Interacting particles on graphs are routinely used to study magnetic behavior in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs typically remains limited to specific dynamics, or assumes cluster-free graphs for which standard approximations based on degrees and pairs are often reasonably accurate. Here, we propose a motif-based mean-field approximation that considers higher-order subgraph structures in large clustered graphs. Numerically, our equations agree with stochastic simulations where existing methods fail.

To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of large matrix dimension. We calculate the average probability $\langle P_{ab}\rangle$ for transition from scattering channel $a$ coupled to the first Hamiltonian to scattering channel $b$ coupled to the second Hamiltonian. Using only the assumption ${\sum }_{b^{\prime }}{T}_{b^{\prime }}\gg 1$ we find $\langle P_{ab}\rangle =P_a{T}_b/{\sum }_{b^{\prime }}{T}_{b^{\prime }}$. Here $P_a$ is the probability of formation of the tunneling channel or the transition state, and the $T_{b^{\prime }}$ are the transmission coefficients for channels $b^{\prime }$ coupled to the second Hamiltonian. That result confirms transition-state theory in its general form. For tunneling through a very thick barrier the condition ${\sum }_{b^{\prime }}{T}_{b^{\prime }}\gg 1$ is relaxed and independence of formation and decay of the tunneling process hold more generally.

Recently, Sá, Ribeiro, and Prosen [Phys. Rev. X 10, 021019 (2020)] introduced complex spacing ratios to analyze eigenvalue correlations in non-Hermitian systems. At present there are no analytical results for the probability distribution of these ratios in the limit of large system size. We derive an approximation formula for the Ginibre universality class of random matrix theory which converges exponentially fast to the limit of infinite matrix size. We also give results for moments of the distribution in this limit.

The transition to turbulence in pipes is characterized by a coexistence of laminar and turbulent states. At the lower end of the transition, localized turbulent pulses, called puffs, can be excited. Puffs can decay when rare fluctuations drive them close to an edge state lying at the phase-space boundary with laminar flow. At higher Reynolds numbers, homogeneous turbulence can be sustained, and dominates over laminar flow. Here we complete this landscape of localized states, placing it within a unified bifurcation picture. We demonstrate our claims within the Barkley model, and motivate them generally. Specifically, we suggest the existence of an antipuff and a gap-edge—states which mirror the puff and related edge state. Previously observed laminar gaps forming within homogeneous turbulence are then naturally identified as antipuffs nucleating and decaying through the gap edge. We also discuss alternatives to the suggested bifurcation diagram, which could be relevant for wall-bounded flows other than straight pipes.

The study of parametric instabilities has played a crucial role in understanding energy transfer to plasma and, with that, the development of key applications such as inertial confinement fusion. When the densities are between $0.11n_c\lesssim n_e\lesssim 0.14n_c$ and the electron temperature is in inertial confinement fusion-relevant temperatures, anomalous hot electrons with kinetic energies above $100\mathrm{keV}$ are generated. Here a new electron acceleration mechanism—the anti-Stokes Langmuir decay instability cascade of forward stimulated Raman scattering—is investigated. This mechanism potentially explains anomalous energetic electron generation in indirectly driven inertial confinement fusion experiments, it also provides a new way of accelerating electrons to higher energy for applications such as novel x-ray sources.

Although collisional electrostatic shock waves have been investigated extensively via theory, simulations, and experiments, there are comparatively few studies about collisional magnetized shock waves. We investigate collisional magnetized shocks by performing one-dimensional full particle-in-cell simulations that incorporate ion-ion, electron-electron, and ion-electron Coulomb collisions, for perpendicular and quasiparallel shock waves. The effect of Coulomb collisions is to drive a shock wave into a more laminar state. For a perpendicular shock, the magnetic overshoot becomes small because the electron pressure perpendicular to the magnetic field is isotropized and decreases due to electron-electron collisions. For the quasiparallel case, we find that ion-electron collisions severely suppress the standing whistler wave, which is present in the form of large amplitude waves in a collisionless shock wave.

Maxwell's demon is the quintessential example of information control, which is necessary for designing quantum devices. In thermodynamics, the demon is an intelligent being who utilizes the entropic nature of information to sort excitations between reservoirs, thus lowering the total entropy. So far, implementations of Maxwell's demon have largely been limited to Markovian baths. In our work, we study the degree to which such a demon may be assisted by non-Markovian effects using a superconducting circuit platform. The setup is two baths connected by a demon-controlled qutrit interface, allowing the transfer of excitations only if the overall entropy of the two baths is lowered. The largest entropy reduction is achieved in a non-Markovian regime and, importantly, due to non-Markovian effects, the demon performance can be optimized through proper timing. Our results demonstrate that non-Markovian effects can be exploited to boost the information transfer rate in quantum Maxwell demons.

In the literature of magnetic phase transitions, in addition to a critical point, the existence of another special point has been discussed. This is related to the broadening of the interface between two different ordering phases and is referred to as the point of roughening transition. While the equilibrium properties associated with this transition are well understood, the influence of this on nonequilibrium dynamics still needs to be investigated. In this paper we present comprehensive results, from Monte Carlo simulations, on coarsening dynamics in a system, over a wide range of temperature, in space dimension $d=3$, for which there exists a roughening transition at a nonzero temperature $T_R$. An advanced analysis of the simulation data, on structure, growth, and aging, shows that the onset of unexpected glasslike slow dynamics in this system, that has received attention in recent times, for quenches to zero temperature, actually occurs at this transition point. This implies that the structure and aging depend upon the final temperature, when the latter lies between 0 and $T_R$. This is a very interesting exception to universality in coarsening dynamics. The results also demonstrate an important structure-dynamics connection in the phase-ordering dynamics. We compare the key results with those from $d=2$, for which there exists no nonzero roughening transition temperature. The absence of the above-mentioned anomalous features in the latter dimension places our conjecture on the role of the roughening transition on a firmer footing.

Eukaryotic cells sense chemical gradients to decide where and when to move. Clusters of cells can sense gradients more accurately than individual cells by integrating measurements of the concentration made across the cluster. Is this gradient-sensing accuracy impeded when cells have limited knowledge of their position within the cluster, i.e., limited positional information? We apply maximum likelihood estimation to study gradient-sensing accuracy of a cluster of cells with finite positional information. If cells must estimate their location within the cluster, this lowers the accuracy of collective gradient sensing. We compare our results with a tug-of-war model where cells respond to the gradient by polarizing away from their neighbors without relying on their positional information. As the cell positional uncertainty increases, there is a trade-off where the tug-of-war model responds more accurately to the chemical gradient. However, for sufficiently large cell clusters or sufficiently shallow chemical gradients, the tug-of-war model will always be suboptimal to one that integrates information from all cells, even if positional uncertainty is high.

We describe simulations of active Brownian particles carried out to explore how dynamics and clustering are influenced by particle shape. Our particles are composed of four disks, held together by springs, whose relative size can be varied. These composite objects can be tuned smoothly from having a predominantly concave to a convex surface. We show that even two of these composite particles can exhibit collective motion which modifies the effective Peclet number. We then investigate how particle geometry can be used to explain the phase behavior of many such particles.

The coherence length of the medium-range order (MRO) in metallic liquids is known to display a Curie-Weiss temperature dependence; its inverse is linearly related to temperature, and when extrapolated from temperatures above the glass transition, the coherence length diverges at a negative temperature with a critical exponent of unity. We propose a mean-field pseudospin model that explains this behavior. Specifically, we model the atoms and their local environment as Ising spins with antiferromagnetic exchange interactions. We further superimpose an exchange interaction between dynamical heterogeneities, or clusters of atoms undergoing cooperative motion. The coherence length in the metallic liquid is thus the correlation length between dynamical heterogeneities. Our results reaffirm the idea that the MRO coherence length is a measure of point-to-set correlations, and that local frustrations in the interatomic interactions are prominent in metallic liquids.

Diffusion-mediated binding of molecules under the influence of discrete spatially confining potentials is a commonly encountered scenario in systems subjected to explicit fields or implicit fields arising from tethering restraints. Here, we derive analytical expressions for the mean binding time of two random walkers geometrically confined by means of two harmonic potentials in one- and two-dimensional systems, which show excellent agreement with Brownian dynamics simulations. As a demonstration of its utility, we use this theory to maximize the communication speed in existing DNA walkers, obtaining quantitative agreement with previously reported experimental findings. The analytical expressions derived in this paper are broadly applicable to diverse systems, providing ways to characterize communication processes and optimize the rate of signal propagation for sensing and computing applications at the nanoscale.

We propose a quantum harmonic oscillator measurement engine fueled by simultaneous quantum measurements of the noncommuting position and momentum quadratures of the quantum oscillator. The engine extracts work by moving the harmonic trap suddenly, conditioned on the measurement outcomes. We present two protocols for work extraction, respectively based on single-shot and time-continuous quantum measurements. In the single-shot limit, the oscillator is measured in a coherent state basis; the measurement adds an average of one quantum of energy to the oscillator, which is then extracted in the feedback step. In the time-continuous limit, continuous weak quantum measurements of both position and momentum of the quantum oscillator result in a coherent state, whose coordinates diffuse in time. We relate the extractable work to the noise added by quadrature measurements, and present exact results for the work distribution at arbitrary finite time. Both protocols can achieve unit work conversion efficiency in principle.

Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the universality class to which they belong. The associated prefactor has instead a nonuniversal amplitude fixed by the microscopic interplay between thermal fluctuations and disorder, usually hidden below experimental resolution. Here we compute numerically the roughness of a one-dimensional elastic interface subject to both thermal fluctuations and a quenched disorder with a finite correlation length. We evidence the existence of a power-law regime at short lengthscales. We determine the corresponding exponent ${\zeta }_{\text{dis}}$ and find compelling numerical evidence that, contrarily to available analytic predictions, one has ${\zeta }_{\text{dis}}<1$. We discuss the consequences on the temperature dependence of the roughness and the connection with the asymptotic random-manifold regime at large lengthscales. We also discuss the implications of our findings for other systems such as the Kardar-Parisi-Zhang equation and the Burgers turbulence.

In active ${\phi }^4$ field theories the nonequilibrium terms play an important role in describing active phase separation; however, they are irrelevant, in the renormalization group sense, at the critical point. Their irrelevance makes the critical exponents the same as those of the Ising universality class. Despite their irrelevance, they contribute to a nontrivial scaling of the entropy production rate at criticality. We consider the nonequilibrium dynamics of a nonconserved scalar field $\phi$ (Model A) driven out-of-equilibrium by a persistent noise that is correlated on a finite timescale $\tau$, as in the case of active baths. We perform the computation of the density of entropy production rate $\sigma$ and we study its scaling near the critical point. We find that similar to the case of active Model A, and although the nonlinearities responsible for nonvanishing entropy production rates in the two models are quite different, the irrelevant parameter $\tau$ makes the critical dynamics irreversible.

Nonequilibrium reaction networks (NRNs) underlie most biological functions. Despite their diverse dynamic properties, NRNs share the signature characteristics of persistent probability fluxes and continuous energy dissipation even in the steady state. Dynamics of NRNs can be described at different coarse-grained levels. Our previous work showed that the apparent energy dissipation rate at a coarse-grained level follows an inverse power-law dependence on the scale of coarse-graining. The scaling exponent is determined by the network structure and correlation of stationary probability fluxes. However, it remains unclear whether and how the (renormalized) flux correlation varies with coarse-graining. Following Kadanoff's real space renormalization group (RG) approach for critical phenomena, we address this question by developing a state-space renormalization group theory for NRNs, which leads to an iterative RG equation for the flux correlation function. In square and hypercubic lattices, we solve the RG equation exactly and find two types of fixed point solutions. There is a family of nontrivial fixed points where the correlation exhibits power-law decay, characterized by a power exponent that can take any value within a continuous range. There is also a trivial fixed point where the correlation vanishes beyond the nearest neighbors. The power-law fixed point is stable if and only if the power exponent is less than the lattice dimension $n$. Consequently, the correlation function converges to the power-law fixed point only when the correlation in the fine-grained network decays slower than $r^{-n}$ and to the trivial fixed point otherwise. If the flux correlation in the fine-grained network contains multiple stable solutions with different exponents, the RG iteration dynamics select the fixed point solution with the smallest exponent. The analytical results are supported by numerical simulations. We also discuss a possible connection between the RG flows of flux correlation with those of the Kosterlitz-Thouless transition.

Limit cycle oscillators have the potential to be resourced as reservoir computers due to their rich dynamics. Here, a Hopf oscillator is used as a physical reservoir computer by discarding the delay line and time-multiplexing procedure. A parametric study is used to uncover computational limits imposed by the dynamics of the oscillator using parity and chaotic time-series prediction benchmark tasks. Resonance, frequency ratios from the Farey sequence, and Arnold tongues were found to strongly affect the computation ability of the reservoir. These results provide insights into fabricating physical reservoir computers from limit cycle systems.

We propose local-biased random walks on general networks where a Markovian walker is defined by different types of biases in each node to establish transitions to its neighbors depending on their degrees. For this ergodic dynamics, we explore the capacity of the random walker to visit all the nodes characterized by a global mean first passage time. This quantity is calculated using eigenvalues and eigenvectors of the transition matrix that defines the dynamics. In the first part, we illustrate how our framework leads to optimal exploration for small-size graphs through the analysis of all the possible bias configurations. In the second part, we study the most favorable configurations in each node by using simulated annealing. This heuristic algorithm allows obtaining approximate solutions of the optimal bias in different types of networks. The results show how the local bias can optimize the exploration of the network in comparison with the unbiased random walk. The methods implemented in this research are general and open the doors to a broad spectrum of tools applicable to different random walk strategies and dynamical processes on networks.

Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e., linking individual particle positions across time series data. The state-of-the-art tracking algorithm is highly effective for systems in which the particles behave mostly independently. However, these algorithms become inaccurate when particle motion is highly correlated, such as in dense or strongly interacting systems. Accurate particle tracking is essential in the study of the physics of dense colloids, such as the study of dislocation formation, nucleation, and shear transformations. Here, we present a method for particle tracking that incorporates information about the correlated motion of the particles. We demonstrate significant improvement over the state-of-the-art tracking algorithm in simulated data on highly correlated systems.