Topographic Control of Order in Quasi-2D Granular Phase Transitions.

We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting granular liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-solid one. The interplay of boundary inelasticity and geometry, either order promoting or inhibiting, controls whether it is the granular crystal or the granular fluid which makes contact with the edge. This order induced wetting has important consequences, determining how coexisting phases separate spatially.

Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems.

We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all to all to short ranged, and the scaling with system size of the lifetime of the time crystal.

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.

Phase Transitions in Electron Spin Resonance Under Continuous Microwave Driving.

We study an ensemble of strongly coupled electrons under continuous microwave irradiation interacting with a dissipative environment, a problem of relevance to the creation of highly polarized nonequilibrium states in nuclear magnetic resonance. We analyze the stationary states of the dynamics, described within a Lindblad master equation framework, at the mean-field approximation level. This approach allows us to identify steady-state phase transitions between phases of high and low polarization controlled by the distribution of disordered electronic interactions. We compare the mean-field predictions to numerically exact simulations of small systems and find good agreement. Our study highlights the possibility of observing collective phenomena, such as metastable states, phase transitions, and critical behavior, in appropriately designed paramagnetic systems. These phenomena occur in a low-temperature regime which is not theoretically tractable by conventional methods, e.g., the spin-temperature approach.

Emergent kinetic constraints, ergodicity breaking, and cooperative dynamics in noisy quantum systems.

Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

Thermalization of a strongly interacting closed spin system: from coherent many-body dynamics to a Fokker-Planck equation.

Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model-in one and two dimensions-for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the nonequilibrium relaxation to it.

Relationship between vibrations and dynamical heterogeneity in a model glass former: extended soft modes but local relaxation.

We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of the low- (high-) frequency vibrational modes and regions of high (low) propensity for motion. This is similar to what was observed in continuous force systems, but our interpretation is different: in our case relaxation is due to localised excitations which propagate through the system; these localised excitations act as background disorder for the elastic network, giving rise to anomalous vibrational modes. Our results provide an example whereby a correlation between spatially extended low-frequency modes and high-propensity regions does not imply that relaxational dynamics originates in extended soft modes but rather belies their common origin. We consider other measures of elastic heterogeneity, such as non-affine displacement fields and mode localisation lengths, and discuss implications of our results to interpretations of dynamic heterogeneity more generally.

Harmful mating tactics in hermaphrodites.

While empirical data suggest that sperm competition and multiple mating both contribute to the evolution of harmful mating tactics in hermaphrodites, a precise understanding of their interaction is lacking. We therefore formulate a game-theoretical model of mating behavior in hermaphrodites, where harmful mating tactics confer an advantage in sperm competition while simultaneously reducing the mating partner's survival. The model predicts evolutionarily stable values of resource allocation between sexual functions and the degree of harmful mating. Our analysis provides support for the empirical observation that harmful mating is associated with multiply mating species in which sperm precedence strongly favors the first mate. The model also shows that this criterion becomes less important as harmful mating tactics become more efficient. As harmful tactics make sperm displacement more effective, a consequence is a more female-biased resource allocation. Provided that fertilized egg production is not limited by availability of sperm, a more female-biased allocation should increase the number of offspring produced, but the model instead shows that harmful mating tactics more than countercompensate, leading to reduced fitness. Hermaphrodites that use harmful mating tactics may therefore be at a disadvantage when competing with other species for a limited resource.

Dynamical first-order phase transition in kinetically constrained models of glasses.

We show that the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. We prove this by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. We present analytic results for dynamic facilitated models in a mean-field approximation, and numerical results for the Fredrickson-Andersen model, the East model, and constrained lattice gases, in various dimensions. This dynamical first-order transition is generic in kinetically constrained models, and we expect it to be present in systems with fully jammed states.

Heterogeneous dynamics of coarsening systems.

We show by means of experiments, theory, and simulations that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multipoint functions which quantify the emergence of dynamic, as opposed to static, correlations of fluctuations. Experiments are performed on a coarsening foam using time-resolved correlation, a recently introduced light scattering method. Theoretically we study the Ising model, and present exact results in one dimension, and numerical results in two dimensions. For all systems the same dynamic scaling of fluctuations with domain size is observed.

Crossover from fragile to strong glassy behavior in kinetically constrained systems.

We show the existence of fragile-to-strong transitions in kinetically constrained systems by studying the equilibrium and out-of-equilibrium dynamics of a generic constrained Ising spin chain that interpolates between the symmetric and fully asymmetric cases. We find that for large but finite asymmetry the model displays a crossover from fragile to strong glassy behavior at finite temperature, which is controlled by the asymmetry parameter. The relaxation in the fragile region presents stretched exponential behavior, with a temperature dependent stretching exponent that is predicted. Our results are confirmed by numerical simulations.