Nonequilibrium Criticality at the Onset of Time-Crystalline Order.

We explore the phase transitions at the onset of time-crystalline order in O(N) models driven out of equilibrium. The spontaneous breaking of time translation symmetry and its Goldstone mode are captured by an effective description with O(N)×SO(2) symmetry, where the emergent external SO(2) results from a transmutation of the internal symmetry of time translations. Using the renormalization group and the ε=4-d expansion in a leading two-loop analysis, we identify a new nonequilibrium universality class. Strikingly, it controls the long-distance physics no matter how small the microscopic breaking of equilibrium conditions is. The O(N=2)×SO(2) symmetry group is realized for magnon condensation in pumped yttrium iron garnet films and in exciton-polariton systems with a polarization degree of freedom.

Impact of climate warming on phenological asynchrony of plankton dynamics across Europe.

Climate warming alters the seasonal timing of biological events. This raises concerns that species-specific responses to warming may de-synchronize co-evolved consumer-resource phenologies, resulting in trophic mismatch and altered ecosystem dynamics. We explored the effects of warming on the synchrony of two events: the onset of the phytoplankton spring bloom and the spring/summer maximum of the grazer Daphnia. Simulation of 16 lake types over 31 years at 1907 North African and European locations under 5 climate scenarios revealed that the current median phenological delay between the two events varies greatly (20-190 days) across lake types and geographic locations. Warming moves both events forward in time and can lengthen or shorten the delay between them by up to ±60 days. Our simulations suggest large geographic and lake-specific variations in phenological synchrony, provide quantitative predictions of its dependence on physical lake properties and geographic location and highlight research needs concerning its ecological consequences.

Emergent Kardar-Parisi-Zhang Phase in Quadratically Driven Condensates.

In bosonic gases at thermal equilibrium, an external quadratic drive can induce a Bose-Einstein condensation described by the Ising transition, as a consequence of the explicitly broken U(1) phase rotation symmetry down to Z_{2}. However, in physical realizations such as exciton polaritons and nonlinear photonic lattices, thermal equilibrium is lost and the state is rather determined by a balance between losses and external drive. A fundamental question is then how nonequilibrium fluctuations affect this transition. Here, we show that in a two-dimensional driven-dissipative Bose system the Ising phase is suppressed and replaced by a nonequilibrium phase featuring Kardar-Parisi-Zhang (KPZ) physics. Its emergence is rooted in a U(1)-symmetry restoration mechanism enabled by the strong fluctuations in reduced dimensionality. Moreover, we show that the presence of the quadratic drive term enhances the visibility of the KPZ scaling, compared to two-dimensional U(1)-symmetric gases, where it has remained so far elusive.

Stoichiometric mismatch causes a warming-induced regime shift in experimental plankton communities.

In many ecosystems, consumers respond to warming differently than their resources, sometimes leading to temporal mismatches between seasonal maxima in consumer demand and resource availability. A potentially equally pervasive, but less acknowledged threat to the temporal coherence of consumer-resource interactions is mismatch in food quality. Many plant and algal communities respond to warming with shifts toward more carbon-rich species and growth forms, thereby diluting essential elements in their biomass and intensifying the stoichiometric mismatch with herbivore nutrient requirements. Here we report on a mesocosm experiment on the spring succession of an assembled plankton community in which we manipulated temperature (ambient vs. +3.6°C) and presence versus absence of two types of grazers (ciliates and Daphnia), and where warming caused a dramatic regime shift that coincided with extreme stoichiometric mismatch. At ambient temperatures, a typical spring succession developed, where a moderate bloom of nutritionally adequate phytoplankton was grazed down to a clear-water phase by a developing Daphnia population. While warming accelerated initial Daphnia population growth, it speeded up algal growth rates even more, triggering a massive phytoplankton bloom of poor food quality. Consistent with the predictions of a stoichiometric producer-grazer model, accelerated phytoplankton growth promoted the emergence of an alternative system attractor, where the extremely low phosphorus content of the abundant algal food eventually drove Daphnia to extinction. Where present, ciliates slowed down the phytoplankton bloom and the deterioration of its nutritional value, but this only delayed the regime shift. Eventually, phytoplankton also grew out of grazer control in the presence of ciliates, and the Daphnia population crashed. To our knowledge, the experiment is the first empirical demonstration of the "paradox of energy enrichment" (grazer starvation in an abundance of energy-rich but nutritionally imbalanced food) in a multispecies phytoplankton community. More generally, our results support the notion that warming can exacerbate the stoichiometric mismatch at the plant-herbivore interface and limit energy transfer to higher trophic levels.

Cavity-induced quantum spin liquids.

Quantum spin liquids provide paradigmatic examples of highly entangled quantum states of matter. Frustration is the key mechanism to favor spin liquids over more conventional magnetically ordered states. Here we propose to engineer frustration by exploiting the coupling of quantum magnets to the quantized light of an optical cavity. The interplay between the quantum fluctuations of the electro-magnetic field and the strongly correlated electrons results in a tunable long-range interaction between localized spins. This cavity-induced frustration robustly stabilizes spin liquid states, which occupy an extensive region in the phase diagram spanned by the range and strength of the tailored interaction. This occurs even in originally unfrustrated systems, as we showcase for the Heisenberg model on the square lattice.

Local and continental-scale controls of the onset of spring phytoplankton blooms: Conclusions from a proxy-based model.

A key phenological event in the annual cycle of many pelagic ecosystems is the onset of the spring algal bloom (OAB). Descriptions of the factors controlling the OAB in temperate to polar lakes have been limited to isolated studies of single systems and conceptual models. Here we present a validated modelling approach that, for the first time, enables a quantitative prediction of the OAB and a systematic assessment of the processes controlling its timing on a continental scale. We used a weather-driven, one-dimensional lake model to simulate the seasonal dynamics of the underwater light climate in 16 lake types characterized by the factorial combination of four lake depths with four levels of water transparency. We did so at 1962 locations across Western Europe and over 31 years (1979-2009). Assuming that phytoplankton production is light-limited in winter, we identified four patterns of OAB control across lake types and climate zones. OAB timing is controlled by (i) the timing of ice-off in ice-covered clear or shallow lakes, (ii) the onset of thermal stratification in sufficiently deep and turbid lakes and (iii) the seasonal increase in incident radiation in all other lakes, except for (iv) ice-free, shallow and clear lakes in the south, where phytoplankton is not light-limited. The model predicts that OAB timing should respond to two pervasive environmental changes, global warming and browning, in opposite ways. OAB timing should be highly sensitive to warming in lakes where it is controlled by either ice-off or the onset of stratification, but resilient to warming in lakes where it is controlled by incident radiation. Conversely, OAB timing should be most sensitive to browning where it is controlled by incident radiation, but resilient to browning where it is controlled by ice-off or the onset of stratification. Available lake data are consistent with our findings.

Evolution of resource specialisation in competitive metacommunities.

Spatial environmental heterogeneity coupled with dispersal can promote ecological persistence of diverse metacommunities. Does this premise hold when metacommunities evolve? Using a two-resource competition model, we studied the evolution of resource-uptake specialisation as a function of resource type (substitutable to essential) and shape of the trade-off between resource uptake affinities (generalist- to specialist-favouring). In spatially homogeneous environments, evolutionarily stable coexistence of consumers is only possible for sufficiently substitutable resources and specialist-favouring trade-offs. Remarkably, these same conditions yield comparatively low diversity in heterogeneous environments, because they promote sympatric evolution of two opposite resource specialists that, together, monopolise the two resources everywhere. Consumer diversity is instead maximised for intermediate trade-offs and clearly substitutable or clearly essential resources, where evolved metacommunities are characterised by contrasting selection regimes. Taken together, our results present new insights into resource-competition-mediated evolutionarily stable diversity in homogeneous and heterogeneous environments, which should be applicable to a wide range of systems.

Absence of Criticality in the Phase Transitions of Open Floquet Systems.

We address the nature of phase transitions in periodically driven systems coupled to a bath. The latter enables a synchronized nonequilibrium Floquet steady state at finite entropy, which we analyze for rapid drives within a nonequilibrium renormalization group (RG) approach. While the infinitely rapidly driven limit exhibits a second-order phase transition, here we reveal that fluctuations turn the transition first order when the driving frequency is finite. This can be traced back to a universal mechanism, which crucially hinges on the competition of degenerate, near critical modes associated with higher Floquet Brillouin zones. The critical exponents of the infinitely rapidly driven system-including a new, independent one-can yet be probed experimentally upon smoothly tuning towards that limit.

Fluctuation-Induced Quantum Zeno Effect.

An isolated quantum gas with a localized loss features a nonmonotonic behavior of the particle loss rate as an incarnation of the quantum Zeno effect, as recently shown in experiments with cold atomic gases. While this effect can be understood in terms of local, microscopic physics, we show that novel many-body effects emerge when nonlinear gapless quantum fluctuations become important. To this end, we investigate the effect of a local dissipative impurity on a one-dimensional gas of interacting fermions. We show that the escape probability for modes close to the Fermi energy vanishes for an arbitrary strength of the dissipation. In addition, transport properties across the impurity are qualitatively modified, similarly to the Kane-Fisher barrier problem. We substantiate these findings using both a microscopic model of spinless fermions and a Luttinger liquid description.

Bottom-up and top-down effects of browning and warming on shallow lake food webs.

Productivity and trophic structure of aquatic ecosystems result from a complex interplay of bottom-up and top-down forces that operate across benthic and pelagic food web compartments. Projected global changes urge the question how this interplay will be affected by browning (increasing input of terrestrial dissolved organic matter), nutrient enrichment and warming. We explored this with a process-based model of a shallow lake food web consisting of benthic and pelagic components (abiotic resources, primary producers, grazers, carnivores), and compared model expectations with the results of a browning and warming experiment in nutrient-poor ponds harboring a boreal lake community. Under low nutrient conditions, the model makes three major predictions. (a) Browning reduces light and increases nutrient supply; this decreases benthic and increases pelagic production, gradually shifting productivity from the benthic to the pelagic habitat. (b) Because of active habitat choice, fish exert top-down control on grazers and benefit primary producers primarily in the more productive of the two habitats. (c) Warming relaxes top-down control of grazers by fish and decreases primary producer biomass, but effects of warming are generally small compared to effects of browning and nutrient supply. Experimental results were consistent with most model predictions for browning: light penetration, benthic algal production, and zoobenthos biomass decreased, and pelagic nutrients and pelagic algal production increased with browning. Also consistent with expectations, warming had negative effects on benthic and pelagic algal biomass and weak effects on algal production and zoobenthos and zooplankton biomass. Inconsistent with expectations, browning had no effect on zooplankton and warming effects on fish depended on browning. The model is applicable also to nutrient-rich systems, and we propose that it is a useful tool for the exploration of the consequences of different climate change scenarios for productivity and food web dynamics in shallow lakes, the worldwide most common lake type.

Vanishing Density of States in Weakly Disordered Weyl Semimetals.

The Brillouin zone of the clean Weyl semimetal contains points at which the density of states (DOS) vanishes. Previous work suggested that below a certain critical concentration of impurities this feature is preserved including in the presence of disorder. This result got criticized for its neglect of rare disorder fluctuations which might bind quantum states and hence generate a finite DOS. We here show that in spite of their existence these states are so fragile that their contribution effectively vanishes when averaged over continuous disorder distributions. This means that the integrity of the nodal points remains protected for weak disorder.

Dynamical Crossovers in Prethermal Critical States.

We study the prethermal dynamics of an interacting quantum field theory with an N-component order parameter and O(N) symmetry, suddenly quenched in the vicinity of a dynamical critical point. Depending on the initial conditions, the evolution of the order parameter, and of the response and correlation functions, can exhibit a temporal crossover between universal dynamical scaling regimes governed, respectively, by a quantum and a classical prethermal fixed point, as well as a crossover from a Gaussian to a non-Gaussian prethermal dynamical scaling. Together with a recent experiment, this suggests that quenches may be used in order to explore the rich variety of dynamical critical points occurring in the nonequilibrium dynamics of a quantum many-body system. We illustrate this fact by using a combination of renormalization group techniques and a nonperturbative large-N limit.

Effects of warming on predator-prey interactions - a resource-based approach and a theoretical synthesis.

We theoretically explore consequences of warming for predator-prey dynamics, broadening previous approaches in three ways: we include beyond-optimal temperatures, predators may have a type III functional response, and prey carrying capacity depends on explicitly modelled resources. Several robust patterns arise. The relationship between prey carrying capacity and temperature can range from near-independence to monotonically declining/increasing to hump-shaped. Predators persist in a U-shaped region in resource supply (=enrichment)-temperature space. Type II responses yield stable persistence in a U-shaped band inside this region, giving way to limit cycles with enrichment at all temperatures. In contrast, type III responses convey stability at intermediate temperatures and confine cycles to low and high temperatures. Warming-induced state shifts can be predicted from system trajectories crossing stability and persistence boundaries in enrichment-temperature space. Results of earlier studies with more restricted assumptions map onto this graph as special cases. Our approach thus provides a unifying framework for understanding warming effects on trophic dynamics.

Determining Selection across Heterogeneous Landscapes: A Perturbation-Based Method and Its Application to Modeling Evolution in Space.

Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.

Space-Time Vortex Driven Crossover and Vortex Turbulence Phase Transition in One-Dimensional Driven Open Condensates.

We find a first-order transition driven by the strength of nonequilibrium conditions of one-dimensional driven open condensates. Associated with this transition is a new stable nonequilibrium phase, space-time vortex turbulence, whose vortex density and quasiparticle distribution show strongly nonthermal behavior. Below the transition, we identify a new time scale associated with noise-activated unbound space-time vortices, beyond which, the temporal coherence function changes from a Kardar-Parisi-Zhang-type subexponential to a disordered exponential decay. Experimental realization of the nonequilibrium vortex turbulent phase is facilitated in driven open condensates with a large diffusion rate.

Asymmetrical competition between aquatic primary producers in a warmer and browner world.

In shallow lakes, pelagic and benthic producers engage in spatially asymmetrical resource competition. Pelagic producers intercept the flux of light to the benthic habitat and benthic producers intercept the flux of sediment-derived nutrients to the pelagic habitat. In boreal and subarctic regions, climate change is affecting this interaction both directly through warming and indirectly through increased loading with colored dissolved organic matter (cDOM) from the catchment ("brownification"). We use a dynamical ecosystem model to explore the consequences of these changing environmental conditions for lake primary production and compare model predictions with the results of an experiment in which we manipulated water temperature and cDOM supply in a 2 × 2 factorial design. The experiment was performed in field mesocosms large enough to harbor reproducing fish populations and was run over an entire growing season. In agreement with model predictions, benthic algal production and biomass declined and pelagic algal production and biomass increased with browning. Pelagic nutrient concentrations diverged over time between low and high cDOM treatments, suggesting that browning alleviated pelagic algal nutrient limitation by shading benthic competitors and preventing them from intercepting the release of nutrients from the sediment. Warming considerably reduced benthic and pelagic algal production as well as pelagic algal biomass and total phosphorus. The warming results are only in partial accordance with model expectations, but can be explained by an indirectly inferred, positive response of macrophyte production (which was not included in the model) to warming. Our study suggests that lake ecosystem responses to climate change are mediated by cross-habitat feedbacks between benthic and pelagic producers.

Background field functional renormalization group for absorbing state phase transitions.

We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions.

Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations.

Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.

Driven Markovian Quantum Criticality.

We identify a new universality class in one-dimensional driven open quantum systems with a dark state. Salient features are the persistence of both the microscopic nonequilibrium conditions as well as the quantum coherence of dynamics close to criticality. This provides a nonequilibrium analogue of quantum criticality, and is sharply distinct from more generic driven systems, where both effective thermalization as well as asymptotic decoherence ensue, paralleling classical dynamical criticality. We quantify universality by computing the full set of independent critical exponents within a functional renormalization group approach.