At low temperatures, glasses exhibit distinctive properties compared to crystalline solids. A notable example is the phonon echo, a phenomenon that motivated the two-level-system (TLS) model. This model has successfully explained many universal anomalies in glasses. Here, we extend the TLS framework to a multilevel system and show that phonon echoes persist when nonlinear energy structures and disorder are included. By incorporating virtual phonon exchange, we introduce many-body interactions between these multilevel systems, leading to nonequidistant energy spacings that enhance the echo signal. Interestingly, we find that phonon echo coherence within the TLS model is suppressed under many-body interactions, originating from the fixed natural frequency inherent to each TLS unit. In stark contrast, the multilevel-system model exhibits remarkable robustness against such interactions, arising from anharmonicity-induced frequency adaptability and multiple parallel transition channels. Even if one transition falls out of resonance, the remaining channels can still preserve quantum coherence collectively. Meanwhile, finite-temperature thermal fluctuations cause dephasing, resulting in a decay of echo amplitude over time. Analytical and numerical results, examined perturbatively in both semiclassical and quantum regimes, show consistent agreement. Our work validates this multilevel extension of the TLS framework and underscores the role of many-body interactions in low-temperature glassy dynamics.

We study the coplanar ground-state manifold of the kagome Heisenberg antiferromagnet using a phase-space network representation, in which nodes correspond to coplanar ground states and edges represent transitions generated by weathervane loop rotations. In the coplanar manifold, each configuration can be mapped to a three-coloring problem on the dual honeycomb lattice, where a weathervane mode corresponds to a closed loop of two alternating colors. By comparing networks that include all weathervane loops with networks restricted to elementary six-spin loops, we examine how energetic constraints shape phase-space structure. We find that connectivity distributions are sharply peaked in large systems, while restrictions to short loops reduce typical connectivity. Spectral properties further distinguish the two cases, with short-loop networks exhibiting Gaussian spectra and full networks displaying non-Gaussian features associated with correlated loop updates. Finally, a box-counting analysis reveals distinct finite-size geometric trends: short-loop networks show algebraic, fractal-like behavior, whereas full networks are more compact in graph distance due to longer-loop shortcuts. These results show that the hierarchy of weathervane loop rotations provides a direct link between microscopic constraints and emergent phase-space geometry in a frustrated magnet.

It has been observed in numerous experiments, simulations, and various theoretical studies that the spreading of particles can be modeled by the continuous-time random walk. We consider two widely used cases, namely Gaussian and discrete displacements, to compute the position distribution and demonstrate the emergence of exponential decay in the far tails when a bias is introduced. We further analyze the temporal rate function and the positional rate function to examine the convergence of the theoretical predictions. For Gaussian displacements, we also discuss the relationship between the position distributions with and without bias in different asymptotic limits.

Strong-anisotropy magnetic multilayers composed of two identical ferromagnetic layers separated by a nonmagnetic spacer are modeled by the Ising model including intralayer dipolar interactions and interlayer exchange coupling (IEC), where frustration emerges from the competition between interactions acting at different length scales. The effects of the IEC on the phase behavior are systematically analyzed by Monte Carlo simulations using the Wang-Landau (WL) and short-time dynamics (STD) methods. For a fixed identical ratio between exchange and dipolar constants, the temperature-IEC phase diagram at zero external magnetic field is determined. It is demonstrated that the layers reproduce the same low- and high-temperature phases as the bidimensional Ising dipolar model (IDM), namely, stripe domains and a tetragonal liquid phase, respectively. The continuous character of the transition line between these phases is independently confirmed by both WL and STD approaches. Remarkably, a scaling law for the reduced critical temperature is uncovered, characterized by a shift exponent close to the critical susceptibility exponent (γ) of the bidimensional IDM. This finding generalizes the scaling predictions previously reported for the order-disorder transition in short-range Ising bilayers to systems with long-range dipolar interactions. Furthermore, STD results reveal that the critical temperature increases monotonically with the IEC strength, reaching values up to twice the critical temperature of the IDM. This behavior demonstrates a strong IEC-induced enhancement of the thermal stability of the stripe phase, thereby extending the short-range bilayer scenario to the dipolar case. Finally, the estimated critical exponents appear to belong to the universality class of the corresponding bidimensional IDM.

In this work we study statistical properties of the extreme eigenstates of the randomly weighted adjacency matrices of random graphs. We focus on two random graph models: Erdős-Rényi graphs and random geometric graphs. Indeed, the adjacency matrices of both graph models are diluted versions of the Gaussian orthogonal ensemble (GOE) of random-matrix theory such that a transition from the Poisson ensemble (PE) to the GOE is observed by increasing the graph average degree 〈k〉. First, we write expressions for the spectral density in terms of 〈k〉 for the regimes below and above the percolation threshold. Then we show that the distributions of the largest λ_{1} and second-largest λ_{2} eigenvalues approach the Tracy-Widom distribution of type 1 for 〈k〉≫1, while 〈λ_{1}〉=sqrt[2〈k〉]. Additionally, we demonstrate that the distributions of the normalized distance between λ_{1} and λ_{2}, the distribution of the ratio between higher consecutive eigenvalue spacings, and the distributions of the inverse participation ratios of the extreme eigenstates display a clear PE-to-GOE transition as a function of 〈k〉. We conclude that any of these distributions can be effectively used to probe the delocalization transition of the graph models without the need of the full spectrum.

We investigate linear perturbations of an incompressible, weakly collisional, anisotropic plasma in the low frequency limit using an extended 16-moment fluid description that retains parallel and perpendicular heat fluxes. We identify a class of linear perturbations associated with a conserved thermomechanic invariant, a time independent, aperiodic structure involving coupled perturbations of heat fluxes, velocity, and magnetic field. In the standard CGL limit, where heat fluxes are neglected, no direct analog of this invariant exists. Retaining heat flux dynamics alters the linear structure of the system promoting third order velocity moments to autonomous variables and gives rise to a thermomechanic mode with coupled thermal, kinetic, and magnetic components. The associated perturbations are inherently localized, favoring compact, filamentary aperiodic structures. The thermomechanic invariant reveals a stationary sector of collisionless anisotropic plasma dynamics, characterized by a fixed algebraic polarization that enforces time independent relations among the relevant perturbation fields.

Neuromodulatory levels in the brain change moment to moment, yet are typically ignored in studies of neural criticality, where empirical support remains varied. Here we show in a biophysical network of bursting neurons that arousal acts as a mechanistic control parameter for a directed percolation phase transition. At intermediate arousal, neuronal activity exhibits peaked susceptibility, power-law avalanche size and duration distributions, universal shape collapse, and anomalous diffusion, jointly satisfying the hyperscaling relation of the 2+1-dimensional directed percolation universality class. Reanalyzing extracellular recordings in awake mice, we find that time-resolved susceptibility tracks pupil-inferred arousal as the model predicts. These results identify arousal as a physiological control parameter for neural criticality, offering a statistical-physics basis for the Yerkes-Dodson effect, and imply that arousal should be tracked at fine temporal resolution to obtain reliable empirical estimates of neural criticality.

Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale oscillations. The analysis and prediction of such dynamics are highly challenging, however, due to the combination of high-dimensionality, nonlinearity and delay. Here, we investigate how structural complexity and delayed feedback are associated with oscillatory dynamics in complex systems, and provide an analytical approach combining theoretical dimension reduction and data-driven prediction. We reveal that oscillations emerge from the interplay of structural complexity and delay, with reduced models uncovering their critical thresholds and showing that greater connectivity lowers the delay required for their onset. Our theory is empirically tested in an experiment on a programmable electronic circuit, where oscillations are observed once structural complexity and feedback delay exceeded the critical thresholds predicted by our theory. Finally, we deploy a reservoir computing pipeline to accurately predict the onset of oscillations directly from time-series data. Our findings deepen understanding of oscillatory regulation and provide useful insights into predicting dynamics in complex networks.

Membrane tethers are long, slender membrane tubes that transport biological cargo (proteins and viruses) and engineered materials (particles and drugs) in organelles, vesicles, and cells. Nanoparticles with enhanced bioavailability and reduced toxicity are attracting great attention in nanomedicine for their ability to target membrane tethers, particularly tunneling nanotubes, which share similar structures and functions with membrane tethers. Nevertheless, the molecular mechanisms that control the cooperative wrapping of nanoparticles within and on membrane tethers are not well understood. Our study aims to map the wrapping behavior and the associated membrane deformation for spherical nanoparticles entering and exiting membrane tethers (modeling both out-to-in and in-to-out wrapping). By integrating continuum membrane models and finite-element analysis, we systematically quantify how the equilibrium shapes, obtained via energy minimization, are governed by membrane spontaneous curvature, nanoparticle size, and interparticle distance. For out-to-in wrapping, the discontinuous binding-envelopment transitions between the nonwrapped and the complete-wrapped states are facilitated by long interparticle distances and small particle sizes, for which both the adhesion strengths and the energy barriers are low. For negative spontaneous curvature, however, the adhesion strengths are low while the energy barriers are high. The deformations of the contact lines that separate the membrane into the bound and unbound segments are larger for the shortest or the longest interparticle distances. For in-to-out wrapping, the stable partial-wrapped states are identified. In particular, the short interparticle distances lead to the discontinuous transitions between the shallow-wrapped and the deep-wrapped states. Negative spontaneous curvature, short interparticle distances, and large particle sizes favor the stable partial-wrapped states. Instead of aggregating into compact linear chains along the membrane tethers, the nanoparticles remain separated at well-defined lowest-energy positions. The deformations of the contact lines are slightly larger than those for out-to-in wrapping. The competition between the local curvature and the spontaneous curvature of the membrane gives rise to rich wrapping diagrams, and our numerically determined adhesion strengths are in agreement with the theoretical predictions. Our findings provide important insights into tether-nanoparticle interactions and offer guidelines for the design of functional nanomedicines.

We study the long-time dynamics of small even perturbations of the soliton in a one-dimensional quadratic nonlinear Klein-Gordon equation. The soliton possesses both an internal mode and an unstable mode. On a codimension-one manifold of fine-tuned initial data, the instability is suppressed and the internal mode decays slowly by transferring energy into the continuum. We show that this decay and the associated nonlinear frequency shift are accurately captured by a cubic resonant approximation, with the damping rate determined by a Fermi golden rule-type coefficient. This provides a quantitative description of an irreversible energy transfer from the internal mode to dispersive radiation.

We numerically investigate percolation of independent frictionless glued-sphere rodlike particles under gravity through a disordered static bed of larger spheres. We identify two distinct regimes: a trapping regime, where rods stop after percolating a limited distance in the bed and a passing regime, where rods percolate continuously with constant mean velocity. The transition between these regimes is governed by the length of the rod and the geometrical trapping threshold for spherical particles based on the rod diameter and the minimum pore throat diameter defined by three touching large spheres. The percolation velocity for all rod geometries, including the single sphere limit, collapses onto a single curve when scaled with the gravitational acceleration and the bed sphere diameter. The results also demonstrate that short rods percolate nearly twice as fast as long rods due to the geometric constraints associated with the disordered pore structure of the static bed. Consequently, long rods are more susceptible to trapping via specific contact configurations with the bed spheres, which differ from those for short rods. These results reveal how shape anisotropy introduces dynamical constraints and thresholds in granular percolation, with implications for predicting segregation in mixtures of nonspherical particles.

Let {ε_{i}}_{i=1}^{∞} represent the set of unfolded energy eigenvalues of a quantized billiard system. Then, the set {δ_{n}=ε_{n+1}-ε_{1}-n} may be considered as a finite time series of size M=n_{m}-n_{0}, in which n plays the role of a discrete time and δ_{n} fluctuates around zero. These random fluctuations are known to exhibit the 1/f^{α} noise characteristic, where α∈[1,2], the limit α=1(2) corresponding to a fully chaotic (regular) classical dynamics. Previously, the presence of 1/f^{α} noise in the δ_{n} statistics has been demonstrated in a family of billiards for which the classical phase space is divided (Kolmogorov-Arnold-Moser systems). Here, the δ_{n} statistics is further explored, so as to include two new features, namely, (i) nonchaotic full ergodicity and (ii) symmetry. Four billiard families, classified as type P and type S, are considered. The type-P families are comprised of polygonal billiards, which are never chaotic, but may exhibit a mixing classical dynamics characterized quantitatively through the position autocorrelation function decay exponent σ. A type-S billiard has a smooth boundary and, correspondingly, a divided phase space with normalized chaotic volume ρ_{c}. Possible correlations between the spectral noise parameter α and the classical quantities, σ for type-P and ρ_{c} for type-S domains, are numerically investigated. Spearman's rank correlation coefficients support that the quantum spectral exponent α scales with the classical quantities. In addition, one family in each class is C_{3} symmetric. In this case, singlets and doublets have different spectral statistics in the chaotic limit, namely, the singlet (doublet) subspectrum follows the Gaussian orthogonal ensemble (Gaussian unitary ensemble) of random matrices. Let α_{1}(α_{2}) be the noise exponent in a singlet (doublet) time series. Numerical calculations of Pearson's correlation coefficients show that α_{1} and α_{2} are compatible with each other for both type-S and type-P within symmetrical families in the regime 1<α<2.

We investigate quantum percolation in a honeycomb lattice with site dilution and random spin-orbit coupling. Using exact diagonalization combined with finite-size scaling analysis, we study the metal-insulator transition, extracting the quantum percolation threshold p_{q}, and the correlation-length exponent ν. In the absence of spin-orbit coupling, we find that p_{q} remains finite and demonstrate that the quantum threshold is significantly higher than the classical site-percolation threshold p_{c} of the honeycomb lattice. When spin-orbit coupling is present, the spectral statistics exhibit a crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble, reflecting the change in symmetry class. Simultaneously, the quantum percolation threshold shifts systematically to lower occupation probabilities, indicating that the spin-orbit coupling favors delocalization. For sufficiently strong spin-orbit coupling, p_{q} tends to saturate, while the critical exponent approaches the expected one of the two-dimensional symplectic universality class.

Plasma spectroscopy is a fundamental tool for diagnosing laboratory and astrophysical plasmas. Accurate interpretation of spectra depends upon precise modeling and comprehension of Stark broadening and other mechanisms affecting spectral lines. In this context, computer simulations have emerged as valuable tools, offering idealized experiments with well-defined conditions. Molecular dynamics simulations, in particular, excel at replicating the particle interactions within the plasma and their impact on the state of a radiating atom or ion. However, these simulations present challenges in tracking electron capture processes, since setting an unambiguous criterion to distinguish between bound and free electrons is not trivial. In this paper we introduce an algorithm that, within a classical framework, precisely identifies the scenario in which an electron is captured by an ion and then follows a stable orbit around it. The algorithm's applicability extends to emitters with charges Z≥1. The procedure enables the correct identification of valid time histories of the electric microfield perturbing the emitting ion, which will be used for subsequent line shape calculations. The ionization balance results obtained from the application of this algorithm are compared with an additional method based on the potential energy of the particles in the simulations and with atomic kinetic simulations. For both methods, we find good agreement, therefore validating the use of this approach.

We study numerically the enveloping ffunction 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 ffunction 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 ffunction of the order parameter of a thermal phase transition defies the monotonic behavior.