most closely related to those of either geminiviruses or gemycircularviruses (a new group of ssDNA viruses that are closely related to geminiviruses). Four possible viral genomes were recovered from Bromus hordeaceus sampled in New Zealand, and two were recovered from B. hordeaceus and Trifolium resupinatum sampled in France. Two of the viral genomes from New Zealand (one from the North Island and one from the South Island each) share >99 % sequence identity, and two genomes recovered from B. hordeaceus and T. resupinatum sampled in France share 74 % identity. All of the viral genomes that were recovered were found to have a major open reading frame on both their complementary and virion-sense strands, one of which likely encodes a Rep and the other a capsid protein. Although future infectivity studies are needed to identify the host range of these viruses, this is the first report of circular DNA viruses associated with grasses in New Zealand.