Linearized moment equations are often used to derive closure models for the hydrodynamic equations of multicomponent plasmas near thermodynamic equilibrium. However, the linearized transport equations lose their validity in rarefied conditions or in the presence of strong electric fields, when the velocity distribution functions (VDFs) of the different species are non-Maxwellian and the drift between the species, i.e., the Mach number of the relative motion, becomes large. In this paper, we develop a nonlinear, high-order moment model for nonmagnetized electrons in partially ionized plasmas. We present a fourteen-moment model using a Hermitian expansion of the VDF that considers density, momentum, anisotropic pressure tensor, contracted heat flux vector, and contracted scalar kurtosis. We consider the relevant collisional processes in partially ionized plasmas, such as elastic and inelastic electron-neutral, electron-impact ionization, electron-electron Coulomb, and electron-ion Coulomb collisions. The collisional terms in the electron moment equations are integrated analytically for finite Mach numbers and accounting for the nonlinear terms in the Boltzmann operator, which are often neglected in linearized closure models. The proposed closure presents novel cross-coupling effects between moments of different tensorial nature within the collisional terms. The present nonlinear fourteen-moment model is benchmarked against a Monte Carlo simulation under a spatially homogeneous configuration, showing good agreement for a wide range of reduced electric field (e.g., up to 1000 Td) before runaway electrons occur, improving the results of a linear fourteen-moment model.

We propose an improved Path Integral Monte Carlo (PIMC) algorithm called harmonic PIMC (H-PIMC) and its generalization, mixed PIMC (M-PIMC). PIMC is a powerful tool for studying quantum condensed phases. However, it often suffers from a low acceptance ratio for solids and dense confined liquids. We develop two sampling schemes especially suited for such problems by dividing the potential into its harmonic and anharmonic contributions. In H-PIMC we generate the imaginary time paths for the harmonic part of the potential exactly and accept or reject it based on the anharmonic part. In M-PIMC we restrict the harmonic sampling to the vicinity of local minimum and use standard PIMC otherwise, in order to optimize efficiency. We benchmark H-PIMC on systems with increasing anharmonicity, improving the acceptance ratio and lowering the autocorrelation time. For weakly to moderately anharmonic systems, at $\beta \hslash \omega =16$, H-PIMC improves the acceptance ratio by a factor of 6–16 and reduces the autocorrelation time by a factor of 7–30. We also find that the method requires a smaller number of imaginary time slices for convergence, which leads to another two- to threefold acceleration. For strongly anharmonic systems, M-PIMC converges with a similar number of imaginary time slices as standard PIMC but allows the optimization of the autocorrelation time. We extend M-PIMC to periodic systems and apply it to a sinusoidal potential. Finally, we combine H- and M-PIMC with the worm algorithm, allowing us to obtain similar efficiency gains for systems of indistinguishable particles.

We analytically investigate the generation of entanglement in a system of two coupled Brownian particles subjected to time-dependent, dual-driving protocols. By modeling the system as a bivariate Ornstein-Uhlenbeck process, we derive the dynamics of the entanglement witness, $\mathcal{W}\left(t\right)$, from the deterministic Lyapunov equation governing the covariance matrix. We compare symmetric and asymmetric driving protocols and show that symmetric driving is fundamentally more efficient at generating entanglement. This advantage is traced to the preservation of variance symmetry, which optimizes the witness function. Furthermore, we develop a predictive model for the optimal interaction strength, $g_{\text{opt}}$, using a time-averaged effective potential. This model demonstrates that optimal coupling is protocol dependent, providing a clear framework for controlling emergent correlations in driven mesoscopic systems.

Thermophoresis is the migration of a particle due to a thermal gradient. Here, we theoretically uncover a quantum version of thermophoresis, where both the bosonic nature of the thermal baths and quantum tunneling play significant roles. First, we find a thermophoretic force on a trapped quantum particle in a double-well potential. Then, we show that thermophoresis also takes place in an $N$-site model, for which we analytically derive a diffusion equation in the continuum limit ($N\to \infty$). We evidence additional quantum thermophoretic signatures in the transient particle-transport regime, which appear in the particle's average position and variance, as well as in the particle currents. Beyond establishing that single quantum particles can undergo thermally induced transport, our results suggest a route for quantum-state preparation with thermal gradients.

In our previous work [Phys. Rev. E 110, 034104 (2024)], we considered the mean-squared displacement (MSD) of particles whose free motion is subdiffusive and is described by a generalized Langevin equation (GLE) with power-law memory kernel under geometric constraints, e.g., when the particles are moving in channels of different shape. The MSD at long times was found to be independent of the channel's shape. Motivated by this finding, we discuss a simple physical model corresponding to such a situation. Here the particle is a tagged end monomer of a Rouse polymer chain, and the bath is represented by the rest of the chain and its surroundings. The constraints correspond to the motion of a monomer on a static, sinusoidally meandering wire. For the case of long chains we find the same independence of the long-time behavior on the wire's modulation as in the case of GLE: The MSD at longer times does not depend on the amplitude of the wire's modulation and is the same as for the straight wire. For shorter chains whose Rouse time lays in the observation domain, for moderate modulation, if the MSD already approached the one for a straight wire at times smaller or comparable to the Rouse time, the independence on the modulation is carried over to the final, diffusion regime at long times. In the case when constraints apply not only to the tagged monomer, but also to the rest of the chain (i.e., to the bath), the sensitivity to the wire's shape never disappears. A simple analytical approach based on homogenization gives a quite satisfactory description of our findings.

We study the coupled twin-diamond chain, a decorated one-dimensional Ising model motivated by the magnetic structure of ${\mathrm{Cu}}_2{\left({\mathrm{TeO}}_3\right)}_2{\mathrm{Br}}_2$. By applying an exact mapping to an effective Ising chain, we obtain the full thermodynamic description of the system through a compact transfer-matrix formulation. The ground-state analysis reveals five distinct phases, including two frustrated sectors with extensive degeneracy. These frustrated regions give rise to characteristic entropy plateaus and separate the ordered phases in the zero-temperature diagram. At low temperatures the model exhibits peculiar sharp yet continuous variations of entropy, magnetization, and response functions, reflecting clear signatures of pseudotransition behavior. The coupled twin-diamond chain thus provides an exactly solvable setting in which competing local configurations and internal frustration lead to pronounced dual pseudocritical features in one dimension.

Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, nonholonomic systems—subject to nonintegrable velocity constraints or position inequality constraints—have long resisted a general extremized action treatment. In this work, we construct an explicit and general action for nonholonomic motion, motivated by the classical limit of the quantum Schwinger-Keldysh action formalism, rediscovered by Galley. Our formulation recovers the correct dynamics of the Lagrange-d'Alembert equations via extremization of a scalar action. We validate the approach on canonical examples using direct numerical optimization of the novel action, bypassing equations of motion. Our framework extends the reach of variational mechanics and offers new analytical and computational tools for constrained systems.

In this work we revisit the axial third-nearest-neighbor Ising chain and examine in detail some aspects of its phase behavior ensuing from competing interactions and resulting frustration. We probe the phase behavior with two complimentary tools: a microscopic two-point correlation function $\mathcal{C}\left(n\right)$, which we carefully construct after appropriate spin transformations, and a macroscopic, thermodynamic curvature $R$ which we obtain from the free entropy. We report observations of phenomena such as hyperscaling breakdown and intermediate-ranged modulations among others. The zero-field thermodynamic curvature $R_0$ is shown to systematically subdivide the ground-state phases into regions of attractive or repulsive effective interactions of varying strength. Furthermore, $R_0$ brings forth the significance of some third-order moments in describing the effects of frustration, including the multiphase lines. Combined use of both the tools in the short-ranged modulated order regime confirms and further clarifies the discussion in [S. Khatua et al., Phys. Rev. E 111, L022105 (2025)] regarding the appropriate measure of high temperature correlation length in this regime.

Understanding how hierarchical topology governs diffusion is essential for explaining transport efficiency in biological networks and designing engineered materials. While prior studies have characterized anomalous diffusion and derived analytical expressions for distance-based indices on fractals, the quantitative relationship between graph-theoretic structure and transport dynamics remains unclear, particularly whether fractal organization offers unique properties beyond those predictable from network size or connectivity. We address this gap by deriving a closed form expression for the Wiener index of the Vicsek fractal and performing systematic diffusion simulations across generations 0 to 4 (up to 3125 nodes). Comparative analysis with 2D lattices, random regular graphs, and the T fractal isolates fractal-specific effects from generic network properties, while spectral gap analysis provides mechanistic insight into mixing dynamics. We identify three phenomena that appear characteristic of self-similar architecture: (1) progressive transport efficiency improvement, where hierarchical redundancy increasingly compensates for path elongation; (2) structured heterogeneity, exhibiting near-maximal entropy alongside persistent spatial gradients; and (3) sustained flux growth, reflecting concentration gradients within recursive substructures. Both the Vicsek and T fractal demonstrate these behaviors, while lattices and random graphs do not, suggesting they may be generic features of deterministic self-similar networks. Although our analysis is limited to five generations and the results are suggestive rather than definitive, the combination of analytical derivations, numerical simulations, and multitopology comparison provides evidence that hierarchical self-similarity enables scalable transport not through distance minimization but through redundancy that mitigates bottleneck-induced delays. These findings offer insight into biological transport systems and suggest design principles for artificial hierarchical materials.

The forcing of a micron sized gas bubble by an acoustic traveling wave in water is considered using a model which includes axisymmetric shape mode interactions to third order. In all cases, the resultant bubble motion is predicted to consist of small scale periodic oscillations superimposed upon a longer timescale, monotonically changing profile. For driving amplitudes below those necessary to cause parametrically induced instabilities to grow on the surface of the bubble, the long timescale bubble speed increases as the amplitude of the forcing increases but the resultant bubble motion induces markedly small scale deformation of the bubble surface which is dominated by the ellipsoidal mode. For cases where parametric instabilities grow but the driving pressure is not sufficient to cause bubble splitting or fragmentation, saturation due to nonlinear shape mode interactions occurs resulting in observable, sustained, finite amplitude shape deformation dominated by the parametrically excited mode. The induced shape deformation is found in turn to modify the bubble motion. In particular the speed of the long timescale monotonic translation is reduced to a new constant value and for sufficiently large forcing, this motion is found to reverse.

In this paper the excluded volume of binary similar hyperparticles with small size difference in $D$-dimensional Euclidean spaces ${\mathbb{R}}^2, {\mathbb{R}}^3$, and ${\mathbb{R}}^4$ is studied using two different statistical geometry approaches. These geometric approaches, concerning orientation geometry and integral geometry, yield the excluded volume of particle pairs. The excluded volume of rectangles, based on orientation geometry, in Euclidean space ${\mathbb{R}}^2$ is used to derive an explicit equation for the bidisperse packing fraction, which is compatible with the expression published previously. Next, the excluded volumes of pairs of convex particles in $D=2,3$, and 4, resulting from integral geometry, are presented. These excluded volumes are identical with the specific ones for circles and rectangles ($D$ = 2) and (sphero)cylinders ($D$ = 3), derived by orientation geometry. Furthermore, these orientation geometry-based excluded volumes contain geometric measures: particle volume, surface area, mean curvature, and the second quermassintegral. They allow for the derivation of closed-form expressions for the random packing fraction of binary convex similar hyperparticles in Euclidean spaces ${\mathbb{R}}^2, {\mathbb{R}}^3$, and ${\mathbb{R}}^4$.

The segregation behavior of active and passive rodlike particles is investigated in two-dimensional systems with reflective and periodic boundary conditions. The influences of particle aspect ratio, packing fraction, propulsion velocity, and rotational diffusion on segregation are systematically analyzed through particle dynamics simulations. Under reflective boundaries, persistent propulsion and collision-induced alignment, reinforced by wall-induced trapping, amplify activity-driven clustering along the boundaries even at low densities, making segregation stronger and more easily triggered. In contrast, under periodic boundaries, comparable segregation requires sufficiently large propulsion strength, particle anisotropy, and moderate density, as ordering arises purely from collision-induced alignment without wall stabilization. These results highlight the crucial role of boundary effects in controlling anisotropic active-passive segregation and provide a theoretical basis for designing efficient separation and microrobotic systems.

The collective frequency that emerges from synchronized neuronal populations—the network resonance—shows a systematic relationship with brain size: a whole-brain large network oscillates slowly, whereas finer parcellations of fixed volume exhibit faster rhythms. This resonance–size scaling has been reported in delayed neural mass models and human neuroimaging, yet the physical mechanism has remained unresolved. Here, we show that size-dependent resonance follows directly from propagation delays in delay-coupled phase oscillators. Starting from a Kuramoto model with heterogeneous delays, we linearize around the near-synchronous solution and obtain a closed-form approximation linking the resonance $\mathrm{\Omega }$ to the mean delay and the effective coupling field. The analysis predicts a generic scaling law: $\mathrm{\Omega }\approx {\left({\sum }_j{c}_{ij}\tau \right)}^{-1}$, so resonance is delay limited and therefore depends systematically on geometric size or parcellation density. We evaluate four growth scenarios—expanding geometry, fixed-volume parcellation, constant geometry, and an unphysical reference case—and show that only geometry-consistent scaling satisfies the analytical prediction. Numerical simulations with heterogeneous delays validate the law and quantify its error as a function of delay dispersion. These results identify a minimal physical mechanism for size-dependent cortical resonance and provide an analytical framework that unifies numeric simulation outputs.

The out-of-time-order correlator (OTOC) quantifies information scrambling in quantum systems and serves as a key diagnostic of quantum chaos. In one-body systems with a classical counterpart, the relaxation of the OTOC is governed by Ruelle-Pollicott resonances. For many-body systems lacking a semiclassical limit, recent studies have identified an analogous role played by the Liouvillian spectrum of weakly open extensions of the dynamics, where the slowest decay rate—the Liouvillian gap—encodes relaxation. Here we study the kicked Ising spin chain and show that the long-time exponential decay of the OTOC in the isolated system occurs at a rate equal to twice this intrinsic gap. This correspondence is demonstrated across parameter regions exhibiting distinct level spacing statistics, indicating that the Liouvillian spectrum provides a robust framework for characterizing relaxation and irreversibility in closed many-body quantum systems.

We propose a paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter $0\le p\le 1$) shapes the structure of the evolving network. We reveal the ability to seamlessly explore a vast landscape of scale-free networks, unlocking a class of complex networks that we call a stars-with-filament structure. Remarkably, the average degree $\overline{k}$ of these networks grows like $lnt$ to some power, where $t$ is time and the average shortest path length grows logarithmically with the system size for intermediate $p$ values, offering fresh insights into the structural dynamics of scale-free systems. Our approach is backed by a robust mean-field theory, which nicely captures the dynamics of $\overline{k}$. We further unveil a rich, $p$-dependent phase diagram, encompassing 47 real-world scale-free networks, shedding light on previously hidden patterns. This work opens avenues for understanding the universal properties of complex networks.

Urban systems often exhibit scale-invariant properties, with power-law distributions observed in various spatial and temporal patterns of human behavior. A prominent example is the distribution of commercial activities and other points of interest (POIs) across cities. However, the mechanisms by which such heavy-tailed behaviors emerge from local urban dynamics remain poorly understood. In this work we demonstrate that global inhomogeneity in the spatial distribution of POIs can arise from the aggregation of locally homogeneous processes. Using Foursquare data from the city of Bologna, we show that POI distributions exhibit clear power-law scaling when analyzed at city scale. We develop a theoretical framework in which this behavior naturally emerges from spatial clusters defined by shared intensity levels across disjoint areas, rather than spatial contiguity. By analytically and empirically linking these local processes to the observed global distribution, we provide a generative explanation for the emergence of scale-free patterns in urban commercial structure. To further relax the assumptions underlying the purely spatial model, and to account for the empirical observation that areas with similar activity intensity can be spatially disjoint, we introduce a hybrid hierarchical approach that combines spatial clustering with statistical heterogeneity across regions of comparable density, modeled via Poisson mixtures. This enables us to capture real-world deviations from local regularity while preserving interpretability. Our findings highlight a key insight: complex global phenomena in cities can arise from the spatial superposition of simple, locally uniform dynamics. This connection between microlevel homogeneity and macroscale complexity offers tools for interpreting, modeling, and classifying urban space.

This article deals with the experimental study of pedestrian behaviors in some situations of one-dimensional traffic. Participants were preorganized in a line and asked to walk either in a straight line with a fast or slow leader or to form a circle. The originality of our experimental protocol compared to previous ones on similar situations is to have left the condition of density free. While the observed density results from individual decisions in the line case, both density and velocity have to be collectively chosen in the case of circle formation. Our major findings are the following. In the case of circle formations, we observe that the resulting velocity is very stable among realizations, as if collective decision was playing the role of an average. For line flows with a slow leader, the same operating point close to the jamming transition is chosen as in previous experiments where it was not velocity but density that was imposed. In the less constrained line experiments, although participants could choose comfortable headways, they rather stuck to short headways requiring a faster adaption—a fact that could come from a “social pressure from behind” and had previously been observed only at high densities. This could be due to the uncertainty and individual responsibility that stem in less constrained situations. Our results open avenues for future research, as they show that the walking values preferred by humans in following tasks depend on more factors than previously considered.

We used filamentation of 940 nm, 90 fs, up to 6.5 mJ pulse to measure the spatial and spectral distributions of the second harmonic with ${10}^{-9}$ conversion efficiency in comparatively long focusing geometry (40 cm and 100 cm focal lengths, $\ge 1$ cm filament), as well as spectral distributions of the second harmonic with about an order of magnitude higher conversion efficiency in tight focusing geometry (8 cm focal length, $\sim 1\mathrm{mm}$ filament). Through integration of the vectorial second-order current over the $(t,r,z)$-simulated plasma channel, we identified the second-harmonic generation region, outside of which the $\omega \text{−}2\omega$ phase mismatch quenches the second-harmonic energy increment. The unified description of the even harmonic emission based on the vectorial second-order current shows that the two lobes of the terahertz beam broken along the laser polarization are oriented perpendicularly to the two lobes of the second harmonic beam, in agreement with the experiment.

There exist numerous problems in nature inherently described by finite $D$-dimensional states. Formulating these problems for execution on qubit-based quantum hardware requires mapping the qudit Hilbert space to that of multiqubit which may be exponentially larger. To exclude the infeasible subspace, one common approach relies on penalizing the objective function. However, this strategy can be inefficient as the size of the illegitimate subspace grows. Here we propose to employ the Hamiltonian-based quantum approximate optimization algorithm (QAOA) through devising appropriate mixing Hamiltonians such that the infeasible configuration space is ruled out. We investigate this idea by employing binary, symmetric, and unary mapping techniques. It is shown that the standard mixing Hamiltonian (sum of the bit-flip operations) is the optimal option within the standard universal gate set for symmetric mapping, where the controlled-NOT gate count is used as a measure of implementation cost. In contrast, the other two encoding schemes witness a $p$-fold increase in this figure for a $p$-layer QAOA. We apply this framework to quantum approximate thermalization and find the ground state of the repulsive Bose-Hubbard model in the strong and weak interaction regimes.