We use a continuum, two-fluid approach to study a mixture of two active nematic fluids. Even in the absence of thermodynamically driven ordering, for mixtures of different activities we observe turbulent microphase separation, where domains form and disintegrate chaotically in an active turbulent background. This is a weak effect if there is no elastic nematic alignment between the two fluid components, but is greatly enhanced in the presence of an elastic alignment or substrate friction. We interpret the results in terms of relative flows between the two species which result from active anchoring at concentration gradients. Our results may have relevance in interpreting epithelial cell sorting and the dynamics of multispecies bacterial colonies.

By enabling the dissemination and storage of information, paper has been central to human culture for more than a millennium. Its use is, however, associated with a common injury: the paper cut. Surprisingly, the physics underpinning a flexible sheet of paper slicing into soft tissues remains unresolved. In particular, the unpredictable occurrence of paper cuts, often restricted to a limited thickness range, has not been explained. Here we visualize and quantify the motion, deformation, and stresses during paper cuts, uncovering a remarkably complex relationship between cutting, geometry, and material properties. A model based on the hypothesis that a competition between slicing and buckling controls the probability of initiating a paper cut is developed and successfully validated. This explains why paper with a specific thickness is most hazardous ($65\mu \text{m}$, corresponding, e.g., to dot matrix paper) and suggests a probabilistic interpretation of irregular occurrence of paper cuts. Stimulated by these findings, we finally show how a recyclable cutting tool can harness the surprising power of paper.

The transition from static to dynamic friction when an elastic body is slid over another is now known to result from the motion of interface rupture fronts. These fronts may be either cracklike or pulselike, with the latter involving reattachment in the wake of the front. How and why these fronts occur remains a subject of active theoretical and experimental investigation, especially given its wide ranging implications. In this work, we investigate the role of boundary loading in answering this question using an elastic lattice-network model under displacement/velocity controlled loading. Bulk elastic and interface bonds are simulated using a network of springs, with a stretch-based detachment and reattachment rule applied to interface bonds. We find that, contrary to commonly used rigid body models with Coulomb-type friction laws, the type of rupture front observed is very closely linked to the location of the applied boundary displacements. Depending on whether the sliding elastic solid is pulled, pushed or sheared—all equivalent in the rigid case—distinct interface rupture modes can occur. We quantify these rupture modes, evaluate the corresponding interface stresses that lead to their formation, and and study their subsequent propagation dynamics. Our results reveal quantitative analogies between the sliding friction problem and mode II fracture, with attendant wave speeds ranging from slow to Rayleigh. We discuss how these fronts mediate interface motion and implications for the general transition mechanism from static to dynamic friction.

This paper introduces a formulation of the particle-in-cell (PIC) method for the modeling of relativistic plasmas, that leverages the ability of the pseudospectral analytical time-domain solver (PSATD) to handle arbitrary time dependencies of the charge and current densities during one PIC cycle (applied to second-order polynomial dependencies here). The formulation is applied to a modified set of Maxwell's equations that was proposed earlier in the context of divergence cleaning, and to recently proposed extensions of the PSATD-PIC algorithm. Detailed analysis and testings revealed that, under some condition, the formulation can expand the range of numerical parameters under which PIC simulations are stable and accurate when modeling relativistic plasmas such as, e.g., plasma-based particle accelerators.

The study of integrable systems has led to significant advancements in our understanding of many-body physics. We design a series of numerical experiments to analyze the integrability of a mass-imbalanced two-body system through energy-level statistics and deep learning of wave functions. The level spacing distributions are fitted by a Brody distribution and the fitting parameter $\omega$ is found to separate the integrable and nonintegrable mass ratios by a critical line $\omega =0$. The convolutional neural network built from the probability density images could identify the transition points between integrable and nonintegrable systems with high accuracy, yet in a much shorter computation time. A brilliant example of the network's ability is to identify a new integrable mass ratio $1/3$ by learning from the known integrable case of equal mass, with a remarkable network confidence of $98.22\%$. The robustness of our neural networks is further enhanced by adversarial learning, where samples are generated by standard and quantum perturbations mixed in the probability density images and the wave functions, respectively.

Recently, a kind of finite-temperature pseudotransition was observed in several quasi-one-dimensional models. In this work, we consider a genuine one-dimensional extended Hubbard model in the atomic limit, influenced by an external magnetic field and with the arbitrary number of particles controlled by the chemical potential. The one-dimensional extended Hubbard model in the atomic limit was initially studied in the seventies and has been investigated over the past decades, but it still surprises us today with its fascinating properties. We rigorously analyze its low-temperature behavior using the transfer matrix technique and provide accurate numerical results. Our analysis confirms that there is an anomalous behavior in the half-filled band, specifically occurring between the alternating pair (AP) and paramagnetic (PM) phases at zero temperature. Previous investigations did not deeply identify this anomalous behavior, maybe due to the numerical simplicity of the model, but from an analytical point of view this is not so easy to manipulate algebraically because one needs to solve an algebraic cubic equation. In this study, we explore this behavior and clearly distinguish the pseudotransition, which could easily be mistaken with a real phase transition. This anomalous behavior mimics features of both first- and second-order phase transitions. However, due to its nature, we cannot expect a finite-temperature phase transition in this model.

We examine continuous random walks that are conditioned to reach one region before another. These conditioned processes are used to generate stochastic trajectories for barrier crossing events, which are generally rare and difficult to sample. The processes are generated using a Brownian bridge technique, resulting in near perfect sampling efficiency without accruing error in the conditional statistics of the process. The construction requires the hitting probability or committer function, which is a solution to the backward Fokker-Planck equation, a partial-differential equation that can be difficult to solve through general means. Therefore, we derive a one-dimensional approximation through asymptotic methods for barrier crossing trajectories. We show that this approximation has a simple analytical representation and approaches the true solution as the barrier height increases. Brownian bridge trajectories generated with this approximate solution are then shown to result in accurate conditional statistics when used in conjunction with importance sampling, even in the case when potential energy barriers are not large. We show this idea's effectiveness by simulating rare events in a stochastic chemical reaction network (Schögl reaction) with multiple steady states. This methodology shows great promise for future implementation to simulate rare barrier crossing events for a wide variety of physical processes.

Triangular billiards whose angles are rational multiples of $\pi$ are one of the simplest examples of pseudo-integrable models with intriguing classical and quantum properties. We perform an extensive numerical study of spectral statistics of eight quantized rational triangles, six belonging to the family of right-angled Veech triangles and two obtuse rational triangles. Large spectral samples of up to one million energy levels were calculated for each triangle, which permits one to determine their spectral statistics with great accuracy. It is demonstrated that they are of the intermediate type, sharing some features with chaotic systems, like level repulsion, and some with integrable systems, like exponential tails of the level spacing distributions. Another distinctive feature of intermediate spectral statistics is a finite value of the level compressibility. The short-range statistics such as the level spacing distributions, and long-range statistics such as the number variance and spectral form factors were analyzed in detail. An excellent agreement between the numerical data and the model of gamma distributions is revealed.

The economic success of individuals is often determined by a combination of talent, luck, and assistance from others. We introduce an agent-based model that simultaneously considers talent, luck, and social interaction. This model allows us to explore how network structure (how agents interact) and talent distribution among agents affect the dynamics of capital accumulation through analytical and numerical methods. We identify a phenomenon that we call the “talent configuration effect,” which refers to the influence of how talent is allocated to individuals (nodes) in the network. We analyze this effect through two key properties: talent assortativity (TA) and talent-degree correlation (TD). In particular, we focus ons three economic indicators: growth rate ($n_{\mathrm{rate}}$), Gini coefficient (inequality: $n_{\mathrm{Gini}}$), and meritocratic fairness ($n_{LT}$). This investigation helps us understand the interplay between talent configuration and network structure on capital dynamics. We find that, in the short term, positive correlations exist between TA and TD for all three economic indicators. Furthermore, the dominant factor influencing capital dynamics depends on the network topology. In scale-free networks, TD has a stronger influence on the economic indices than TA. Conversely, in lattice-like networks, TA plays a more significant role. Our findings address that high socioeconomic homophily can create a dilemma between growth and equality and that hub monopolization by a few highly talented agents makes economic growth strongly dependent on their performances.

Rotating quasipaired particles (torsions) are observed within a two-dimensional monolayer crystal suspended in an argon complex plasma for discharge powers of 1–10 W and pressures of 135–155 mTorr. The inclusion of a torsion in a crystal lattice fundamentally changes the overall lattice state to a “hot crystal.” A torsion increases the particle motion and kinetic energy of other particles in the crystal, with the strongest effects on neighboring particles. The apparent effective range is to the third nearest neighbor, with the kinetic energy in the first three shells of particles increasing by at least 200% over baseline values for the crystal. However, the variance of the motion of all particles in the crystal increases by more than two times over the average background kinetic fluctuations for the whole crystal. The formation of a torsion perturbs the structure and symmetry of a plasma crystal. A single torsion causes the average interparticle spacing to increase by 11% compared to the same crystal without a torsion. Particles in the first two shells surrounding a torsion also display reduced hexagonal symmetry. The combination of the perturbed lattice structure and the larger range of motion for the microparticles contribute to a higher-energy-state crystal when torsions are present.

Keldysh field theory, based on adiabatic assumptions, serves as a widely used framework for addressing nonequilibrium many-body systems. Nonetheless, the validity of such adiabatic assumption when addressing interacting Gibbs states remains a topic of contention. Interestingly, the knowledge of work statistics developed in nonequilibrium thermodynamics helps us to quantitatively explore this problem. Consequently, we deduce a universal theorem delineating the characteristics of evolutions that transition an initial Gibbs state to another. Based on this theorem, we analytically ascertain that adiabatic evolutions fail to transition a noninteracting Gibbs state to its interacting counterpart. However, the adiabatic evolution remains a superior approximation relative to its nonadiabatic counterparts. Numerics verifying our theory and predictions are also provided. Furthermore, our findings render insights into the Gibbs state preparation within the domain of quantum computation.

We present an extension of the Kuramoto-Sakaguchi model for networks, deriving the second-order phase approximation for a paradigmatic model of oscillatory networks—an ensemble of nonidentical Stuart-Landau oscillators coupled pairwisely via an arbitrary coupling matrix. We explicitly demonstrate how this matrix translates into the coupling structure in the phase equations. To illustrate the power of our approach and the crucial importance of high-order phase reduction, we tackle a trendy setup of nonlocally coupled oscillators exhibiting a chimera state. We reveal that our second-order phase model reproduces the dependence of the chimera shape on the coupling strength that is not captured by the typically used first-order Kuramoto-like model. Our derivation contributes to a better understanding of complex networks' dynamics, establishing a relation between the coupling matrix and multibody interaction terms in the high-order phase model.

We study the nonequilibrium work in a pedagogical model of relativistic ideal gas. We obtain the exact work distribution and verify Jarzynski's equality. In the nonrelativistic limit, our results recover the nonrelativistic results of Lua and Grosberg [J. Phys. Chem. B 109, 6805 (2005)]. We also find that, unlike the nonrelativistic case, the work distribution no longer has zeros and the number of collisions in this relativistic gas model is finite. In addition, based on an analysis of the experimental parameters, we conclude that it is difficult to detect the relativistic effects of the work distribution of the ideal gas in a piston system with the current experimental techniques.

Steady solutions of a single droplet or bubble in the van der Waals fluid are investigated on the basis of the kinetic model equation that has been recently proposed by Miyauchi et al. [Gas Dynamics with Applications in Industry and Life Sciences (Springer, Cham, 2023), pp. 19–39]. Under the thermal equilibrium condition and isotropic assumption with respect to the origin of the coordinates, the kinetic equation is reduced to an ordinary differential equation for the density, which can be regarded as a low-dimensional dynamical system. The possible density distribution is studied as a flow in the low-dimensional phase space. It is clarified that a single droplet or bubble can be understood as a flow that goes into a fixed point and that the flow is qualitatively different in the unstable and metastable parameter regions. The features of the obtained density distributions in individual regions are also clarified. Finally, the stability of those solutions is studied by direct numerical experiments of the kinetic equation.

Bronin et al. [Phys. Rev. E 108, 045209 (2023)] recently reported molecular-dynamics simulations of ultracold neutral plasmas expanding in a quadrupole magnetic field. While the main results are in agreement with prior experimental measurements, we present data showing oscillations not captured in the simulations of Bronin et al. Plasmas formed using pulsed or continuous-wave ionization processes have similar confinement times.

In this Reply, we respond to the Comment by Schlitters et al. on our recent work [Phys. Rev. E 108, 045209 (2023)], where we present simulation results of ultracold Sr plasma expansion in a quadrupole magnetic field using a molecular-dynamics method. In the Comment, Schlitters et al. present their experimental results, some of which, from their point of view, contradict our simulation results and others that confirm the experiments of Gorman et al. [Phys. Rev. Lett. 126, 085002 (2021)] and our results. In addition, Schlitters et al. also provide results that were not described in our work. Here we show that there is not a contradiction but a misunderstanding of our results. This is due to the fact that simulations allow the use of processing methods that are difficult to obtain in experiment. We also present different simulation results related to expansion velocity variations that reflect the experimental results of Schlitters et al. and provide an explanation for the origin of these variations.

We investigate the elastic behavior of two-dimensional crystalline membrane embedded into real space taking into account the presence an arbitrary number of flexural phonon modes $d_c$ (the number of out-of-plane deformation field components). The bending rigidity exponent $\eta$ is extracted by numerical simulation via Fourier Monte Carlo technique of the system behavior in the universal regime. This universal quantity governs the correlation function of out-of-plane deformations at long wavelengths and defines the behavior of renormalized bending rigidity at small momentum $\varkappa \sim 1/q^{\eta }$. The resulting numerical estimates of the exponent for various $d_c$ are compared with the numbers obtained from the approximate analytical techniques.

We consider an autocorrelation function of a quantum mechanical system through the lens of the so-called recursive method, by iteratively evaluating Lanczos coefficients or solving a system of coupled differential equations in the Mori formalism. We first show that both methods are mathematically equivalent, each offering certain practical advantages. We then propose an approximation scheme to evaluate the autocorrelation function and use it to estimate the equilibration time $\tau$ for the observable in question. With only a handful of Lanczos coefficients as the input, this scheme yields an accurate order of magnitude estimate of $\tau$, matching state-of-the-art numerical approaches. We develop a simple numerical scheme to estimate the precision of our method. We test our approach using several numerical examples exhibiting different relaxation dynamics. Our findings provide a practical way to quantify the equilibration time of isolated quantum systems, a question which is both crucial and notoriously difficult.

Driven by growing computational power and algorithmic developments, machine learning methods have become valuable tools for analyzing vast amounts of data. Simultaneously, the fast technological progress of quantum information processing suggests employing quantum hardware for machine learning purposes. Recent works discuss different architectures of quantum perceptrons, but the abilities of such quantum devices remain debated. Here, we investigate the storage capacity of a particular quantum perceptron architecture by using statistical mechanics techniques and connect our analysis to the theory of classical spin glasses. Specifically, we focus on one concrete quantum perceptron model and explore its storage properties in the limit of a large number of inputs.