Rationally independent free fermions are those where sums of single-particle energies multiplied by arbitrary rational coefficients vanish only if the coefficients are all zero. This property guaranties that they have no degeneracies in the many-body spectrum and gives them relaxation properties more similar to those of generic systems. Using classic results from number theory we provide minimal examples of rationally independent free fermion models for every system size in one dimension. This is accomplished by considering a free fermion model with a chemical potential, and hopping terms corresponding to all the divisors of the number of sites, each one with an incommensurate complex amplitude. We then move on to discuss the many-body spectral statistics for these models. Indeed, because of their nondegenerate spectrum, these systems are potentially compatible with Poissonian spectral statistics, as opposed to most noninteracting systems. We show that local probes—like the ratio of consecutive level spacings—look very similar to what is expected for the Poisson statistics. We however demonstrate that free fermion models can never have Poisson statistics with an analysis of the moments of the spectral form factor.

Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous work demonstrated the effectiveness of Langevin-like equations in capturing the statistical properties of pedestrian dynamics in simple settings, such as almost straight trajectories. However, modeling more complex dynamics, such as when multiple routes and origin destinations are involved, remains a significant challenge. In this work, we introduce a novel and generic framework to describe the dynamics of pedestrians in any geometric setting, significantly extending previous works. Our model is based on Langevin dynamics with two timescales. The fast timescale corresponds to the stochastic fluctuations present when a pedestrian is walking. The slow timescale is associated with the dynamics that a pedestrian plans to follow, thus a smoother path without stochastic fluctuations. Employing a data-driven approach inspired by statistical field theories, we learn the complex potentials directly from the data, namely a high-statistics database of real-life pedestrian trajectories. This approach makes the model generic as the potentials can be read from any trajectory data set and the underlying Langevin structure enables physics-based insights. We validate our model through a comprehensive statistical analysis, comparing simulated trajectories with actual pedestrian measurements across five complementary settings of increasing complexity, including a real-life train platform scenario, underscoring its practical societal relevance. We show that our model, by learning the effective potential, captures fluctuation statistics in the dynamics of individual pedestrians, both in dilute (no interaction with other pedestrians) as well as in dense crowds conditions (in presence of interactions). Our results can be reproduced with our generic open-source Python implementation [Pouw et al. (2024) [Software] doi:10.5281/zenodo.13362271] and validated with the supplemented data set [Pouw et al. (2024) [Dataset] doi:10.5281/zenodo.13784588]. Beyond providing fundamental insights and predictive capabilities in pedestrian dynamics, our model could be used to investigate generic active dynamics such as vehicular traffic and collective animal behavior.

We describe a general procedure which allows to construct, given a family of Hamiltonians $H(\underline{q},\underline{p};\underline{\lambda })$, a single new Hamiltonian $\tilde{H}(\underline{q},\underline{p})$ such that, on each level set of $\tilde{H}$, the unparametrized orbits are those of a level set of $H$ with the values of parameters $\underline{\lambda }$ varying with the value of $\tilde{H}$. The symmetry structure of $\tilde{H}$ can be completely characterized, provided the symmetries of initial family are known. Our approach covers numerous models considered in literature as well as it allows to construct novel ones. It provides a far reaching generalization of the Hietarinta et al. coupling-constant metamorphosis method and another proof of the Darboux theorem.

Observational evidence strongly supports the existence of a Super Massive Black Hole at the Galactic center, surrounded by dense stellar clusters. Modeling galactic centers with intricate structures like shells and rings pose challenges, prompting the use of simplified models such as a spherical monopole potential with a multipolar halo mass distribution. This approach, employing a multipolar expansion model, provides versatility for numerical analyses, revealing the complex dynamics of stars in this region. Pseudopotentials like Paczynsky-Wiita and Artemova-Bjornsson-Novikov are utilized to simulate the impacts of strong gravity from nonrotating and rotating compact objects respectively, elucidating their influence on stellar dynamics. Chaos naturally arises due to noncentral forces, visualized using the Poincaré section technique. Of particular importance is the utilization of the Smaller Alignment Index (SALI), a powerful nonlinear dynamical tool, which categorizes particle orbits as escaping, regular, sticky, or chaotic. We exhaustively examine all combinations of multipolar moments up to the octupolar term along with spin using this tool, which had not been studied earlier. SALI provides a straightforward yet efficient method for assessing the interplay between the system's different multipolar moments, their combinations, and spin. Thus, our findings offer insights into the dynamics of compact objects enshrouded in a halo mass distribution and lay the groundwork for understanding complex astrophysical systems in galactic centers.

A systematic comparative study of two-disk dynamo models without friction (the Rikitake model) and with friction has been carried out. It is shown that the sets of chaotic and periodic modes realized in both models are qualitatively similar. We introduce a simple measure of the complexity of a solution, which allows finding the chaotic mode characterized by long-lived quasistationary states with very weak oscillations of variables, ending with a sharp burst of oscillations with a possible transition to the attraction area of the other stationary solution. This transition corresponds to the change in the magnetic field sign. Such a behavior of the field is somewhat similar to the dynamics of the Earth's large-scale field in terms of the chaotic change of zones from one polarity to another. This rare reversal chaos was found in both two-disk dynamo models (without friction and with friction), but in the viscous case, it appears only at weak friction.

The design of coherent and efficient policies to address infectious diseases and their consequences requires modeling not only epidemics dynamics but also individual behaviors, as the latter has a strong influence on the former. In our work, we provide a theoretical model for this problem, taking into account the social structure of a population. This model is based on a mean-field-game version of a SIR compartmental model, in which individuals are grouped by their age class and interact together in different settings. This social heterogeneity allows us to reproduce realistic situations while remaining usable in practice. In our game theoretical approach, individuals can choose to limit their contacts by making a trade-off between the risks incurred by infection and the cost of being confined. The aggregation of all these individual choices and optimizations forms a Nash equilibrium through a system of coupled equations that we derive and solve numerically. The global cost born by the population within this scenario is then compared to its societal optimum counterpart (i.e., the cost associated with the optimal set of strategies from the point of view of the society as a whole), and we investigate how the gap between these two costs can be partially bridged within a constrained Nash equilibrium for which a governmental institution would, under specific conditions, impose “partial lockdowns” such as the ones that were imposed during the COVID-19 pandemic. Finally, we consider the consequences of the finiteness of the population size $N_{\mathrm{tot}}$, or of a time $T$ at which an external event (e.g., a vaccine) would end the epidemic, and show that the variation of these parameters could lead to first-order phase transitions in the choice of optimal strategies. In this paper, all the strategies considered to mitigate epidemics correspond to nonpharmaceutical interventions, and we provide here a theoretical framework within which guidelines for public policies depending on the characteristics of an epidemic and on the cost of restrictions on the society could be assessed.

A model is proposed for mesoscopic dynamics of a magnetoactive elastomer (MAE). The elementary cell comprises two spherical linearly magnetizing particles embedded in an elastoviscous medium of the Kelvin type. The forced oscillations of this system induced by an ac field are studied. Under a static field, this system is prone to bistability that entails the magnetomechanical hysteresis: being initially separated by a finite distance, the particles move jumplike to a tight contact. The initial configuration is restored under a field that is lower than that of its onset. It is shown that in the oscillatory regime, depending on the material parameters of the system and the characteristics of the oscillating field, the pair may display steady cycles of several types. Upon enhancing the frequency, the occurrence of the particle contact may be blocked or, on the contrary, they might be “quenched” in the vicinity of each other. The behavior of the pair at a high frequency is analyzed. Estimations are given for the energy dissipation caused by the hysteretic regimes of the particle oscillations.

The self-organization of active particles on a two-dimensional single-occupancy lattice is investigated, with an emphasis on the effects of boundary confinement and the influence of an external mean fluid flow. The study examines collective behaviors, particularly the transition from a disordered phase to the formation of orientationally ordered patterns, and their impact on particle transport and flux. In the absence of fluid flow, confinement causes particles to accumulate near the walls, leading to clogs or obstructions that hinder movement, or to the formation of bands aligned with the channel. Although these bands limit the particles' ability to freely self-propel, they still result in a net flux along the channel. The introduction of an external Poiseuille fluid flow induces vorticity, shifts the phase transition to higher alignment sensitivities, and promotes particle clustering at the channel center, significantly enhancing overall flux.

A multipore membrane with current-rectifying nanofluidic diodes exhibits memristive properties based on the surface-charge-regulated ionic transport. The neuromorphiclike potentiation of the conductance by voltage pulses provides different functionalities that can be modulated not only by the amplitude and frequency of the driving oscillatory signal but also by the ionic concentration and $p\text{H}$ values of the external solutions. This fact allows one to implement a broad range of logical functions by the external reconfiguration of the nanofluidic diodes. As a proof of concept, we show Boolean (and, nand, and xor) and reversible (feynman) logical functions obtained by controlling chemical ($p\text{H}$ and ionic concentration) and electrical (voltage and current) signals in an electrochemical cell. The system displays some reminiscences to channel biophysics signaling in cell membranes and provides a suitable logical environment for sensing and information processing in iontronics hybrid devices. Model simulations that explain the experimental data and explore future applications are also included.

Systems of oscillators whose internal phases and spatial dynamics are coupled, swarmalators, present diverse collective behaviors which in some cases lead to explosive synchronization in a finite population as a function of the coupling parameter between internal phases. Near the synchronization transition, the phase energy of the particles is represented by the XY model, and they undergo a transition which can be of the first order or the second depending on the distribution of natural frequencies of their internal dynamics. The first-order transition is obtained after an intermediate state (static wings phase wave state) from which the nodes, in cascade over time, achieve complete phase synchronization at a precise value of the coupling constant. For a particular case of natural frequencies distribution, a new phenomenon, the rotational splintered phase wave state, is observed and leads progressively to synchronization through clusters switching alternatively from one to two and for which the frequency decreases as the phase coupling increases.

The transmission of cytoskeletal forces to the extracellular matrix through focal adhesion complexes is essential for a multitude of biological processes, such as cell migration, cell differentiation, tissue development, and cancer progression, among others. During migration, focal adhesions arrest the actin retrograde flow towards the cell interior, allowing the cell front to move forward. Here, we address a puzzling observation of the existence of two distinct phenomena: a biphasic vs a monotonic relationship of the retrograde flow and cell traction force with substrate rigidity. In the former, maximum traction force and minimum retrograde flow velocity are observed at an intermediate optimal substrate stiffness; while in the latter, the actin retrograde flow decreases and traction force increases with increasing substrate stiffness. We propose a theoretical model for cell-matrix adhesions at the leading edge of a migrating cell, incorporating a novel approach in force loading rate sensitive binding and reinforcement of focal adhesions assembly and the subsequent force-induced slowing down of actin flow. Our model exhibits both biphasic and monotonic responses of the retrograde flow and cell traction force with increasing substrate rigidity, owing to the cell's ability to sense and adapt to the fast-growing forces. Furthermore, our analysis shows how competition between different timescales regulated by loading rate sensitivity influences the biphasic versus monotonic behavior and the emergence of optimal substrate rigidity in the biphasic scenario. We also elucidate how the viscoelastic properties of the substrate regulate these nonlinear responses and predict the loss of cell sensitivity to variation in substrate rigidity when adhesions are subjected to high forces.

We present a technique for efficiently transitioning a quantum system from an initial to a final stationary state in less time than is required by an adiabatic (quasistatic) process. Our approach makes use of Nelson's stochastic quantization, which represents the quantum system as a classical Brownian process. Thanks to this mathematical analogy, known protocols for classical overdamped systems can be translated into quantum protocols. In particular, one can use classical methods to find optimal quantum protocols that minimize both the time duration and some other cost function to be freely specified. We have applied this method to the time-dependent harmonic oscillator and tested it on two different cost functions: (i) the cumulative energy of the system over time and (ii) the dynamical phase of the wave function. In the latter case, it is possible to construct protocols that are “adiabatically optimal,” i.e., they minimize their distance from an adiabatic process for a given duration.

By means of analytical calculations and numerical simulations, we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realization is possible in systems where fast and slow exciton subsystems appear. For substantially different diffusion coefficients of the species, the negative diffusion can be observed if one measures the transport properties of only a single subsystem, just as was obtained in experimental studies for quasi-two-dimensional semiconductor systems. The initial transition from a fast subsystem to a slow one results in a delayed release of fast excitons in the area close to the original excitation spot. Hence, the signal from the fast excitons alone includes the delayed replenishment from the transition of slow quasiparticles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. We show that the analytical theory matches the available experimental data for negative diffusion quite well. The average diffusion coefficients for the combined population are analytically expressed through the diffusion coefficients of fast and slow excitons. Simple analytical expressions for effective diffusion coefficients obtained in limiting cases are of interest both for theoretical and experimental analysis of not only the exciton transport, but also for a variety of systems, where fast and slow moving subsystems are present.

We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular nonlocal correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model.

Coupled oscillator systems can lead to states in which synchrony and chaos coexist. These states are called “chimera states.” The mechanism that explains the occurrence of chimera states is not well understood, especially in pulse-coupled oscillators. We study a variation of a pulse-coupled oscillator model that has been shown to produce chimera states, demonstrate that it reproduces several of the expected chimera properties, like the formation of multiple heads and the ability to control the natural drift that Kuramoto's chimera states experience in a ring, and explain how chimera states emerge. Our contribution is defining the model, analyzing the mechanism leading to chimera states, and comparing it with examples from the field of Kuramoto oscillators.

We present a solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. It is achieved using a cavity or message passing approach, which allows one to obtain the essential ingredient required for the solution, viz. a self-consistent determination of locally varying percolation probabilities. The cavity solution can be evaluated both for single large instances of locally treelike graphs, and in the thermodynamic limit of random graphs of finite mean degree in the configuration model class. The critical level $h_c$ of the percolation transition is obtained through the condition that the largest eigenvalue of a weighted version $B$ of a nonbacktracking matrix satisfies ${\lambda }_{\max }{\left(B\right)|}_{h_c}=1$. We present level-dependent distributions of local percolation probabilities for Erdős-Rényi networks and and for networks with degree distributions described by power laws. We find that there is a strong correlation between marginal single-node variances of a massless multivariate Gaussian and local percolation probabilities at a given level $h$, which is nearly perfect at negative values $h$, but weakens as $h\nearrow 0$ for the system with power-law degree distribution, and generally also for negative values of $h$, if the multivariate Gaussian acquires a nonzero mass. The theoretical analysis simplifies in the case of random regular graphs with uniform edge weights of the weighted graph Laplacian of the system and uniform mass parameter of the Gaussian field. An asymptotic analysis reveals that for edge weights $K=K\left(c\right)\equiv 1$ the critical percolation threshold $h_c$ decreases to 0, as the degree $c$ of the random regular graph diverges. For $K=\left(c\right)=1/c$, however, the critical percolation threshold $h_c$ is shown to diverge as $c\to \infty$.

We conduct experiments on a class of two-dimensional semiwet foams generated through compressing a three-dimensional soap foam between two glass plates. To induce a spatially uniform rupturing process on foam boundaries, an additional plate is heated and placed on top of the unheated plates. For 30 separate foam samples, we record network statistics related to cell side numbers and areas as the foam coarsens over a half-minute. We find that the Aboav law and a quadratic Lewis Law, two commonly used relations between network topology and geometry, hold well for preheated foams. To track how well these laws are maintained as the foam ages, we introduce metrics for measuring a foam's disorder over time and build simple autonomous models for these metrics. While the quadratic Lewis Law is found to hold well throughout the rupture process, the Aboav law breaks down rapidly when the Gini coefficient, used for measuring disparity of cell areas, is approximately 0.8.

The properties of energy transfer in the kinetic range of plasma turbulence have fundamental implications on the turbulent heating of space and astrophysical plasmas. It was suggested that magnetic reconnection may be responsible for driving the subion scale cascade, and that this process would be characterized by a direct energy transfer toward even smaller scales (until dissipation), and a simultaneous inverse transfer of energy toward larger scales, until the ion break. Here we employ the space-filter technique on high-resolution 2D3V hybrid-Vlasov simulations of continuously driven turbulence providing quantitative evidence that magnetic reconnection is indeed able to trigger a dual energy transfer originating at subion scales.

Geometric frustration is a fundamental concept in various areas of physics, and its role in self-assembly processes has recently been recognized as a source of intricate self-limited structures. Here we present an analytic theory of the geometrically frustrated self-assembly of regular icosahedral nanoparticle based on the non-Euclidean crystal $\{3,5,3\}$ formed by icosahedra in hyperbolic space. By considering the minimization of elastic and repulsion energies, we characterize prestressed morphologies in this self-assembly system. Notably, the morphology exhibits a transition that is controlled by the size of the assembled cluster, leading to the spontaneous breaking of rotational symmetry.

The cross-entropy loss function is widely used in machine learning to measure the performance of a classification model. Interestingly, our study find that this function has scaling behavior when deep neural networks are used to investigate percolation models. Specifically, we use convolutional neural networks with different pooling methods to study the site percolation on square lattices under two labeling methods (labeling based on spanning cluster and the exact solution of the critical point). Subsequently, graph convolutional neural networks (GCNs) with different pooling methods are utilized to do the same kind of experiment. Finally, the GCN with different pooling methods is used to study the percolation phase transitions on the Erdős-Rényi (ER) networks under labeling based on the critical point. The reliability of the classifiers is detected by the values of the critical point $p_c$ and critical exponent $\nu$ which are obtained by the scaling behaviors of the percolation probability. The results demonstrate that the scaling exponent of cross-entropy $\psi /\nu$ depends on the labeling and pooling methods. Labeling based on critical points, which is equivalent to labeling based on spanning clusters in infinite systems, can be used to investigate the critical behaviors in finite systems. SAGPooling-Mean is an effective pooling method to study the scaling behavior of cross-entropy loss on two-dimensional square lattices and ER networks.