The stationary equilibria of $N$ point vortices in a rectangular domain with doubly periodic boundary conditions offer a foundational framework for understanding the stationary lattices of coherent vortex structures. In this paper, we obtain new continuous families of these lattices. These solutions are constructed using methods from complex analysis including conformal mapping and special function theory. First, the doubly periodic rectangular domain is mapped to an annulus by a conformal mapping. Next, a loxodromic function is used to construct a solution consisting of stationary point vortices embedded in a smooth background vorticity field which is exponentially related to the stream function (Liouville-type background vorticity). This solution contains three continuous parameters, and by considering the limits of one of these parameters, a stationary point vortex solution without a background vorticity field is constructed. Until now, stationary point vortex solutions under doubly periodic boundary conditions have been mainly symmetric. Varying the other two parameters noted above, we generate families of asymmetric stationary point vortex lattices.

Wave-like spatial statistics in walking-droplet systems are often associated with wave-mediated interactions and wave-memory effects. Here we explore how similar statistical structure can arise from the low-dimensional nonlinear dynamics of an inertial active particle with internal degrees of freedom. In this framework, steady propulsion corresponds to internal-state fixed points whose spiral or transiently chaotic relaxation organizes oscillatory ensemble densities. Local perturbations then generate wave-like statistics in both open and closed geometries, suggesting that wave-like ensemble behavior may emerge more generally from internal-state attractor dynamics in inertial active matter.

The critical behavior of the equilibrium Ising model, famously governed by the Wilson-Fisher universality class (UC), is a cornerstone of statistical physics. A natural question is whether its properties are modified when the interacting spins are allowed to move. This can be explored within the framework of active motility by, e.g., prescribing that the spins self-propel along the direction of their orientation. In such a system, the spin number density necessarily constitutes a soft hydrodynamic mode and can therefore modify the scaling behavior. In this letter, we show that this is indeed the case in a critical active Ising model where density impedes the system's collective motion. Using a perturbative dynamic renormalization group analysis at a one-loop level, We identify six UCs, including three previously unidentified ones, one of which supersedes the Wilson–Fisher UC as the generic UC governing the critical behavior.

Fingerprint labyrinthine patterns exhibit a level of structural complexity beyond simple stripe phases, combining local stripe order with a dense network of pointlike defects. Unlike symmetry-breaking phases, where coarsening proceeds via diffusive defect annihilation, or conventional stripe phases, where curvature-driven motion of extended grain boundaries dominates, the coarsening of fingerprint labyrinths is governed primarily by localized junction and terminal defects. Using the Turing-Swift-Hohenberg equation, we study the nonequilibrium relaxation of fingerprint labyrinthine patterns following a quench. To go beyond conventional Fourier-based diagnostics, we employ a template-matching convolutional neural network to identify and track junctions and terminals directly in real space, enabling a quantitative characterization of defect statistics and spatial correlations. We show that, although these pointlike defects drive coarsening, their motion is strongly constrained by the surrounding stripe geometry, leading to slow, nondiffusive dynamics that are qualitatively distinct from both conventional phase ordering and stripe coarsening. Together, these results establish defect-mediated dynamics as the central organizing principle of fingerprint labyrinthine coarsening and demonstrate the effectiveness of machine learning–assisted approaches for complex pattern-forming systems.

Changing geometry creates its own overdamped thermodynamic anomaly. This is the geometric analog of the underdamped-overdamped anomaly known for Langevin systems in nonuniform or time-dependent temperature fields. We show this for Langevin dynamics in ${\mathbb{R}}^3$ under a time-dependent potential and a moving holonomic constraint. The moving constraint imposes a normal control velocity on the overdamped motion. Starting from a one-parameter family of underdamped parent models indexed by $\chi$, with exact hard constraints, we show that the small-mass overdamped limit leaves a finite geometric contribution proportional to the surface divergence of the control velocity. This term is absent from the naive overdamped heat-work split. It is therefore a genuine geometric anomaly. Once restored, it reorganizes the first law into a modified heat-work pair. On the heat side, the detailed fluctuation theorem recovers its Clausius form. On the work side, the Jarzynski equality is closed on effective work. The same identification also clarifies the relative-entropy balance. Our results identify changing geometry as a source of thermodynamic structure in the overdamped Langevin dynamics.

We study caging/trapping in Sokoban-type models, featuring a random walker moving through a disordered medium of obstacles and capable of pushing some obstacles blocking its path. In one-dimension, we allow the walker to push up to an arbitrary $N_{\mathrm{P}}$ number of obstacles. For $N_{\mathrm{P}}\gg 1$, we use large-deviation theory to show that the survival probability to remain uncaged exhibits crossover from an exponential decay with time at intermediate times to a stretched-exponential decay at long times, with an exponent $1/3$ independent of $N_{\mathrm{P}}$. The long-time exponent matches the Balagurov-Vaks-Donsker-Varadhan (BVDV) theory of the classical trapping problem, while the exponential decay is qualitatively distinct from the Rosenstock's intermediate-time theory for classical trapping. Similarly, in two dimensions, numerical simulations reveal that both the Sokoban model and its generalized version exhibit long-time stretched-exponential relaxation with exponent $1/2$, again consistent with the BVDV theory. Finally, in two dimensions, we find that the mean trap size is nonmonotonic in $\rho$: it is small at both low and high densities, but reaches a peak at a characteristic density ${\rho }_{*}$. We estimate ${\rho }_{*}\approx 0.55$ for the Sokoban model and ${\rho }_{*}\approx 0.675$ for the generalized Sokoban model.

We present a semianalytical method based on the backward master equation to find the optimal transition path time (TPT) of self-propelled run-and-tumble particles (RTPs) under stochastic resetting. The particle moves in a one-dimensional transition region $[x_A,x_B]$ with two absorbing boundaries. It resets at rate $\gamma$ to position $x_R$. Upon each resetting event, the particle either reverses its velocity direction with probability $\eta \in [0,1]$ or retains it with probability $1-\eta$. From the backward master equation we derive exact analytical results for the splitting probability, the mean TPT, and the coefficient of variation ($\mathrm{CV}$) of the TPT distribution. A semianalytical solution for the optimal TPT is also obtained. The mean TPT depends nonmonotonically on $\gamma , \alpha$, and $\eta$, reaching a minimum at optimal parameter values. For large transition regions, resetting the particle to its initial position can accelerate escape compared with reset-free dynamics. In the strong-resetting limit for $\eta >0$ when $x_R=x_A$, the probabilistic reversal upon resetting effectively replaces natural tumbling. The asymptotic TPT then becomes independent of the tumbling rate $\alpha$ and reduces to the ballistic traversal time $L/v$. A speed-reliability trade-off emerges: the parameters that minimize the mean TPT do not generally minimize the $\mathrm{CV}$. Efficient search requires balancing a short mean TPT against high predictability.

Random quantum states drawn from the Haar ensemble with a constraint on the energy expectation value $E_{\text{av}}=\langle \psi \left|H\right|\psi \rangle$ display eigenstate condensation: For $E_{\text{av}}$ below a critical value $E_{c-}$ or above $E_{c+}$, they develop macroscopic overlap with the ground state or anti–ground state. We use analytical calculations and state-of-the-art numerical methods to investigate the eigenstate condensation phase transition. We give compact expressions for the critical energies, derive an analytical scaling form for the order parameter in systems with an extensive free energy, show that in those systems the phase transition itself has exponential rather than power-law finite-size scaling, and test these results with large-scale numerical sampling in random matrices and a range of local spin Hamiltonians. In local spin systems the two critical energies approach the middle of the spectrum as $1/V$ with $V$ the number of spins. Our scaling form, however, demonstrates that the condensation phase transitions have exponential, rather than polynomial, finite-size scaling, which justifies treating the high-temperature phase as an extended phase.

We study numerically the enveloping $f$function of the fluctuation term in eigenstate thermalization hypothesis statement. We concentrate on the energy (or entropy) dependence of this function in two-dimensional systems. Our numerical results show that it is, in general, a monotonically increasing function of the entropy. This is in agreement with the general expectation that fluctuations increase with increasing entropy. We observe that the $f$function locally flattens with increasing system size. The flattening rate is directly proportional to the system size. We also observe that the flattening rate is directly proportional to the particle number for systems of same spatial size. This variation of the $f$ function is important for physics at subleading order of the system-size. So, it is relevant for intermediate-size systems (upto a few hundred qubits) which are experimentally accessible. One exception we find is that the $f$function of the order parameter of a thermal phase transition defies the monotonic behavior.

A wide range of real-world systems, ranging from physical and biological systems to social systems, can be described as temporal networks, where link temporality has profound effects on many dynamical processes taking place on networks. Here we study the susceptible-infected-susceptible model on temporal complex networks, where edges are randomly activated or terminated at each time step. We analytically obtain the epidemic threshold for temporal complex networks with arbitrary initial degree distributions. The approximate endemic equilibrium prevalence for temporal complex networks with arbitrary initial degree distributions is derived analytically for the system close to the epidemic threshold and far away from it. In addition, we demonstrate that the system undergoes a continuous transition from the disease-free state to the endemic state. Our results pave the way to understand how the degree distributions will affect a wide variety of binary-state dynamics on temporal complex networks.

Instabilities are a common occurrence in plasma discharges where they play an important role in system behavior and performance. While such instabilities are typically in the kHz and MHz range, this work reports a low frequency ($\sim 100\mathrm{Hz}$) instability observed in supersonic inductively coupled plasmas. Using a novel swirl gas injection, two concentric, counter-propagating vortices are produced that segment the flow field. While discharge properties only vary moderately within the outer vortex, intense plasma-gas heating leads to pressure fluctuations that drive a large-amplitude instability within the inner vortex. By adjusting the injection conditions, the instability can be damped or amplified.

Photochromic materials enable dynamic optical modulation through reversible transitions between distinct absorption states, with broad potential for smart windows, adaptive optics, and reconfigurable photonic devices. Micron-scale photochromic hybrid films present a particularly attractive platform for these applications, combining straightforward preparation with substantial optical modulation and scalability for high-volume fabrication. However, rational design of such films remains fundamentally constrained by the absence of well-defined optical constants. Unlike homogeneous thin films, micron-scale hybrid photochromic materials comprise active particles dispersed nonuniformly within polymer matrices. Conventional first-principles electromagnetic simulations face substantial computational costs and discrepancies between simulated and experimental particle distributions. Here, we introduce a data-driven framework that extracts effective optical constants directly from minimal experimental transmittance measurements. Our dual-state effective model approximates the complex inhomogeneous photochromic layer as a compressed homogeneous medium characterized by pseudorefractive indices and pseudoextinction coefficients for both pristine and UV-irradiated states. Through systematic optimization against experimental data from tungsten oxide–polyvinylpyrrolidone hybrid films, we determine wavelength-dependent pseudooptical constants and compression ratios that enable accurate prediction of optical modulation within the tested thickness range. Our methodology establishes a framework for engineering hybrid photochromic systems and demonstrates how data-driven modeling can overcome limitations in characterizing complex nanostructured materials.

We introduce a generalized version of the Biswas-Chatterjee-Sen (BChS) model [S. Biswas et al., Physica A 391, 3257 (2012)] with group interactions of size $q$, extending the original pairwise interaction dynamics. Within a mean-field framework, we derive an exact expression for the critical noise $p_c\left(q\right)$, showing that it increases monotonically with $q$ and approaches $1/2$ in the large $q$-limit, consistent with a Gaussian approximation. Despite this shift in the phase boundary, the critical behavior remains unchanged across all $q$: the order parameter scales as ${(p_c\left(q\right)-p)}^{1/2}$ and the relaxation timescale diverges as $|p-p_c{\left(q\right)|}^{-1}$, identical to the original BChS model [S. Biswas et al., Physica A 391, 3257 (2012)]. Finite-size scaling of the Binder cumulant, order parameter, and its fluctuations confirm that the system belongs to the mean-field Ising universality class for all $q$. Our results demonstrate that higher-order interactions modify the location of the transition without altering its universality class.

The critical behavior of the Baxter-Wu model belongs to the universality class of the four-state Potts model. While the introduction of annealed vacancies does not alter the criticality of the four-state Potts model, the dilute Baxter-Wu model has remained the subject of several competing scenarios. Here we investigate the phase diagram of the spin-1 Baxter-Wu model in the presence of a crystal field using transfer-matrix calculations and large-scale Monte Carlo simulations. Our results reveal a systematic evolution of the effective critical behavior with increasing crystal field, accompanied by increasingly strong finite-size corrections near the crossover to the first-order regime. Along the line of continuous transitions, the central charge remains close to $c=1$, while the scaling dimensions systematically deviate from the spin-$1/2$ limit as the crystal field increases, consistent with either continuously varying effective critical exponents or a slow crossover between competing critical behaviors. The first-order regime is independently characterized through multicanonical simulations, which confirm the expected finite-size scaling and interfacial behavior. Taken together, our results provide a unified picture of the dilute spin-1 Baxter-Wu model, substantially narrowing the range of possible scenarios for the crossover between continuous and first-order phase transitions.

When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets altered when transport is investigated on top of long-lived nonthermal states. Remarkably, for states noninvariant under parity we find the Burgers equation arising in the hydrodynamic limit. We explicitly compute the diffusion constant and nonlinear advective coefficient of the Burgers equation using a variant of the Chapman-Enskog theory. We find an excellent agreement between our theory and numerical simulations of a simplified model of stochastic two-body collisions. Our conclusions are based only on Galilean invariance, existence of a small system-bath coupling parameter, and a small momentum exchange between the system and the bath particles during two-body scattering.

We numerically revisit the transfer-matrix formulation of directed polymers in random media and show that a common finite-dimensional framework organizes the canonical one-point fluctuation laws in $(1+1)$ dimensions. For a fixed realization of the bulk disorder, full-space partition functions are obtained from the same time-ordered product $W\left(t\right)$ through endpoint contractions or a Brownian-weighted initial vector, while the half-space construction modifies only the transfer rule at the absorbing boundary. These choices yield distributions consistent with the standard KPZ subclasses: Tracy-Widom GUE for point-to-point geometry, Tracy-Widom GOE for point-to-line geometry, Tracy-Widom GSE for half-space point-to-point geometry, and Baik-Rains for the stationary line-to-point construction. In all four cases, the free-energy fluctuations grow as $t^{1/3}$, and the low-order cumulants approach the corresponding universal benchmarks. The matrix-product formulation also provides access to intrinsic spectral observables. For the leading eigenvalue ${\lambda }_1\left(t\right)$, the fluctuations of $ln{\lambda }_1\left(t\right)$ exhibit an intermediate $t^{1/3}$ regime, while the standardized distribution remains distinct from the canonical benchmark laws over the studied time range.

First-passage theory usually emphasizes when absorption occurs. Here, we instead treat where absorption occurs—the first-hitting location (FHL)—as a primary boundary observable of drift–diffusion processes. We formulate its law as the exit measure induced by the diffusion generator and recover its density from the normal derivative of an elliptic Green function. This yields exact half-space kernels in arbitrary ambient dimension $d$ for constant drift, with the two- and three-dimensional cases validated by Monte Carlo simulations. In the zero-drift limit, the kernels reduce to scale-free Cauchy-type laws with algebraic tails; drift introduces exponential screening and the characteristic length ${\ell }_u={\sigma }^2/\parallel \mathit{v}\parallel$, where $\sigma$ is the noise strength and $\mathit{v}$ is the constant drift vector, thereby localizing the boundary footprint. An entropy-based effective width provides a finite diagnostic of this crossover. To test the geometric reach of the planar theory, we also analyze drift-free exterior hitting of a circle. Its exact Poisson kernel recovers the planar Cauchy law as a local near-boundary limit, admits an exact Cauchy–Poisson composition through an intermediate line, and yields a finite-time supporting-line bound. These results organize geometry, drift, and pathwise constraints within a unified description of first-hitting location laws.

Synchronization of self-sustained oscillators under fixed frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow deterministic modulation of the drive amplitude or frequency can lead to a peculiar synchronization regime characterized by intermittent locking of the oscillation phase beyond the Arnold-tongue boundaries associated with fixed harmonic forcing. We test these predictions in a controllable aeroacoustic self oscillator, i.e., a whistle, that exhibits a robust limit cycle and is subject to external acoustic forcing with programmable frequency and amplitude modulation. Under both slowly varying frequency and amplitude of the forcing, three regimes are observed: (i) strict synchronization, (ii) intermittent synchronization, characterized by alternating phase-locking and brief phase-slip episodes, and (iii) no synchronization, with regular phase slips. Particularly in the strict synchronization regime, the phase of the oscillator will follow an arbitrary, slowly varying drive phase and under amplitude modulation its amplitude fluctuations are strongly suppressed.

Swarmalators are active agents that move in position space and exhibit internal degrees of freedom. Due to interactions of their positions and phases of oscillation, they show on the one hand swarming, similar to the effect of flocking of birds. In addition, they exhibit synchronization behavior, analogous to what has been observed in fireflies. Previous works studied scenarios in which the phases are forced externally. Here, we consider a pseudoforce that acts on the positions of the swarmalators. Due to the resulting attraction toward the center of position space, transitions from the splintered and active phase-wave state to the static asynchronized state are induced. To quantify the crystal order of swarmalators, we introduce an order parameter that is based on the Fourier transform of their positions.