This paper explores the stochastic bifurcations of a birhythmic vibroimpact oscillator incorporating two types of fractional derivative elements under Gaussian white noise excitation. The analysis begins with a nonsmooth coordinate transformation of the state variables, followed by the application of the stochastic averaging method to derive analytical solutions. To validate the proposed approach, numerical simulations based on the Monte Carlo method are conducted, demonstrating excellent agreement with the analytical predictions. A key finding of this study is that the fractional orders, fractional coefficients, and restitution coefficient play a significant role in triggering stochastic P bifurcations within the system.

Population annealing is a variant of the simulated annealing algorithm that improves the quality of the thermalization process in systems with rough free-energy landscapes by introducing a resampling process. We consider the diluted Sherrington-Kirkpatrick Ising model using population annealing to study its efficiency in finding solutions to combinatorial optimization problems. From this study, we find an easy-hard-easy transition in the model hardness as the problem instances become more diluted and associate this behavior to the clusterization and connectivity of the underlying Erdős-Rényi graphs. We calculate the efficiency of obtaining minimum energy configurations and find that population annealing outperforms simulated annealing for the cases close to this hardness peak while reaching similar efficiencies in the easy limits. Finally, it is known that population annealing can be used to define an adaptive inverse temperature annealing schedule. We compare this adaptive method to a linear schedule and find that the adaptive method achieves improved efficiencies while being robust against final temperature miscalibrations.

We introduce a matrix version of the stochastic heat equation, the MSHE, and obtain its explicit invariant measure in spatial dimension $D=1$. We show that it is classically integrable in the weak-noise regime in terms of the matrix extension of the imaginary-time one-dimensional (1D) nonlinear Schrödinger equation, which allows us to study its short-time large deviations through inverse scattering. The MSHE can be viewed as a continuum limit of the matrix log-Gamma polymer on the square lattice introduced recently. We also show classical integrability of that discrete model, as well as of other extensions such as of the semi-discrete matrix O'Connell-Yor polymer and the matrix strict-weak polymer. For all these models, we obtain the Lax pairs of their weak-noise regime, as well as the invariant measure, using a fluctuation-dissipation transformation on the dynamical action.

Understanding collective self-organization in active matter, such as bird flocks and fish schools, remains a grand challenge in physics. Interactions that induce alignment are essential for flocking; however, alignment alone is generally insufficient to maintain group cohesion in the presence of noise, leading traditional models to introduce artificial boundaries or explicit attractive forces. Here we propose a model that achieves cohesive flocking through predictive alignment, in which agents predict their own future positions for each possible reorientation and adopt the orientation that maximizes a compromise between the number of neighbors and the degree of alignment with them. Implemented in a discrete-time Vicsek-type framework, this approach delivers robust, noise-resistant cohesion without additional parameters. In the stable regime, flock size scales linearly with interaction radius, remaining nearly immune to noise or propulsion speed, and the group coherently follows a leader under noise. These findings reveal how predictive strategies enhance self-organization, paving the way for a new class of active matter models blending physics and cognitivelike dynamics.

An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including those defined on irregular lattices, systems with frustration, and systems exhibiting partial orders, provided some degree of spin ordering is present. This approach offers a unified framework for investigating phase transitions in such complex systems. The associated critical exponents are estimated via finite-size scaling analysis and show good agreement with established values.

Quantum thermodynamic uncertainty relations establish fundamental trade-offs between the precision achievable in quantum systems and associated thermodynamic quantities such as entropy production or dynamical activity. While foundational, empirical demonstrations have thus far been confined to specific cases, either assuming time-reversal symmetry or involving particular measurement types, leaving the verification of their universal validity unrealized. This work leverages a quantum computer to present the first empirical verification of a general quantum thermodynamic uncertainty relation, valid for arbitrary dynamics and observables. We theoretically derive the relation, identifying survival activity as the pivotal thermodynamic quantity governing the precision bound. The verification is demonstrated on IBM's cloud-based quantum processor, which is treated as a real thermodynamic system. To achieve accurate results despite substantial device errors, we introduce a generic protocol for measuring survival activity and employ circuit reduction techniques based on the relation's properties. This strategy allows us to empirically measure survival activity for the first time and confirm the derived relation. Furthermore, the quantum computer's versatility enables the implementation of optimal observables, leading to the saturation of the relation and demonstrating the sharpness of our bound on a physical device. The method's broad applicability is further illustrated by verifying the trade-off for quantum time correlators. Our findings establish quantum computers as effective platforms for investigating fundamental thermodynamic trade-off relations.

Synchronization is a core issue in the study of complex systems. Hypergraphs-based synchronization has received much attention due to its superiority of capturing higher-order relationship between different units in complex systems. In simple hypergraphs, using a weighted method, hyperedges can be transformed into corresponding maximal cliques of appropriate size. This process simplifies the synchronization problem of higher-order complex networks, allowing synchronization on weighted networks. However, this approach is not suitable for nested hypergraphs. In this work, we focus on the case of diffusive coupling and propose a novel framework based on the master stability method to address this limitation. Specifically, we transform the nested hypergraph into a multilayer simple hypergraph, and further map it onto a multilayer weighted graph, allowing for an equivalent description of higher-order dynamics near the synchronization manifold. The core of this multilayer transformation method lies in its ability to preserve the interaction relationships within the nested hypergraph while simplifying its higher-order structure using layer-by-layer decomposition approach. Furthermore, through numerical experiments, this paper reveals the synchronization behaviors of nested hypergraphs under different coupling strengths, particularly phenomena such as synchronization reversals, cluster synchronization, complete synchronization, and amplitude death. The proposed method provides a new perspective and theoretical framework for understanding and analyzing synchronization dynamics in multilayer, nested structural networks.

Following a general heuristic approach, algebraic constraints are established between the parallel and perpendicular power-law exponents of nonaxisymmetric, highly aligned magnetohydrodynamic turbulence, both with and without a strong imbalance between the Elsässer variables. Such relations are universal for both regimes of weak and strong turbulence and are useful to predict the corresponding turbulent power spectra. For a scale-dependent alignment, a Boldyrev-type $-3/2$ perpendicular spectrum emerges transverse to the direction of alignment, whereas a $-5/3$ spectrum is obtained for the same if the alignment becomes scale-independent. However, regardless of the nature of alignment, our analysis consistently yields a $k_{\parallel }^{-2}$ spectrum commonly observed in both numerical simulations and in situ data of solar wind. In the appropriate limit, previously obtained algebraic relations and power spectra for axisymmetric MHD turbulence (Galtier, Pouquet, and Mangeney, Physics of Plasmas, 2005) are successfully recovered. Finally, more realistic relations capturing weak Alfvén turbulence (with constant $k_{\parallel }$) and the transition to strong turbulence are derived along with their corresponding power spectra.

We study the retrieval accuracy and capacity of modern Hopfield networks of with two-state (Ising) spins interacting via modified Hebbian $n$-spin interactions. In particular, we consider systems where the interactions deviate from the Hebb rule through additive or multiplicative noise or through clipping or deleting interactions. We find that the capacity scales as $N^{n-1}$ with the number of spins $N$ in all cases, but with a prefactor reduced compared to the Hebbian case. For $n=2$ our results agree with the previously known results for the conventional $n=2$ Hopfield network.

We perform a comprehensive numerical investigation of the coarsening kinetics of active Brownian particles modeled by the Active Model $\mathrm{B}+$ ($\mathrm{AMB}+$). This model was introduced by Tjhung et al. [E. Tjhung et al., Phys. Rev. X 8, 031080 (2018)] and is a generalization of Model B for a conserved order parameter, with two additional activity terms. These terms correspond to rotation-free current (of strength $\lambda$) and rotational current (of strength $\xi$). There is a range of $(\lambda ,\xi )$ values for which the system undergoes macroscale phase separation (MPS). In this case, the order parameter current develops a structured pattern consisting of alternating clockwise and anticlockwise loops along domain walls. These pairs are separated by nodal points where the current magnitude is very small. The mass transfer is driven by the overlap of loops on neighboring droplets. Thus, the mass has to undergo circular trajectories while transferring from smaller droplets to larger droplets. This slows down domain growth in comparison to Model B, where the current is transported by the shortest route between droplets. Thus, there is slower coarsening in $\mathrm{AMB}+$, with an asymptotic growth exponent of $1/4$. For another range of $(\lambda ,\xi )$ values, the system undergoes microscale phase separation ($\mu \mathrm{PS}$), i.e., it reaches a steady-state morphology characterized by a crystal of monodisperse droplets, whose size depends on the parameters. We present detailed results for the kinetics of MPS and $\mu \mathrm{PS}$ in $\mathrm{AMB}+$ with a critical composition, where the system undergoes spinodal decomposition.

In amorphous solids, the vibrational density of states shows an excess of modes over the Debye model, known as the boson peak, whose origin remains unclear. Studies suggest a link to quasi-localized nonphononic vibrations or "defects," but identifying them is challenging due to hybridization with phonons that renders methods based on localization properties, such as the participation ratio, unreliable. We introduce a practical method to separate hybridized phonons from localized vibrations and find that boson peak phonons hybridize with compact, two-dimensional defects exhibiting oscillatory pure shear deformations. These two-dimensional defects are also exposed by the procedure recently employed to identify stringlets (Y.-C. Hu et al. [Nat. Phys. 18, 669 (2022)]), suggesting that these may not be one-dimensional objects as speculated. Our work demonstrates the presence of localized defects at the boson peak frequency and provides a comprehensive characterization of their vibrational and geometric properties, resolving the tension between the concepts of quasi-localized quadrupolar defects and stringlets.

We study the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction in disordered systems, focusing on its static and dynamic behavior in one-, two-, and three-dimensional geometries. To model disorder, we introduce the fractional Laplacian, characterized by the Lévy index $\alpha <2$, into the problem Hamiltonian. Our results demonstrate that disorder, modeled phenomenologically through the Lévy index $\alpha <2$, significantly modifies the character of the RKKY interaction by suppressing and localizing Friedel oscillations, both statically and dynamically. As the disorder strength increases (i.e., as $\alpha$ decreases), the oscillations become increasingly localized, distorted, and rapidly damped. In the time domain, we show that dynamic spin-density excitations generated by magnetic impurities exhibit delayed and confined propagation in two dimensions, with significant attenuation at moderate distances. Our approach provides a unified framework for understanding indirect exchange interactions in disordered and low-dimensional systems such as diluted magnetic semiconductors like GaMnAs and InMnAs, which have significant implications for spintronic applications and magnetic quantum devices.

Recent work has shown that the entanglement of finite-temperature eigenstates in chaotic quantum many-body local Hamiltonians can be accurately described by an ensemble of random states with an internal $U\left(1\right)$ symmetry. We build upon this result to investigate the universal symmetry-breaking properties of such eigenstates. As a probe of symmetry breaking, we employ the entanglement asymmetry, a quantum information observable that quantifies the extent to which symmetry is broken in a subsystem. This measure enables us to explore the finer structure of finite-temperature eigenstates in terms of the $U\left(1\right)$-symmetric random state ensemble; in particular, the relation between the Hamiltonian and the effective conserved charge in the ensemble. Our analysis is supported by analytical calculations for the symmetric random states, as well as exact numerical results for the Mixed-Field Ising spin-$1/2$ chain, a paradigmatic model of quantum chaoticity.

We present a stochastic framework for describing the transition from regular to chaotic dynamics in quantum billiards by incorporating a background scale of fluctuations in the level spacing evolution. Analytic expressions for the nearest-neighbor spacing distribution and power spectral density accurately capture the behavior across integrable, chaotic, and mixed-dynamics regimes. Remarkably, our model predicts a plateau formation in the level repulsion strength as the system approaches chaos—a behavior related to the plasma model of many-body localization and freezing transitions in Gaussian free fields. Comparisons to numerical results for quantum limaçon and mushroom billiards confirm the reliable description of the complex crossover between order and chaos. Our approach provides a complementary perspective to microscopic methods, particularly valuable for understanding the emergence of non-Gaussian statistics and multiscale phenomena in the crossover regime.

A social network is often divided into many factions. People are friends within each faction, while they are enemies of the other factions, and even my enemy's enemy is not necessarily my friend. This configuration can be described in terms of a weak form of structural balance. Although weak balance explains a number of real social networks, which dynamical rule achieves it has remained relatively unexplored. In this work, we show that the answer can be found in the field of indirect reciprocity, which assumes that people assess each other's behavior and choose how to behave to others based on the assessment according to a social norm. We begin by showing that weak structural balance is equivalent to stationarity when the rule is given by a norm called ‘judging’. By analyzing its cluster dynamics of merging, fission, and migration induced by assessment error in complete graphs, we obtain the cluster size distribution in a steady state, which shows the coexistence of a giant cluster and smaller ones. This study suggests that indirect reciprocity can provide insight into the interplay between a norm that individuals abide by and the macroscopic group structure in society.

We numerically investigate the stability of universal properties at continuous phase transitions against perturbations of the Markov chain Monte Carlo algorithm used to simulate the system. We consider the three-dimensional XY model as a test bed, and both local (single-site Metropolis) and global (single-cluster) updates, introducing deterministic truncation-like perturbations and stochastic perturbations in the acceptance probabilities. In (almost) all the cases, we find a remarkable stability of the universal properties, even against large perturbations of the Markov chain Monte Carlo algorithm, with critical exponents and scaling curves consistent with those of the standard XY model within statistical uncertainties. Only for the single-cluster update with very large truncation error does something different happen, but large scaling corrections prevent us from precisely assessing the critical properties of the transition, and, in particular, to understand whether the critical behavior observed corresponds to a known universality class.

In two-dimensional nonmagnetic systems, the influence of strong correlations between random forces in the equations of motion for the components of the charge carrier momentum on electric conductivity is studied within the framework of the non-Markovian quantum Langevin approach. Analytical expressions for the electric conductivity tensor are obtained. The transverse component of the electric field at zero external magnetic field is predicted. The role of nondiagonal dissipative kernels and the non-Markovian effect in electric conductivity, orbital diamagnetism, quantum Hall effect and Shubnikov–de Haas oscillations is emphasized. The conditions for the dynamic growth of electric conductivity and the magnetic moment are analyzed.

Hyperbolic network models exhibit very fundamental and essential features, like small worldness, scale freeness, a high-clustering coefficient, and community structure. In this paper, we comprehensively explore the presence of an important feature, the core-periphery structure, in the hyperbolic network models, which is often exhibited by real-world networks. We focused on well-known hyperbolic models such as the popularity-similarity optimization model (PSO) and ${\mathbb{S}}^1\text{/}{\mathbb{H}}^2$ models and studied core-periphery structures using well-established methods. The observed core-periphery centralization values indicate that the core-periphery structure can be very pronounced under certain conditions. We also validate our findings by statistically testing for the significance of the observed core-periphery structure in the network geometry. This study extends network science and reveals core-periphery insights applicable to various domains, enhancing network performance and resiliency in transportation and information systems.

We investigate a variant of the two-state $q$-voter model in which agents update their states under a random external field (which points upward with probability $s$ and downward with probability $1-s$) with probability $p$ or adopt the unanimous opinion of $q$ randomly selected neighbors with probability $1-p$. Using mean-field analysis and Monte Carlo simulations, we identify an order-disorder transition at $p_c$ when $s=\frac{1}{2}$. Notably, in the regime of $p>p_c$, we estimate the time for systems to reach disordered state from consensus state and find the logarithmic scaling $T_{\text{dis}}\sim \mathcal{B}lnN$, with $\mathcal{B}=1/\left(2p\right)$ for $q=1$, while for $q>1$, $\mathcal{B}$ depends on both $p>p_c$ and $q$. We observe that disordering dynamics slow down significantly for nonlinear strengths $q$ between 2 and 3, independent of the probability $p$. However, when $s=0$ or $s=1$, the system is bound to reach consensus, with the consensus time scaling logarithmically with system size as $T_{\text{con}}\sim \mathcal{B}lnN$, where $\mathcal{B}=1/p$ for $q=1$ and $\mathcal{B}=1$ for $q>1$. Furthermore, in the limit of $p=0$, we derive a closed-form exit probability valid for arbitrary values of $q$ and demonstrate a finite-size scaling collapse. These results clarify how external cues and peer conformity jointly control ordering and disordering in binary opinion dynamics.