We explore interpretations of the power-law banded random matrix (PLBRM) ensemble as Hamiltonians of one-dimensional quantum many-body systems. We introduce and compare a number of labeling schemes for assigning random matrix basis indices to many-body basis vectors. We compare the physical properties of the resulting Hamiltonians, focusing on the half-system eigenstate bipartite entanglement entropy. We show and quantify how the different PLBRM phases (ergodic, weakly ergodic, localized), known from the single-particle interpretation, can be interpreted as entanglement transitions in the quantum many-body interpretation. For the weakly ergodic phase, where spectral edge and bulk eigenstates show distinct behavior, we perform a detailed scaling analysis to provide a quantitative picture of the boundaries between different types of entanglement scaling behaviors. In particular, we identify and characterize an intermediate set of eigenstates whose entanglement entropy have volume law scaling but nonvanishing deviation from the Page value expected for maximally ergodic states.

For statistics of rare events in systems obeying a large-deviation principle, the rate function is a key quantity. When numerically estimating the rate function, one is always restricted to finite system sizes. Thus, if the interest is in the limiting rate function for infinite system sizes, first, several system sizes have to be studied numerically. Here, rare-event algorithms using biased ensembles give access to the low-probability region. Second, some kind of system-size extrapolation has to be performed. Here, we demonstrate how rare-event importance sampling schemes can be combined with multihistogram reweighting. We study two ways of performing the system-size extrapolation, either directly acting on the empirical rate functions or on the scaled cumulant generating functions, to obtain the infinite-size limit. The presented method is demonstrated for a binomial distributed variable, a Markov process of random bits, and the largest connected component of Erdős-Rényi random graphs. Analytical solutions are available in all cases for direct comparison. It is observed in particular that phase transitions appearing in the biased ensembles can lead to systematic deviations from the true result.

Chimera states in coupled oscillator networks are paradigmatic examples of partial synchronization in nonlinear systems, with direct relevance to real-world network dynamics, such as neuronal dynamics. Since real-world networks are not isolated, but embedded in larger interacting systems, chimeras have also been studied under the influence of other networks and external signals. In particular, most prior work has treated periodic forcing of chimeras in the thermodynamic limit. As a consequence, it remains unclear how chimera states respond to external driving in finite-size networks, where they can spontaneously collapse into full synchronization. It is also largely unknown how realistic noisy drivers, rather than periodic signals, affect driver-response synchronization. To address these open questions, we drive a finite-size oscillator network that exhibits a chimera state with constant-angular-frequency phases and with the same phases superimposed with noise. We find that, for a specific range of angular-frequency mismatch and driving strength, we can entrain chimeras without causing them to collapse into full synchronization. Adding noise, in turn, reduces entrainment and facilitates collapses. As a real-world application of the driven chimera state framework, we also drive chimeras with phases from focal and nonfocal electroencephalography (EEG) signals recorded during seizure-free periods in patients with epilepsy. We observe that focal signals yield higher entrainment power, within-network coherence, and collapse power than nonfocal signals when the driver EEG's dominant frequency is close to the chimera's mean angular frequency. Away from this regime, nonfocal signals yield higher values of all three measures. The observed differences not only characterize focal and nonfocal signals, but may also provide additional insight into the seizure-free brain dynamics of epilepsy patients. In conclusion, beyond quantifying how external driving signals, with or without noise, affect the dynamics of chimera states that can collapse into full synchronization, this work further bridges the study of chimera states and epilepsy research.

We study an explosive percolation model in which a link is randomly added and neighboring nodes sequentially rewire their links to suppress the growth of large clusters. In this manner, the rewiring nodes spread outward starting from the initial node closest to the added link. We show that a discontinuous transition emerges even when the total number of rewiring nodes after each link addition is finite. This finding implies that adding a link using the information of the cluster sizes attached to a finite set of link candidates (local information) can lead to a discontinuous transition if link rewiring is allowed. This result thus extends the previous result that a discontinuous transition arises only when a link is added using the information of the cluster sizes attached to an infinite number of link candidates (global information) in the absence of rewiring.

Michaelis-Menten kinetics is one of the most recognized models in enzyme kinetics, crucial for understanding biochemical reactions in various metabolic processes. In this study, we perform a stochastic analysis of the Michaelis-Menten kinetics with inhibitory mechanisms, which significantly enriches the description of the reaction. Using the Fock space formalism, we reformulate the master equation into a Schrödinger-type form. We examine reversible inhibitions and analyze the averaged number of participating substances, identifying a stiffness behavior in all scenarios. For partial inhibition, we show that the formalism correctly captures the phenomenon of inhibitor-activator duality, where the inhibitor transition from pure inhibition role to functionally favors product formation. We calculate the first product formation time distribution, which characterizes the time statistic of the first product formation. An intermediate timescale emerges in addition to the two known regimes typically observed in first-passage problems. This timescale is associated with the introduction of new pathways by inhibitory mechanisms. Altogether, the results offer a perspective on inhibited enzymatic reactions and illustrate how the Fock space formalism can be applied to the analysis of low-copy-number chemical reactions.

Plasma, as a dispersive medium, is widely utilized to control the propagation of electromagnetic waves, particularly in structures such as plasma photonic crystals. Here we propose a plasma photonic crystal heterostructure (PPCH) by strategic integration of Lieb superlattice and honeycomb superlattice in dielectric barrier discharges. Flexible control over the structural geometry of the PPCHs has been achieved, enabling dynamic switching between frequency-selection function and optical switching function. An interesting alternative jumping behavior between upper Lieb superlattice and bottom honeycomb superlattice is observed. A phenomenological reaction diffusion model, with incorporation of spatial modulations, is developed to simulate the formation of various PPCHs. Our findings provide insights into the mechanisms of patterned discharges and offer new clues for designing tunable PPCHs, with potential applications in areas such as photoswitchs and microwave filters.

A theory of a new magnetodynamic effect describing the energy exchange between the degrees of freedom of a conducting cylinder moving in a helical magnetic field has been developed. The possibility of effectively converting the translational motion of the cylinder into its angular rotation around the system axis [translational-rotational conversion (TRC)] has been demonstrated. A connection between this effect and the formation of helical trajectories of electrons in undulators in free-electron lasers and the inverse Faraday effect has been revealed. In TRC, unlike many known effects associated with the interaction of a moving conductor with a magnetic field, the conductor has no electrical contact with any external circuit, which makes it especially attractive for various applications. The TRC is also possible in a magnetohydrodynamic flow moving along the axis of a helical magnetic field. The theory is formulated in the limit of large magnetic Reynolds numbers, which corresponds to a sufficiently fast motion of well-conducting objects. In this scenario, the dynamics of the system is described by a nonlinear pendulum equation or a nonlinear pendulum equation with a nonzero right-hand side. In the latter case, a system dynamic mode corresponding to phase lock can be implemented.

The frequency of word usage in major Western languages has exhibited small-amplitude regular cycles over the past two centuries. Using large linguistic and economic datasets that allow for long-term quantitative analysis, we demonstrate that these cycles of word usage organize into semantically coherent clusters that track, interact with, or precede macroeconomic rhythms. To explore the nature of this interaction, we develop a minimal mathematical model of word usage that incorporates a delay linked to collective attention. Parameter fitting reveals that word usage operates near a Hopf bifurcation, a critical regime associated with heightened sensitivity, uncovering a robust and specific coupling that manifests as oscillatory dynamics between language usage and economic activity. Our findings characterize language usage as a dynamical system operating at criticality, where the observed oscillations emerge from a robust coupling with large-scale economic fluctuations. These results position language not merely as a passive reflection of economic conditions, but as an active component in a coupled system that mirrors and interacts with macroeconomic dynamics.

This article presents an encoding for the quantum Lattice Boltzmann method algorithm using Carleman linearization. In contrast to previous articles [C. Sanavio et al., AVS Quantum Sci. 6, 023802 (2024); Phys. Fluids 37, 037123 (2025)], the encoding used allows for local collision rules while keeping a higher probability to obtain the correct result, which is of the order of ${10}^{-2}$. The algorithm scales as $O[{log}_2^2\left(N\right)+Q^3]$ at each time step with $N$ the number of lattice sites of the two-dimensional lattice and $Q$ the number of channels with a constant number of qubits when using dynamical circuits.

In quantum thermodynamics, understanding the interplay between locality, thermal constraints, and communication remains an open challenge. In this manuscript, we introduce local thermal operations and classical communication (LTOCC), an operational framework that unifies the distant laboratories paradigm with thermodynamic restrictions, defining the fundamental limits on transformations between spatially separated systems. We establish a hierarchy of LTOCC protocols, demonstrating inclusion relations between different levels and revealing their deep connection to semilocal thermal operations. To formalize this framework, we develop thermal tensors and bithermal tensors, extending stochastic and tristochastic tensors to thermodynamic settings and providing new mathematical tools for constrained quantum processes. Finally, we present limitations imposed by LTOCC on single- and multicopy CHSH scenario, demonstrating no violation in the former and a gap between thermal and athermal local operations in the latter with respect to their capability to detect entanglement.

An outstanding challenge in the field of topological insulators is the realization of nonlinear systems that support coherent traveling waves. Highly nonlinear lattices can suffer from significant radiation losses due to Peierls-Nabarro effects. In this work a nonlinear tight-binding model that supports robust traveling edge states is proposed and examined. This system possess a nontrivial local Chern topology and soliton-like states. When a traveling solitary wave collides with a stationary mode, the two are observed to interact inelastically. These results suggest future directions for the modeling, realization, and application of nonlinear Chern insulators.

Projective synchronization, a form of synchronization in which the state variables of the response system are proportional to those of the drive system via a constant scaling factor, was first predicted theoretically and verified numerically [Phys. Rev. Lett. 82, 3042 (1999)]. Here, we report the experimental realization of projective synchronization using coupled nonlinear electronic circuits based on Sprott oscillators. In the electronic circuit implementation, amplitude scaling emerges between the drive and response systems. The coupling preserves the shape of the chaotic attractor, while intrinsic heterogeneities in the experimental circuits induce switching between in-phase and anti-phase projective synchronization—both of which are the solutions of the system. Our results demonstrate the robustness of projective synchronization in physical hardware and establish a reconfigurable platform for exploring scalable synchronization in chaotic systems. These findings open avenues for potential applications in secure communications and signal processing.

In models of opinion dynamics, agents interact with each other and can change their opinions as a result of those interactions. One type of opinion model is a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents compromise their opinions with each other if their opinions are sufficiently similar. In studies of BCMs, researchers typically assume that interactions between agents occur at deterministic times. This assumption neglects an inherent element of randomness in social interactions, and it is desirable to account for it. In this paper, we study BCMs on networks and allow agents to interact at random times. To incorporate random-time interactions, we use renewal processes to determine social-interaction event times, which can follow arbitrary interevent-time distributions (ITDs). We establish connections between these random-time-interaction BCMs and deterministic-time-interaction BCMs. We analyze the quantitative impact of ITDs on the transient dynamics of BCMs and derive approximate governing equations for the time-dependent expectations of the BCM dynamics. We find that BCMs with Markovian ITDs have consistent statistical properties (in particular, they have the same expected time-dependent opinions) when the ITDs have the same mean but that the statistical properties of BCMs with non-Markovian ITDs depend on the type of ITD even when the ITDs have the same mean. We numerically examine the transient and steady-state dynamics of our BCMs with various ITDs on different networks, and we compare their expected order-parameter values and expected convergence times.

How a magnetic-bead-laden droplet is manipulated by a magnetic field remains a challenging topic of quantitative investigation. In this paper, we propose a theoretical model to investigate the equilibrium states of a magnetic-bead-laden droplet placed over either a bottomed superhydrophobic cylindrical hole or a bottomless one in the presence of an external magnetic field. The position, the contact angle, and the deflection angle of the droplet in equilibrium are obtained for the two systems by applying the principle of energy minimization. Two phase diagrams are constructed correspondingly for the two cases. It is found that a loss of stability exists, leading to a slipping off of the droplet down the bottomless hole.

We investigate the complex nonlinear dynamics of a quasi-one-dimensional single-component plasma confined in a time-dependent harmonic trap. The system is described as a fluid in a hydrodynamic framework, incorporating electrostatic and thermal effects. By applying a time-dependent variational method, with a Gaussian ansatz for the number density distribution, we reduce the plasma complexity to that of a system of ordinary differential equations and follow up with a systematic analysis of the corresponding Noether symmetries in three distinct regimes: electrostatic, thermal, and combined effects. For each studied case, proper conserved quantities are identified, including a generalized Ermakov-Lewis invariant. We illustrate our results in the antiproton and positron confinement problems.

Chiral environments can bias the diffusion of enantiomers, a phenomenon known as chiral diffusive asymmetry (CDA). Such asymmetry provides a potential route to chiral symmetry breaking (CSB), a central process in deracemization and the emergence of homochirality. Here, we combine a Kondepudi-type reaction scheme with reaction-diffusion simulations to demonstrate that CDA, when coupled to a spatially nonuniform concentration of an achiral precursor, can induce CSB even in the absence of an initial enantiomeric excess. The resulting handedness is determined by the precursor distribution, providing a control parameter that is more experimentally accessible than diffusion asymmetry itself. We identify a mechanism in which CSB arises through the nucleation and growth of chiral domains, fueled by the mean precursor concentration and guided by its gradient. We further show that a linear relation captures the balance between CDA and precursor distribution, enabling predictive control of CSB.

We investigate the capacity of a flat partially reactive patch of arbitrary shape to trap independent particles that undergo steady-state diffusion in the three-dimensional space. We focus on the total flux of particles onto the patch that determines its reactive capacitance. To disentangle the respective roles of the reactivity and the shape of the patch, we employ a spectral expansion of the reactive capacitance over a suitable Steklov eigenvalue problem. We derive several bounds on the reactive capacitance to reveal its monotonicity with respect to the reactivity and the shape. Two probabilistic interpretations are presented as well. An efficient numerical tool is developed for solving the associated Steklov spectral problem for patches of arbitrary shape. We propose and validate, both theoretically and numerically, a simple, fully explicit approximation for the reactive capacitance that depends only on the surface area and the electrostatic capacitance of the patch. This approximation opens promising ways to access various characteristics of diffusion-controlled reactions in general domains with multiple small well-separated patches. Direct applications of these results in statistical physics and physical chemistry are discussed.

The inner membrane of mitochondria presents folds, the cristae, which are the production place of ATP. This synthesis is catalized by transmembrane proteins and relies on a flow of protons confined to the surface of the membrane. We posit that, in turn, the proton flux shapes the crista membrane in a way that suits these proteins. To study this hypothesis, we model a crista as a spherical vesicle submitted to a diffusive proton gradient flowing from the poles to the equator. Using Helfrich model, we introduce a pH-dependent spontaneous curvature for the membrane and determine the shape of the vesicle, in the regime of small deformations. We show that the pH gradient can produce shapes featuring flat zones at the poles and curved zones at the equator. These correspond to the geometry of the proteins involved in the process. Based on biophysical arguments, we define a functionality score for the vesicle and construct a phase diagram identifying the zones of “well-functioning” cristae, which we compare to experimental measurements.

Energy partition between ions and electrons in collisionless shocks has been a long-standing unsolved fundamental physical question. We show that kinetic simulations of moderate Alfvénic Mach number, magnetized, collisionless shocks reveal rapid, faster-than-Coulomb, energy exchange between ions and electrons when the plasma is sufficiently magnetized. Using kinetic and multifluid models with counter-streaming ions, we identify resonances between electron whistler and ion magnetohydrodynamic waves that account for this rapid energy exchange.

We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong enough to prevent localization, i.e., extreme concentration on the fastest growing site. In the presence of an additional temporal noise in the growth rates, a third partially localized phase is predicted theoretically, using results from Derrida's random energy model. Such temporal fluctuations mitigate concentration effects, but do not make them disappear. We discuss our results in the context of population growth and wealth inequalities.