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Supersolid states simultaneously feature properties typically associated with a solid and with a superfluid. Like a solid, they possess crystalline order, manifesting as a periodic modulation of the particle density; but unlike a typical solid, they also have superfluid properties, resulting from coherent particle delocalization across the system. Such states were initially envisioned in the context of bulk solid helium, as a possible answer to the question of whether a solid could have superfluid properties 1 – 5 . Although supersolidity has not been observed in solid helium (despite much effort) 6 , ultracold atomic gases provide an alternative approach, recently enabling the observation and study of supersolids with dipolar atoms 7 – 16 . However, unlike the proposed phenomena in helium, these gaseous systems have so far only shown supersolidity along a single direction. Here we demonstrate the extension of supersolid properties into two dimensions by preparing a supersolid quantum gas of dysprosium atoms on both sides of a structural phase transition similar to those occurring in ionic chains 17 – 20 , quantum wires 21 , 22 and theoretically in chains of individual dipolar particles 23 , 24 . This opens the possibility of studying rich excitation properties 25 – 28 , including vortex formation 29 – 31 , and ground-state phases with varied geometrical structure 7 , 32 in a highly flexible and controllable system. Two-dimensional supersolidity is demonstrated using highly magnetic, ultracold dysprosium atoms.

The purpose of the study was to access the particle production. Tracklets was adopted to measure the relationship between centrality ranged from outermost (70–80%) to central (0–5%) collisions and the primary charged-particle density d N c h d η at S N N = 2. 76 TeV. It reveals that the dependence of centrality and that measured at lower collision energies ( S N N < 2.76 TeV) are similar.

Active-matter systems operate far from equilibrium because of the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: It vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces, with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wave-vector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.

We unravel the nonequilibrium correlated quantum quench dynamics of an impurity traveling through a harmonically confined Bose-Einstein condensate in one-dimension. For weak repulsive interspecies interactions the impurity oscillates within the bosonic gas. At strong repulsions and depending on its prequench position the impurity moves towards an edge of the bosonic medium and subsequently equilibrates. This equilibration being present independently of the initial velocity, the position and the mass of the impurity is inherently related to the generation of entanglement in the many-body system. Focusing on attractive interactions the impurity performs a damped oscillatory motion within the bosonic bath, a behavior that becomes more evident for stronger attractions. To elucidate our understanding of the dynamics an effective potential picture is constructed. The effective mass of the emergent quasiparticle is measured and found to be generically larger than the bare one, especially for strong attractions. In all cases, a transfer of energy from the impurity to the bosonic medium takes place. Finally, by averaging over a sample of simulated in situ single-shot images we expose how the single-particle density distributions and the two-body interspecies correlations can be probed.

Two- or three-dimensional metals are usually well described by weakly interacting, fermionic quasiparticles. This concept breaks down in one dimension due to strong Coulomb interactions. There, low-energy electronic excitations are expected to be bosonic collective modes, which fractionalize into independent spin- and charge-density waves. Experimental research on one-dimensional metals is still hampered by their difficult realization, their limited accessibility to measurements, and by competing or obscuring effects such as Peierls distortions or zero bias anomalies. Here we overcome these difficulties by constructing a well-isolated, one-dimensional metal of finite length present inMoS2mirror-twin boundaries. Using scanning tunneling spectroscopy we measure the single-particle density of the interacting electron system as a function of energy and position in the 1D box. Comparison to theoretical modeling provides unambiguous evidence that we are observing spin-charge separation in real space.

To significantly increase the amount of exsolved particles, the complete phase reconstruction from simple perovskite to Ruddlesden-Popper (R-P) perovskite is greatly desirable. However, a comprehensive understanding of key parameters affecting the phase reconstruction to R-P perovskite is still unexplored. Herein, we propose the Gibbs free energy for oxygen vacancy formation in Pr 0.5 (Ba/Sr) 0.5 TO 3- δ (T = Mn, Fe, Co, and Ni) as the important factor in determining the type of phase reconstruction. Furthermore, using in-situ temperature & environment-controlled X-ray diffraction measurements, we report the phase diagram and optimum ‘ x ’ range required for the complete phase reconstruction to R-P perovskite in Pr 0.5 Ba 0.5- x Sr x FeO 3- δ system. Among the Pr 0.5 Ba 0.5- x Sr x FeO 3- δ , (Pr 0.5 Ba 0.2 Sr 0.3 ) 2 FeO 4+ δ – Fe metal demonstrates the smallest size of exsolved Fe metal particles when the phase reconstruction occurs under reducing condition. The exsolved nano-Fe metal particles exhibit high particle density and are well-distributed on the perovskite surface, showing great catalytic activity in fuel cell and syngas production. The complete phase reconstruction to Ruddlesden-Popper perovskite is greatly desirable to increase the exsolved particle distribution. Here, the authors report a key factor for the complete phase reconstruction in perovskites, leading to good catalytic activity in fuel cell and syngas production.

Diffusion relaxes density fluctuations toward a uniform random state whose variance in regions of volume v = ℓd scales as σ ρ 2 ≡ 〈 ρ 2 ( l ) 〉 − 〈 ρ 〉 2 ∼ l − d . Systems whose fluctuations decay faster, σ ρ 2 ∼ l − λ with d < λ ≤ d + 1, are called hyperuniform. The larger λ, the more uniform, with systems like crystals achieving the maximum value: λ = d + 1. Although finite temperature equilibrium dynamics will not yield hyperuniform states, driven, nonequilibrium dynamics may. Such is the case, for example, in a simple model where overlapping particles are each given a small random displacement. Above a critical particle density ρc , the system evolves forever, never finding a configuration where no particles overlap. Below ρc , however, it eventually finds such a state, and stops evolving. This “absorbing state” is hyperuniform up to a length scale ε, which diverges at ρc . An important question is whether hyperuniformity survives noise and thermal fluctuations. We find that hyperuniformity of the absorbing state is not only robust against noise, diffusion, or activity, but that such perturbations reduce fluctuations toward their limiting behavior, λ → d + 1, a uniformity similar to random close packing and early universe fluctuations, but with arbitrary controllable density.

In the high-temperature environments needed to perform catalytic processes, supported precious metal catalysts lose their activity severely over time. Generally, loss of catalytic activity is attributed to nanoparticle sintering or processes by which larger particles grow at the expense of smaller ones. Here, by independently controlling particle size and particle loading using colloidal nanocrystals, we reveal the opposite process as an alternative deactivation mechanism: nanoparticles rapidly lose activity for methane oxidation by high-temperature decomposition into inactive single atoms. This deactivation route is remarkably fast, leading to severe loss of activity in as little as 10 min. Importantly, this deactivation pathway is strongly dependent on particle density and the concentration of support defect sites. A quantitative statistical model explains how, for certain reactions, higher particle densities can lead to more stable catalysts. Traditional modes of catalyst deactivation such as Ostwald ripening and particle migration and coalescence eventually lead to sintering and particle growth. Now, Cargnello and colleagues identify loading-dependent particle decomposition into single atoms as an important deactivation mechanism during methane combustion on colloidal Pd nanocrystals.

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS 2 /WSe 2 heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by observing a suppression of exciton diffusion with increasing pump intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model. Strongly interacting interlayer excitons and the interplay between excitons and electronic states have recently been studied in moire superlattices. Here the authors study moire WS 2 /WSe 2 heterobilayer with tuneable electron and exciton populations and find signatures of an excitonic Mott insulating state.

Fokker–Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker–Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker–Planck equations in low and moderate dimensions. The proposed gradient–log–density estimator is also of independent interest, for example, in the context of optimal control.