We present results of experiments in which a subnanosecond high-power microwave pulse ($\sim 600$-MW peak power, 9.6 GHz, <1 ns) traverses a neutral He-filled waveguide (<2.6 kPa) in the presence and absence of an axial external magnetic field. The pulse ionizes the gas along its track forming a temporally and spatially dependent plasma density within its time frame. This plasma, when it becomes sufficiently dense, affects the pulse so that it becomes positively chirped, with higher frequency at its tail than at its front. This chirped pulse exits the gas-filled region and while it propagates through the vacuum waveguide, it compresses due to the waveguide dispersion. The highest power of compressed pulses obtained is $\sim 1.05$ GW with a pulse width of $\sim 0.26$ ns. The results indicate that the presence of an axial magnetic field has a favorable influence on the level of compression. To the best of our knowledge, this is the first time ionization-induced chirping and compression is observed experimentally when a microwave pulse propagates in a neutral gas-filled waveguide.

This article complements a recent experimental study [A. Haim et al., Phys. Rev. E 114, 045208 (2026)] in which high-power microwave subnanosecond pulses traverse a gas-filled circular waveguide and exit it as a chirped pulse. The reason for this phenomenon is that the ionization of the neutral gas propagates together with the microwave pulse and affects its frequency, resulting in a positively chirped pulse which becomes compressed as it propagates from a gas-filled section into an empty waveguide. In the present article, three-dimensional PIC Monte Carlo simulation results are reported that demonstrate this mechanism. A physical model is developed to explain this complex behavior, which agrees with the simulation results and supports the experimental observations.

Nonequilibrium conditions fundamentally change how systems undergo phase separation. In lattice gases with attractive interactions under temperature gradients, particles have been shown to form periodic patterns and steady convective currents; however, a clear theoretical explanation of this convective phase separation is still missing. Here we present a dynamical mean-field model that describes the mechanism behind this convective phase separation. Using linear stability analysis, we show that the transition from a uniform state to a periodic pattern is driven by the emergence of a dominant unstable mode. Numerical simulations confirm the predicted phase diagram and demonstrate that these convective currents are a robust feature of the steady state, appearing regardless of the initial conditions. These results provide a direct approach for understanding how temperature gradients drive the formation of steady-state convective patterns.

Reentrant transitions and temperature chaos are two unusual properties of spin glasses. We recently established a general logical relation between these two phenomena [Phys. Rev. E 112, 044140 (2025)]. In the present paper, we provide an explicit example of this logical relation in the fully connected Ising $p$-spin glass with a ferromagnetic bias. By expanding the free energy around the triple point, we show analytically that the ferromagnetic-spin glass boundary is reentrant in the vicinity of the triple point throughout the examined range of finite $p>2$. It then follows from the above logical relation that there exists at least one pair of distinct temperatures in the spin-glass phase for which the overlap of spin configurations vanishes. This is a necessary condition for temperature chaos, but it would be quite unusual for the overlap to vanish only for selected temperature pairs but not for others within a single spin-glass phase. These results therefore strongly suggest the existence of temperature chaos in the sense that the overlaps of spin configurations vanish for all temperature pairs throughout the spin-glass phase. Independent evidence for this behavior is provided by a two-temperature replica calculation.

Efficient coding of dynamical signals requires neural activity to balance information transmission against firing cost on the timescale of the input. We study this balance in a stochastic escape-rate population with membrane filtering, adaptation, and weak mean-field feedback. A cross-validated decoding rate is optimized against mean firing rate and sparse hazard complexity. Across eleven stimulus correlation times, the optimized rate varies nonmonotonically over the tested range rather than following a scale-free law: it is highest for inputs faster than the membrane timescale, reaches a local minimum at the membrane timescale, rebounds into a broad 5–6 Hz plateau, and falls for the slowest input. Switching-variance stimuli produce lower efficiency than stationary Gaussian stimuli and evoke transient rate changes after variance transitions. Sparse quadratic terms extend the low-rate Pareto front mainly through the interaction between membrane state and population activity. Under a matched restart budget, warm-started six-parameter searches reach a higher objective than direct six-parameter searches at nine of eleven input timescales. Null, spike-feature, finite-size, baseline-cost, and estimator checks support the stability of these comparisons. The results show how the relation between stimulus and intrinsic model timescales organizes the information-energy operating point.

Low-temperature spin dynamics can become trapped in long-lived patterns shaped by the geometry of the interaction network. We introduce Chladni states, the binary spin configurations obtained by applying the sign function to Laplacian eigenmodes, and show that their Ising energy collapses onto a size-independent spectral curve in ferromagnets and frustrated antiferromagnets. This graph-spectral decomposition reconstructs frozen configurations, tracks memory of initial conditions, and detects, through the number of modes it requires, the loss of mesoscopic order in frustrated and spin-glass regimes. Finally, in spin-glass instances, a restricted search over low signed-Laplacian modes reaches energies comparable to those of simulated annealing while exploring a space of far smaller dimension.

We investigate the purification dynamics of a single qubit under continuous-in-time monitoring. By employing a collisional model framework where the system interacts sequentially with ancillary qubits, we describe the conditioned evolution of the system's density matrix through a stochastic master equation. We show that for initial mixed states, the dynamics reduce to a multiplicative Langevin equation for a single scalar parameter representing the state's purity. This stochastic process is solved exactly using the Onsager-Machlup path-integral formalism, allowing us to derive the full probability distribution for the qubit's trajectories. Our analytical results reveal that purification is characterized by a dynamical crossover from a diffusion-dominated regime to a measurement-dominated regime, visible in the emergence of a bimodal state distribution. The analytical solutions are in strong agreement with numerical simulations, providing a robust theoretical benchmark for the study of information extraction in monitored quantum systems.

Fractional Brownian motion is a paradigmatic non-Markovian Gaussian process characterized by the Hurst exponent $H$. Despite its simple scaling form, extremal observables of fractional Brownian motion are notoriously difficult to analyze, and exact results are rare. We consider the mean of the maximum $M_H\left(1\right)={sup}_{0\le t\le 1}{B}_H\left(t\right)$ of standard fractional Brownian motion and put forward the conjecture $\langle M_H\left(1\right)\rangle =\frac{1}{H\sqrt{2\pi }},0<H\le 1$. The formula is exact for Brownian motion, $H=1/2$, and at the degenerate Gaussian endpoint $H=1$. We provide numerical evidence over a range of Hurst exponents and give a heuristic motivation based on a continuum form of the Kac-Spitzer identity. The main analytical test is obtained by comparing the conjecture with the perturbative density of the maximum derived by Delorme and Wiese for $H=1/2+\varepsilon$. After accounting for normalization conventions, the perturbative density gives $\langle M_{1/2+\varepsilon }\left(1\right)\rangle =\sqrt{\frac{2}{\pi }\phantom{{}^1}}\left(1-2\varepsilon \right)+O\left({\varepsilon }^2\right)$, in exact agreement with the first-order expansion of the conjecture. These results provide nontrivial support for a simple expression for an otherwise difficult non-Markovian extremal observable.

Quantifying the degree of order and disorder in many-particle systems remains an outstanding problem in physics, materials science, and mathematics. To this end, we consider the translational order metric ${\tau }_T$, defined as the squared $L^2$ norm of the total correlation function $h\left(\mathbf{r}\right)$, and introduce its bond-orientational analog ${\tau }_O$, defined from the weighted total correlation function $h_{\mathbf{f}}\left(\mathbf{r}\right)$ using local orientational weights [S. Torquato et al., Phys. Rev. X 16, 011042 (2026)]. Unlike conventional metrics that quantify either positional order or spatially averaged orientational order, the pair $({\tau }_T,{\tau }_O)$ places both forms of order on a common two-point statistical footing, with each sensitive to the amplitude and spatial persistence of the corresponding correlation function. The translational order metric ${\tau }_T$ vanishes for a Poisson point process, whereas the geometry-derived weights yield a small, construction-dependent positive reference value of ${\tau }_O$; each metric diverges in systems possessing its corresponding form of long-range order. We compute both metrics for two nonhyperuniform sphere-packing models in two and three dimensions as functions of packing fraction $\varphi$: (1) equilibrium hard particles along the stable fluid branches up to near freezing and at selected values of $\varphi$ along the stable crystal branches, and (2) nonequilibrium random sequential addition (RSA) packings from the dilute regime to just below saturation. For the nonhyperuniform systems, bond-orientational order remains subdominant along the equilibrium-fluid and RSA configurations; however, its magnitude relative to the translational metric increases near the upper end of the equilibrium-fluid branches, much more strongly in two than in three dimensions, and the two metrics become comparable along the sampled crystal branches. At common packing fractions, equilibrium fluids and RSA packings trace distinct $({\tau }_T,{\tau }_O)$ trajectories, revealing preparation-dependent differences in structural order. As a representative hyperuniform family, we study 2D disordered stealthy hyperuniform (SHU) ground states for $0<\chi <1/2$, where $\chi$ is the stealthiness parameter. Within the disordered SHU phase, bond-orientational order remains subdominant, but its magnitude relative to the translational metric increases toward the disorder-to-order threshold. In all three models, ${\tau }_T$ and ${\tau }_O$ are positively correlated beyond the Poisson-reference regime: ${\tau }_O$ increases monotonically with ${\tau }_T$ across the sampled state points. These metrics may ultimately serve as collective structural coordinates for mapping freezing, melting, glass formation, jamming, self-assembly, and driven nonequilibrium transitions, as well as for enhanced sampling, phase classification, and inverse design.

Frequency-dependent directed heat transport and heat-current reversal have been identified in nonlinear asymmetric lattices driven by a zero-mean thermal bias, but the microscopic dynamics associated with heat-current reversal remain incompletely understood. Here we introduce an eigenmicrostate-based approach to characterize the internal dynamical structure associated with heat-current reversal by constructing a kinetic-energy microstate matrix from steady-state trajectories and analyzing its dominant fluctuation patterns using singular-value decomposition and low-rank reconstruction. The results show that the kinetic-energy fluctuations near the reversal frequency are not dominated by a single isolated mode; rather, several low-order eigenmicrostates are enhanced concurrently, and the low-rank-reconstructed fluctuations exhibit stronger short-range spatial correlations near the reversal point. These results provide a microscopic structural picture of heat-current reversal in nonlinear lattices driven by a periodically modulated heat reservoir under zero-mean thermal bias and establish an eigenmicrostate-based framework for studying and controlling heat transport in low-dimensional systems.

Mixed-mode oscillations (MMOs) represent a fundamental type of complex rhythm in systems with multiple timescales. While their mechanisms are well-established in two-timescale settings, arising from either canard dynamics near folded singularities or a delayed Hopf bifurcation (DHB) of the fast subsystem, the transition to systems with three distinct timescales introduces a qualitatively richer landscape that remains poorly understood. Here, we investigate the mechanisms underlying MMOs in a general three-dimensional model with three timescales. We identify a novel scenario where folded-saddle canards and DHB coexist and interact synergistically to shape MMOs. Systematic timescale analysis reveals two distinct dynamical prototypes. In the 1-fast/2-slow regime, large-amplitude oscillations originate from a folded homoclinic bifurcation involving a folded saddle. In the 2-slow/1-superslow regime, “fold/Hopf” bursting is mediated by a supercritical Hopf bifurcation on the superslow manifold. Together, these two prototypes illustrate that MMOs in the three-timescale context are coregulated by canards and DHB mechanisms, with the timescale separation and the manifold geometry jointly tuning their relative dominance. This coexistence is related to a canard-delayed-Hopf singularity, where the folded saddle and the DHB converge in the double singular limit. This work provides a geometric picture of how distinct two-timescale mechanisms integrate into a three-timescale framework.

Demographic stochasticity in predator-prey (or activator-inhibitor) systems can generate persistent oscillations driven by intrinsic fluctuations, even when the corresponding deterministic mean-field descriptions exhibit only damped oscillations that vanish asymptotically as the system approaches a stable fixed point. Here we demonstrate that sustained stochastic oscillations may also emerge when the prey population responds deterministically to fluctuations in the predator population. In this framework, predator dynamics is governed by a stochastic process, whereas prey dynamics obeys an equation that is continuous in both time and population density, as expected in the limit of a large, homogeneous prey population. We compare the behavior of this hybrid stochastic-deterministic system with that of its mean-field counterpart and quantitatively characterize the resulting stochastic oscillatory regime, with particular emphasis on its dependence on the predator population size and the prey response time.

Diffusively coupled heterogeneous oscillators in large networks exhibit complex transitions between ordered and disordered states. Understanding the mechanisms governing the onset of disorder and the emergence of order in such systems remains a central challenge in nonlinear dynamics, statistical physics, and control theory. Here we investigate the collective dynamics of three ensembles of complex Ginzburg-Landau-type oscillators—antirotating, counterrotating, and uniformly rotating—coupled diffusively on a directed ring network. As the coupling strength increases, the system initially exhibits enhanced disorder before undergoing a discontinuous transition to a frequency-locked ordered state, accompanied by hysteresis upon reversing the coupling sweep. Disorder is quantified by the root-mean-square deviations of the frequencies and amplitudes, while ensemble-averaging theory provides analytical predictions for the mean dynamics that are in excellent agreement with numerical simulations. Further, we find that finite-size effects become increasingly pronounced as the network size increases, with the hysteresis width exhibiting a nonlinear, quadratic dependence on $N$. These results provide insight into the self-organization of heterogeneous, nonisochronous limit-cycle oscillators under unidirectional diffusive coupling in ring networks.

In the modern world, many prediction algorithms are based on data collected over a long time. Could we still use such an algorithm after a major change takes place? In the present study we explore predictability of events in order to see how it changes with system parameters if the prediction algorithm remains the same. We keep both the model and the algorithm simple enough to avoid unnecessary complexity and maximize the clearness of the presentation. We explore the chain model of coupled Kuramoto oscillators, whose typical state is synchronization. We consider a slowly oscillating forcing applied to the edges of the chain. The imposed symmetries allow the model to be represented by two key parameters: fragility and forcing amplitude. A special type of desynchronization event, namely, solitary decoherence, is the subject of prediction. We consider four precursors based on the order parameter and quantify the predictability by the sum of type I and type II errors. The study reveals four parametric zones of predictability. We suggest that the predictability of desynchronization events may be considered as a measure of complexity and is similar to the order parameter.

We numerically explore data-driven cluster-based control of a noisy Van der Pol oscillator, with the aim of elucidating the underlying feedback suppression mechanisms. The controller behavior is examined under three distinct conditions: a deterministic oscillator, an oscillator perturbed by additive white Gaussian noise, and an oscillator perturbed by correlated disturbances modeled by Ornstein–Uhlenbeck colored noise. Across all cases, we find that cluster-based actuation suppresses self-excited oscillations by reshaping the phase-space dynamics and steering the trajectories toward a stable equilibrium. Analysis of the cluster transitions reveals that this quenching is achieved by interrupting the natural limit-cycle progression at a small number of strategic switching clusters, a mechanism that persists even under substantial stochastic disturbances. The influence of a cost penalization parameter is further examined, revealing distinct regimes that balance oscillation suppression against actuation effort. These results provide mechanistic insight and practical guidance for the application of data-driven, model-free cluster-based control to nonlinear self-excited systems.

What are the fundamental limitations for finite-time engines that extract work from active nonequilibrium systems and what are the optimal protocols that approach them? We show that the finite-time work extraction for nonconservative overdamped Langevin systems may be rewritten as a Lorentz force Lagrangian action, with the kinetic term corresponding to a thermodynamic metric term that is an $L_2$-optimal transport cost for the time-dependent probability density, and the magnetic field coupling term corresponding to an effective quasistatic work extraction, proving that optimal protocols counterdiabatically steer the thermodynamic state trajectory to satisfy a Lorentz force law defined on thermodynamic state space. We utilize and reinterpret classic concepts from electromagnetism in the setting of cyclical nonequilibrium processes. We show that the housekeeping heat can be controlled to be arbitrarily close to zero by minimizing nonequilibrium fluctuations. It immediately follows from our results that the constant-velocity angle clamp protocol applied to the $F_1$ molecular motor in a recent experiment [T. Mishima et al., Phys. Rev. Lett. 135, 148402 (2025)] is, in fact, the globally optimal protocol: it produces zero housekeeping heat, while simultaneously minimizing dissipation and maximizing work transduction.

Anomalous diffusion is well studied in complex environments where viscoelasticity, crowding, and nonequilibrium activity strongly influence particle motion. Several biological systems are not independent; rather, they are coupled to another system, which shows distinct viscoelastic responses and heterogeneous transport behavior. We have developed a theoretical model of an active and a passive particle, coupled via a harmonic interaction, whose motion is restricted to a plane within a viscoelastic medium described by a generalized Langevin framework with a long-tailed power-law memory kernel. We obtained analytical expressions for the mean-squared displacement (MSD) and interparticle separation. We demonstrate that the coupled system shows multiple dynamical crossovers such as subdiffusive, ballistic, and diffusive transport regimes, whose emergence is controlled by the relative viscoelastic exponents and coupling strength. Specifically, we show that long-term dynamics is mainly controlled by the subdiffusive component, where the passive particle can suppress activity and the active particle can dominate and drive enhanced transport. Our results also highlight non-Gaussian displacement statistics at intermediate lag times. These findings provide insight into coupled transport in active matter systems, including tethered biomolecules, molecular motors, cytoskeletal networks, and synthetic microswimmers in complex media.

We analyze the critical temperature of the one-dimensional Ising model with inverse-square interactions. In the Anderson-Yuval-Kosterlitz (AYK) renormalization-group framework the transition temperature depends sensitively on the bare domain-wall fugacity, which is controlled by the domain-wall core energy. We replace the standard Euler-Mascheroni approximation for the core energy by a brute-force microscopic evaluation of domain-flip energies, thereby fixing the bare fugacity consistently with the microscopic Hamiltonian used in Monte Carlo simulations. With this input, integrating the AYK equations yields $T_c^{\mathrm{RG}}=1.557\left(3\right)$ (in units of the coupling). We then perform Monte Carlo simulations using a long-range cluster algorithm for system sizes up to $L=7.3\times {10}^4$ and analyze the full magnetization distribution $P_{L,T}\left(m\right)$. We show that near criticality, finite-size bimodality above $T_c$ produces a systematic upward bias in $\langle m^2\rangle$ and drives moment-based pseudocritical estimators (including Thouless-jump matching) to underestimate $T_c$. Using the peak of the modulus susceptibility $Q=\langle m^2\rangle -{\langle \left|m\right|\rangle }^2$ and Kosterlitz-Thouless (KT)/AYK finite-size scaling, we obtain $T_c^{\mathrm{MC}}=1.544\left(3\right)$ and argue that the residual offset from $T_c^{\mathrm{RG}}$ is consistent with slow KT-like finite-size drift and distributional contamination that decays only logarithmically with $L$.

The dynamics of symmetric cyclically competing subpopulations is well known to lead to oscillatory dynamics. However, in some situations the competition is fundamentally asymmetric in that it is better modeled by binary interactions all of which involve the same subpopulation. Here we analyze a conceptual model of this second kind, motivated by design principles for communications networks where binary interactions inform decisions made by individual transmitters according to their competing operating policies, which may be to reduce overall network energy consumption, to improve coverage, or to limit interference between transmitters. We show that the mean-field dynamics in the asymmetric case always converges to equilibrium and cannot generate periodic oscillations. However, for a large but finite population of interacting agents, the intrinsic noise generated by the stochastic dynamics contains a dominant positive frequency component. We also analyze the robustness of the system to cyclically competing switching.