The duration of incoherent XUV pulses down to the femtoseconds (fs) can be retrieved through a statistical analysis of the modulations on the observed radiation spectrum. Uncorrelated shot-noise fluctuations in the pulse temporal profile result in incoherent radiation showing a multispike spectrum where the spike width is inversely proportional to the pulse length. In this Letter, single-shot temporal characterization of the betatron radiation pulses emitted by fs-long, 100's MeV electron bunches undergoing acceleration, and propagating through a plasma wiggler was performed in the XUV domain. The retrieved pulse lengths agree with independent measurements performed in the THz spectral range and with theoretical predictions.

Several dynamical processes can be modeled as Markov jump processes among a finite number $N$ of sites (the distinct physical states). Here we consider strongly connected networks with time-independent site-to-site jump rate constants, and focus on the steady-state occupation probabilities of the sites. We provide a physically framed expression of the steady-state distribution in terms of arrival probabilities, here defined as the probabilities of going from starting sites to target sites with a given number of jumps (regardless of the time required). In particular, the full set of return probabilities (for all the sites of the network) up to $N-1$ jumps is necessary and sufficient. A few examples illustrate the outcomes, including the case of stochastic chemical kinetics.

The marginal correlation between two variables is a measure of the linear dependence of one variable on the other. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The underlying network of direct interactions can be captured by a weighted graphical model. The connection between two variables can be weighted by their partial correlation, defined as the residual correlation left after accounting for the linear effects of mediating variables. While matrix inversion can be used to obtain marginal correlations from partial correlations, in large systems this approach does not reveal how the former emerge from the latter. Here we present an expansion of marginal correlations in terms of partial correlations, which shows that the effect of mediating variables can be quantified by the weight of the paths in the graphical model that connect the original pair of variables. The expansion is proved to converge for arbitrary probability distributions. The graphical interpretation reveals a close connection between the topology of the graph and the marginal correlations. Moreover, the expansion shows how marginal correlations change when some variables are severed from the graph, and how partial correlations change when some variables are marginalized out from the description. It also establishes the minimum number of latent variables required to replicate the exact effect of a collection of variables that are marginalized out, ensuring that the partial and marginal correlations of the remaining variables remain unchanged. Notably, the number of latent variables may be significantly smaller than the number of variables that they effectively replicate. Finally, for Gaussian variables, marginal correlations are shown to be related to the efficacy with which information propagates along the paths in the graph.

Significant attention has been devoted to the problem of thermalization of observables in isolated quantum setups by individual eigenstates. Here, we address this issue from an open quantum system perspective, examining an isolated setup where a small system (specifically, a single fermionic level) is coupled to a macroscopic fermionic bath. We argue that in such a model, despite its full integrability, the system observables exhibit thermalization when the system-bath setup resides in a typical eigenstate of its Hamiltonian, a phenomenon known as weak eigenstate thermalization. This thermalization occurs unless it is suppressed by localization due to strong coupling. We further show that, following the quench of the system Hamiltonian, the system occupancy typically relaxes to the thermal value corresponding to the new Hamiltonian. Finally, we demonstrate that system thermalization also arises when the system is coupled to a bath that has been initialized in a typical eigenstate of its Hamiltonian. Our findings suggest that nonintegrability is not the sole driver of thermalization, highlighting the need for complementary approaches to fully understand the emergence of statistical mechanics.

Quantum mechanics provides various pictures for understanding physical phenomena, yet the full potential of these pictures' equivalence remains underutilized. This work introduces a novel picture, opposite to the interaction picture, achieved through a transformation of the time evolution operator. This new approach permits the manipulation of the relative weight of Hamiltonian components. Utilizing picture equivalence, we investigate dynamical quantum phase transitions and quantum thermodynamics. Our findings reveal a significant relationship between dynamical topological quantum phase transitions and accidental ones through time-reversal operations, offering new insights into their fundamental connections. Moreover, our picture-based transformation addresses the challenge of defining thermodynamic quantities in systems with strong system-reservoir coupling, maintaining the robustness of weak coupling analyses.

Analytically, finding the origins of cooperative behavior in infinite-player games is an exciting topic of current interest. In this paper, we compare three analytical methods, i.e., Nash equilibrium mapping (NEM), Darwinian selection (DS), and aggregate selection (AS), with a numerical agent-based method (ABM) via the game susceptibility, correlation, and payoff capacity as indicators of cooperative behavior. While the analytical NEM model shows excellent agreement with the numerical ABM, the other analytical models like AS and DS show notable divergence with ABM in the thermodynamic limit for the indicators in question. Previously, cooperative behavior was studied by considering game magnetization and individual players' average payoff as indicators. This paper shows that game susceptibility, correlation, and payoff capacity can aid in understanding cooperative behavior in social dilemmas in the thermodynamic limit. The results obtained via NEM and ABM are in good agreement for all three indicators in question, for both hawk-dove and the public goods games. After comparing the results obtained for all five indicators, we see that individual players' average payoff and payoff capacity serve as the best indicators to study cooperative behavior among players in the thermodynamic limit.

Recent cutting-edge experiments have provided in situ structure characterization and measurements of the pressure $\left(P\right)$, density $\left(\overline{\rho }\right)$, and temperature $\left(T\right)$ of shock compressed silicon in the 100 GPa range of pressures and up to $\sim 10000\mathrm{K}$. We present first-principles calculations in this $P,T,\overline{\rho }$ regime to reveal a plethora of novel liquid-liquid phase transitions (LPTs) identifiable via discontinuities in the pressure and the compressibility. Evidence for the presence of a highly-correlated liquid (CL) phase, as well as a normal-liquid (NL) phase at the LPTs is presented by a detailed study of one LPT. The LPTs make the interpretation of these experiments more challenging. The LPTs preserve the short-ranged ionic structure of the fluid by collective adjustments of many distant atoms when subject to compression and heating, with minimal change in the ion-ion pair-distribution functions, and in transport properties such as the electrical and thermal conductivities $\sigma$ and $\kappa$. We match the experimental x-ray Thomson scattering and x-ray diffraction data theoretically, and provide pressure isotherms, ionization data, and compressibilities that support the above picture of liquid silicon as a highly complex LPT-driven “glassy” metallic liquid. These novel results are relevant to materials research, studies of planetary interiors, high-energy-density physics, and in laser-fusion studies.

Sufficiently dense intrinsically out-of-equilibrium suspensions, such as those observed in biological systems, can be modeled as active fluids characterized by their orientational symmetry. While mesoscale numerical approaches to active nematic fluids have been developed, polar fluids are simulated as either ensembles of microscopic self-propelled particles or continuous hydrodynamic-scale equations of motion. To better simulate active polar fluids in complex geometries or as a solvent for suspensions, mesoscale numerical approaches are needed. In this work, the coarse-graining multiparticle collision dynamics (MPCD) framework is applied to three active particle models to produce mesoscale simulations of polar active fluids. The first active-polar MPCD (AP-MPCD) is a variant of the Vicsek model, while the second and third variants allow the speed of the particles to relax towards a self-propulsion speed subject to Andersen and Langevin thermostats, respectively. Each of these AP-MPCD variants exhibits a flocking transition at a critical activity and banding in the vicinity of the transition point. We leverage the mesoscale nature of AP-MPCD to explore flocking in the presence of external fields, which destroys banding, and anisotropic obstacles, which act as a ratchet that biases the flocking direction. These results demonstrate the capacity of AP-MPCD to capture the known phenomenology of polar active suspensions and its versatility to study active polar fluids in complex scenarios.

Contact electrification of identical materials happens during collisions, rubbing, and mixing of granular materials. Fractures often accompany these processes, and the resulting fracture surfaces are typically charged. Based on visible-light and X-ray observations of fracture, we demonstrate that the charge density on fracture surfaces of organic and inorganic materials is consistent with those observed in collisions, rubbing, and mixing. This indicates that fractures involve contact electrification of identical materials.

We consider the fractional Langevin equation far from equilibrium (FLEFE) to describe stochastic dynamics which do not obey the fluctuation-dissipation theorem, unlike the conventional fractional Langevin equation (FLE). The solution of this equation is Riemann-Liouville fractional Brownian motion (RL-FBM), also known in the literature as FBM II. Spurious nonergodicity, stationarity, and aging properties of the solution are explored for all admissible values $\alpha >1/2$ of the order $\alpha$ of the time-fractional Caputo derivative in the FLEFE. The increments of the process are asymptotically stationary. However when $1/2<\alpha <3/2$, the time-averaged mean-squared displacement (TAMSD) does not converge to the mean-squared displacement (MSD). Instead, it converges to the mean-squared increment (MSI) or structure function, leading to the phenomenon of spurious nonergodicity. When $\alpha \ge 3/2$, the increments of FLEFE motion are nonergodic, however the higher order increments are asymptotically ergodic. We also discuss the aging effect in the FLEFE by investigating the influence of an aging time $t_a$ on the MSD, TAMSD and autocovariance function of the increments. We find that under strong aging conditions the process becomes ergodic, and the increments become stationary in the domain $1/2<\alpha <3/2$.

Active systems exhibit fascinating self-organized structures and rich motility patterns, yet the underlying mechanisms governing their emergence and characteristics remain elusive. Here, we develop a chiral self-propelled rod (CSPR) model with mechanical contact-induced quorum sensing to investigate the spatiotemporal dynamics of dense bacteria populations. Our findings show that the CSPR model showcases spontaneous nonequilibrium oscillatory clustering of active systems. The motion characteristics of these clusters depend on colony features (microswimmers' morphology and density) and mechanical contact-induced sensing mechanisms (polarization alignment and angular velocity alignment of CSPR). Interestingly, reinforced strength of polar alignment accelerates the formation of stable oscillations, while decreased density and angular velocity alignment strength modify their emergence pattern. Significantly, our study identifies three distinct oscillation patterns: global stable oscillation, bistable oscillation, and multistable oscillation, and reveals that their phase transitions are driven by variations in the spatial correlation of CSPR. These insights provide a new perspective on understanding the intricate evolution of active matter, opening possible avenues for emerging applications.

We introduce a transfer-matrix-based sequential sampling scheme for generating random samples of ligand arrangements on one-dimensional templates. The number of ligand types is arbitrary, the binding constants can have positional dependence, and cooperativity parameters are included. From the random arrangements, any (linear or nonlinear) observable can be calculated using sample averaging. As an example case study, we investigate the competitive binding of three ligand types (the sequence-specific binder netropsin, YOYO-1, and ethidium bromide) to a DNA molecule. We also employ our random sampling method of ligands to determine the quality of synthetically generated DNA barcodes as a function of concentration of a ligand (e.g., netropsin) in optical DNA mapping (ODM) experiments. We provide publically available softwares, with a computational time that scales linearly with the lattice size, for generating random ligand arrangements and for generating synthetic barcodes.

By performing an ensemble of molecular dynamics simulations, the model-dependent ionization state is computed for strongly interacting systems self-consistently. This is accomplished through a free energy minimization framework based on the technique of thermodynamic integration. To illustrate the method, two simple models applicable to partially ionized hydrogen plasma are presented in which pair potentials are employed between ions and neutral particles. Within the models, electrons are either bound in the hydrogen ground state or distributed in a uniform charge-neutralizing background. Particular attention is given to the transition between atomic gas and ionized plasma, where the effect of neutral interactions is explored beyond commonly used models in the chemical picture. Furthermore, pressure ionization is observed when short-range repulsion effects are included between neutrals. The developed technique is general, and we discuss the applicability to a variety of molecular dynamics models for partially ionized warm dense matter.

In this study, instead of an approximate hard Gaussian overlap model, the effects of confinement on a system of oblate hard ellipsoid (OHE) particles interacting with planar substrates through the hard-disk-wall potential (HDW) were studied via computer simulation. In HDW, the thick oblate molecule with elongation $k=a/b<1$ is replaced by a thin disk with a diameter $D=D_s{\sigma }_0$, where ${\sigma }_0=2b$. We used NVT Monte Carlo simulations and showed that for small and large $D_s$, planar (edge-on arrangement) and homeotropic (face-on arrangement) anchoring are stable. The molecular volume absorbed by the substrates for each $D_s$ is calculated analytically and the critical values of the transition parameter $D_s^T$ were predicted from planar to homeotropic anchoring. Also, the transition parameters for two particles’ elongations, $k=0.2$ and $0.345$, are achieved via simulation. The results are approximately in agreement with the predicted values. Our results for the OHE particles with $k=0.345$ correspond to the hard Gaussian overlap results of Teixeira et al., qualitatively. We used an NPT Monte Carlo simulation to study the system in the region of $D_s\approx D_s^T$ and checked the influence of the packing fraction on the anchoring competition. The system in two cases, maximally penetrable and impenetrable substrates with $D_s=0$ and $D_s=1.0$, are investigated via NPT Monte Carlo simulations, and the isotropic-nematic transition packing fraction was compared. In addition, the orientational structure of $k=0.2$ and $0.345$ OHEs confined between thin symmetry walls was studied as a function of wall separation. In addition, for $k=0.2,D_s=0$, and $1.0$, the isotropic-nematic transition packing fraction of confined HGO particles and OHE particles were calculated and compared.

Particle shape has a profound impact on the flow behaviors of granular materials, yet effectively incorporating the role of particle shape into granular rheology remains challenging. In this study, we employ three representative types of nonconvex particles generated through the multisphere approach and identify a consistent one-to-one relationship between the rescaled friction coefficient and the inertial number $I$ across both inertial and quasistatic flow regimes. However, variations in particle shape cause notable deviations in rheological data compared to their spherical counterparts. Based on the observed dependence of rheological data on $I$ for various nonconvex particles and their convergence at high $I$, we propose an inertial number $I_s$ to effectively capture the impact of particle shape on flow states. The model parameters defining $I_s$ are shown to be nearly independent of flow states and configurations, with physical interpretations related to particle rotational characteristics during shear. For practical application, we propose an empirical formula to capture the dependence of model parameters on particle geometrical shapes. The robustness of the proposed model is validated by predicting flow in an inclined flow configuration and applying it to additional nonconvex particles with more irregular and asymmetric features. This establishes a crucial foundation for extending the application of this generalized rheological model to other complex granular flows.

The interaction between thin sheets and fluid droplets has recently attracted attention due to its frequent occurrence in natural systems and extensive use in technological applications. Motivated by these applications, this paper focuses on the interaction resulting from a drop that rests at the center of a circular superhydrophobic thin sheet. We investigate how the size and surface tension of the drop, together with the elastic and geometric parameters of the sheet, determine the overall deformation of the system. To this end, we formulate an analytical model based on energetic considerations that can predict the mutual interaction between the drop and the sheet. We show that the deformation of the sheet outside the contact region is almost unaffected by the exact shape of the drop, and thus mimics the problem of a rigid indentation. However, inside the contact region, there is a strong coupling between the drop's shape and the sheet's deformation. We derive analytical predictions for the size of the contact region and show that its shape comprises a constant curvature. These findings are in good quantitative agreement with the numerical minimization of the energy.

The impact of noise in coupled oscillators with pairwise interactions has been extensively explored. Here, we study stochastic second-order coupled Kuramoto oscillators with higher-order interactions and show that as noise strength increases, the critical points associated with synchronization transitions shift toward higher coupling values. By employing the perturbation analysis, we obtain an expression for the forward critical point as a function of inertia and noise strength. Further, for overdamped systems, we show that as noise strength increases, the first-order transition switches to second-order even for higher-order couplings. We include a discussion on the nature of critical points obtained through Ott-Antonsen ansatz.