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Since the discovery of topological insulators, many topological phases have been predicted and realized in a range of different systems, providing both fascinating physics and exciting opportunities for devices. And although new materials are being developed and explored all the time, the prospects for probing exotic topological phases would be greatly enhanced if they could be realized in systems that were easily tuned. The flexibility offered by ultracold atoms could provide such a platform. Here, we review the tools available for creating topological states using ultracold atoms in optical lattices, give an overview of the theoretical and experimental advances and provide an outlook towards realizing strongly correlated topological phases. Using optical lattices to trap ultracold atoms provides a powerful platform for probing topological phases, analogues to those found in condensed matter. But as these systems are highly tunable, they could be used to engineer even more exotic phases. Using optical lattices to trap ultracold atoms provides a powerful platform for probing topological phases, analogues to those found in condensed matter. But as these systems are highly tunable, they could be used to engineer even more exotic phases.

Intracellular organelles are either membrane-bound vesicles or membrane-less compartments that are made up of proteins and RNA. These organelles play key biological roles, by compartmentalizing the cell to enable spatiotemporal control of biological reactions. Recent studies suggest that membrane-less intracellular compartments are multicomponent viscous liquid droplets that form via phase separation. Proteins that have an intrinsic tendency for being conformationally heterogeneous seem to be the main drivers of liquid–liquid phase separation in the cell. These findings highlight the relevance of classical concepts from the physics of polymeric phase transitions for understanding the assembly of intracellular membrane-less compartments. However, applying these concepts is challenging, given the heteropolymeric nature of protein sequences, the complex intracellular environment, and non-equilibrium features intrinsic to cells. This provides new opportunities for adapting established theories and for the emergence of new physics. The internal structure of cells is organized into compartments, many of which lack a confining membrane and instead resemble viscous liquid droplets. Evidence is mounting that these compartments form via spontaneous phase transitions. The internal structure of cells is organized into compartments, many of which lack a confining membrane and instead resemble viscous liquid droplets. Evidence is mounting that these compartments form via spontaneous phase transitions.

Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or ‘multiplexity’) between their components. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure. Reshaping network theory to describe the multilayered structures of the real world has formed a focus in complex networks research in recent years. Progress in our understanding of dynamical processes is but one of the fruits of this labour.

Marine macroalgae are dominant primary producers in coastal zones. A review of the published literature suggests that macroalgae may play an important role in carbon sequestration. Vegetated coastal habitats have been identified as important carbon sinks. In contrast to angiosperm-based habitats such as seagrass meadows, salt marshes and mangroves, marine macroalgae have largely been excluded from discussions of marine carbon sinks. Macroalgae are the dominant primary producers in the coastal zone, but they typically do not grow in habitats that are considered to accumulate large stocks of organic carbon. However, the presence of macroalgal carbon in the deep sea and sediments, where it is effectively sequestered from the atmosphere, has been reported. A synthesis of these data suggests that macroalgae could represent an important source of the carbon sequestered in marine sediments and the deep ocean. We propose two main modes for the transport of macroalgae to the deep ocean and sediments: macroalgal material drifting through submarine canyons, and the sinking of negatively buoyant macroalgal detritus. A rough estimate suggests that macroalgae could sequester about 173 TgC yr −1 (with a range of 61–268 TgC yr −1 ) globally. About 90% of this sequestration occurs through export to the deep sea, and the rest through burial in coastal sediments. This estimate exceeds that for carbon sequestered in angiosperm-based coastal habitats.

Equilibrium thermodynamics is characterized by two fundamental ideas: thermalization—that systems approach a late time thermal state; and phase structure—that thermal states exhibit singular changes as various parameters characterizing the system are changed. We summarize recent progress that has established generalizations of these ideas to periodically driven, or Floquet, closed quantum systems. This has resulted in the discovery of entirely new phases which exist only out of equilibrium, such as the π-spin glass/Floquet time crystal. Over the past decade, remarkable progress has occurred in the physics of closed quantum systems away from equilibrium, culminating in the recent experimental realization of so-called time crystals. This Progress Article surveys these developments.

Much like ordinary matter, dark matter might consist of elementary particles, and weakly interacting massive particles are one of the prime suspects. During the past decade, the sensitivity of experiments trying to directly detect them has improved by three to four orders of magnitude, but solid evidence for their existence is yet to come. We overview the recent progress in direct dark matter detection experiments and discuss future directions. Direct dark matter searches are pushing the limits on the scattering of weakly interacting massive particles on normal matter so WIMPs are running out of places to hide.

Compared to atoms, molecules possess additional degrees of freedom that can be exploited in fundamental tests, ultracold chemistry, and engineering new quantum phases in many-body systems. Here, we review the recent progress in creating and manipulating ultracold bialkali molecules to study quantum gases of polar molecules. Recent progress in engineering quantum gases of polar molecules brings closer their application in fundamental tests, ultracold chemistry and the study of new quantum phases of matter.

Research in quantum information processing has followed two different directions: the use of discrete variables (qubits) and that of high-dimensional, continuous-variable Gaussian states (coherent and squeezed states). Recently, these two approaches have been converging in potentially more powerful hybrid protocols. The traditional approaches to quantum information processing using either discrete or continuous variables can be combined in hybrid protocols for tasks including quantum teleportation, computation, entanglement distillation or Bell tests.

The amount of carbon stored in peats exceeds that stored in vegetation. A synthesis of the literature suggests that smouldering fires in peatlands could become more common as the climate warms, and release old carbon to the air. Globally, the amount of carbon stored in peats exceeds that stored in vegetation and is similar in size to the current atmospheric carbon pool. Fire is a threat to many peat-rich biomes and has the potential to disturb these carbon stocks. Peat fires are dominated by smouldering combustion, which is ignited more readily than flaming combustion and can persist in wet conditions. In undisturbed peatlands, most of the peat carbon stock typically is protected from smouldering, and resistance to fire has led to a build-up of peat carbon storage in boreal and tropical regions over long timescales. But drying as a result of climate change and human activity lowers the water table in peatlands and increases the frequency and extent of peat fires. The combustion of deep peat affects older soil carbon that has not been part of the active carbon cycle for centuries to millennia, and thus will dictate the importance of peat fire emissions to the carbon cycle and feedbacks to the climate.

The mechanical behaviour of cells is largely controlled by a structure that is fundamentally out of thermodynamic equilibrium: a network of crosslinked filaments subjected to the action of energy-transducing molecular motors. The study of this kind of active system was absent from conventional physics and there was a need for both new theories and new experiments. The field that has emerged in recent years to fill this gap is underpinned by a theory that takes into account the transduction of chemical energy on the molecular scale. This formalism has advanced our understanding of living systems, but it has also had an impact on research in physics per se . Here, we describe this developing field, its relevance to biology, the novelty it conveys to other areas of physics and some of the challenges in store for the future of active gel physics. Equilibrium physics is ill-equipped to explain all of life’s subtleties, largely because living systems are out of equilibrium. Attempts to overcome this problem have given rise to a lively field of research—and some surprising biological findings.