Mean squared displacement has been widely used as the primary metric for comparing quantum and classical random walks, with quantum walks showing quadratic scaling versus linear scaling for classical walks. However, this comparison may not capture the full picture: while the mean squared displacement is well suited for Gaussian distributions, quantum walk distributions exhibit distinctly non-Gaussian features. We propose that the mean hitting time offers a complementary perspective with clear operational meaning for search algorithms. Through analytical calculations, we show that quantum and classical walks yield identical MHT for symmetric initial conditions with two detectors, suggesting that the apparent quantum advantage seen in MSD comparisons may be context dependent. Interestingly, introducing stochastic resetting reveals more dynamics. We demonstrate analytically that quantum walks can achieve reduced MHT under stochastic reset through quasimomentum redistribution, while classical walks see no benefit. This quantum advantage naturally degrades with noise, and the quantum walk converges to classical behavior. We suggest that MHT reduction under stochastic reset can serve as an additional signature of quantum behavior, particularly useful for characterizing quantum walk implementations on noisy quantum devices. Our results indicate that different metrics can reveal different aspects of quantum-classical comparisons in walk-based algorithms.

We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here a tiling may concomitantly employ $K$-mers comprising any number $K$ of cells, provided a maximality constraint is satisfied. In essence, this constraint requires each of the $K$-mers in use to be as lengthy as possible, given its surroundings in the resulting tiling. Maximality aims to limit the variety of possible tilings while allowing for interesting behavior in terms of the statistical physical observables of interest. In fact, by introducing an energy function based on cell contacts and parametrizing it appropriately, we have been able to observe relatively unexpected behavior, including the suggestion of phase transitions as the system's temperature evolves.

We consider the scaling behavior of the fluctuation susceptibility associated with the average activation in the Greenberg-Hastings neural network model and its relation to microscopic spontaneous activation. We found that, as the spontaneous activation probability tends to zero, a clear finite-size scaling behavior in the susceptibility emerges, characterized by critical exponents which follow already known scaling laws. This shows that the spontaneous activation probability plays the role of an external field conjugated to the order parameter of the dynamical activation transition. The roles of different kinds of activation mechanisms around the different dynamical phase transitions exhibited by the model are characterized numerically and using a mean-field approximation. However, while mean-field approximations predict directed percolation critical exponents, numerical simulations on Watts-Strogatz networks provide critical exponents estimations which do not seem to agree with any known universality class.

We consider injection and subsequent acceleration of electrons in narrow plasma channels irradiated by linearly and radially polarized ultraintense laser pulses. Using three-dimensional particle-in-cell simulations, we show that radially polarized beams significantly promote electron release from the channel walls and lead to enhanced injection. We compare an $\mathrm{f}/10$ linearly polarized laser beam with two radially polarized cases: one focused more tightly ($\mathrm{f}/5$) to match peak intensity, and one at equal $\mathrm{f}/10$ to capture polarization effects. The radially polarized $\mathrm{f}/10$ case injects approximately one-third more charge than the linearly polarized case, while the $\mathrm{f}/5$ radially polarized case outperforms the linearly polarized one by about a factor of two in terms of maximum electron energy. This work provides a controlled three-dimensional comparison that clarifies how laser polarization and focusing geometry influence electron injection efficiency, acceleration pathways, and beam collimation in plasma channels.

Packing of charged micron-sized particles on surfaces is ubiquitous in both natural and industrial processes, where the packing structures critically determine system properties and performance. In practice, the materials of the surfaces can vary widely, giving rise to distinct particle-wall electrostatic interactions that drastically modulate the packing process. Therefore, we perform numerical simulations to study the packing of identically charged micron particles under different electric boundary conditions. We show that the maximum number of deposited particles is strongly influenced by particle-wall interactions, governed by the competition between incident particle kinetic energy and the repulsion from previously deposited particles. Furthermore, the resulting packing structures differ qualitatively: looser packings form near noninteracting or dielectric walls, whereas conducting walls yield much denser configurations. By quantifying energy changes induced by both deposited particles and other incoming particles, we identify two competing electrostatic mechanisms and derive an effective adhesion parameter that captures these effects in a unified framework. Our results highlight the critical role of particle-wall electrostatic interactions in predicting and controlling the packing behavior of charged particles.

The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with stochastic resetting drives a sharp dynamical phase transition: we show that the Lyapunov spectrum, i.e., the complete set of Lyapunov exponents, abruptly collapses to zero above a critical resetting rate. At criticality, we find a sudden loss of analyticity of the velocity-dependent Lyapunov exponent, which we relate to the transition from ballistic scrambling of information to an arrested regime where information becomes exponentially localized over a characteristic length diverging at criticality with an exponent $\nu =1/2$ and a dynamical exponent $z=2$. We illustrate our analytical results on generic chaotic dynamics by numerical simulations of coupled map lattices.

Time-integrated state observables, which quantify the fraction of time spent by the system in a specific pool of states, are important in many fields, such as chemical sensing or the theory of fluorescence spectroscopy. We derive exact identities, called fluctuation-response relations, that connect the fluctuations of such observables to their response to external perturbations in nonequilibrium steady state of Markov jump processes. Using these results, we derive an upper bound on fluctuations of state observables, as well as some lower bounds. We further demonstrate how our identities provide a deeper understanding of the mechanistic origin of fluctuations and reveal their properties dependent only on system topology, which may be relevant for model inference using measured data.

Recently, exact identities known as fluctuation-response relations (FRRs) have been derived for nonequilibrium steady states of Markov jump processes. These identities link the fluctuations of state or current observables to a combination of responses of these observables to perturbations of transition rates. Here, we complement these results by deriving analogous FRRs applicable to mixed covariances of one state and one current observable. We further derive inverse FRRs expressing individual state or current response in terms of a combination of covariances rather than vice versa. Using these relations, we demonstrate that the breaking of the Onsager symmetry requires the presence of state-current correlations. On the practical side, we demonstrate the applicability of FRRs for explaining the behavior of fluctuations in quantum dot devices or enzymatic reaction networks.

The frequency exponent of $1/f$ noise in graphene–boron nitride heterostructures is known to have multiple extrema in its dependence on the charge carrier concentration. This behavior is explained in the present paper as a result of the charge carrier trapping by impurities in the boron nitride. A kinetic equation for the charge carriers subject to trapping and interacting with acoustic phonons is derived. This equation is solved numerically, and the equilibrium solutions are used to evaluate the frequency exponent according to the quantum theory of $1/f$ noise. It is found that the frequency exponent does develop several minima and maxima, provided that the trapping probability is sufficiently wide and has a threshold with respect to the charge carrier energy. A detailed comparison with the experimental data is made, and the results are used to estimate the energy threshold and the trapping cross-section.

We investigate the tunneling mechanism in a rounded-step potential under a time-periodic perturbation, where instanton tunneling is substantially prohibited. The tunneling probability exhibits a characteristic sawtoothlike structure as a function of the inverse Planck's constant $1/\hslash$. This structure arises from the multiquanta absorption tunneling mechanism, specifically owing to the replacement of the dominant harmonic channel at every edge. Indeed, the replacement causes a sudden change in tunneling probability. Furthermore, the interference between the dominant and subdominant harmonic channels plays a crucial role in forming detailed properties, specifically probability oscillations superposed on the sawtooth structure. By employing a semiclassical approach, we show that the sawtooth structure is reproduced by the superposition of many complex branches, i.e., complex classical trajectories over many periods of the perturbation. The semiclassical decomposition of the wave operator to many complex branches is analogous to frequency decomposition and reproduces the sawtooth structure. We analyze the convergence of the semiclassical results to the quantum calculations as the number of time periods increases and elucidate the underlying mechanism of constructing the sawtooth structure from the viewpoint of semiclassics. Furthermore, the semiclassical method reproduces the probability oscillations induced by the interference between dominant and subdominant harmonic channels.

This research investigates the stability of localized charge modes in a Holstein-SSH DNA model incorporating a mass impurity. By deriving a semidiscrete nonlinear Schrödinger equation through Hamiltonian formalism and the adiabatic approximation, we analyze the modulational instability to assess the impact of impurity parameters on mode stability. Analytical results reveal that impurity mass significantly influences charge localization, especially near the Brillouin zone edges, with low coupling parameters favoring localized modes and higher values promoting charge delocalization. Numerical simulations confirm that the impurity's mass and sign critically affect energy and charge localization, with negative masses acting as potential wells and positive masses inducing dispersive effects. These findings highlight the crucial role of mass impurities in modulating charge transport in DNA, offering insights for designing biomolecular and nanotechnological systems with controlled electronic properties.

The collective behavior of numerous animal species, including insects, exhibits scale-free behavior indicative of the critical (second-order) phase transition. Previous research uncovered such phenomena in the behavior of honeybees, most notably the long-range correlations in space and time. Furthermore, it was demonstrated that the bee activity in the hive manifests the hallmarks of the jamming process. We follow up by presenting a discrete model of the system that faithfully replicates some of the key features found in the data, such as the divergence of correlation length and scale-free distribution of jammed clusters. The dependence of the correlation length on the control parameter, density, is demonstrated for both the real data and the model. We conclude with a brief discussion on the contribution of the insights provided by the model to our understanding of the insects' collective behavior.

We use confocal microscopy to image colloidal gels formed from highly polydisperse particles. We suspend our polydisperse particles in a density matched solvent, and let the particles spontaneously aggregate through the van der Waals force. The particle size distribution $P\left(R\right)$ is roughly log-normal, with the largest particles more than 15 times the size of the smallest particles. The pairing of nearest-neighbor particles is consistent with a null hypothesis that pairings are made randomly, that is, any two particle sizes have a probability of being neighbors consistent with their proportionality in $P\left(R\right)$. That being said, as expected, larger particles have more nearest neighbors than small ones. This leads to an over-representation of large particles in tetrahedral structures where four particles are mutually nearest neighbors, showing that large particles help provide rigidity to the gel structure. The tetrahedral structures also suggest that particles are able to rearrange during the gelation process, until their motion is stabilized by the multiple contacts with their neighbors. We discuss the implications of how other size distributions $P\left(R\right)$ would affect the gel structure.

Seismic interferometry retrieves inter-receiver Green's functions by correlating wave fields from distributed sources, but practical implementations differ in how amplitudes are handled. This study analyzes three correlation formulations—crosscorrelation, deconvolution, and crosscoherence—using a stationary-phase approximation to clarify how normalization choices affect direct and scattered waves. I show that crosscorrelation reproduces the causal and acausal Green's functions, with spurious terms canceling under the generalized optical theorem. In contrast, deconvolution and crosscoherence generate additional pseudo arrivals that do not correspond to physical propagation between receivers, and crosscoherence further modulates direct-wave amplitudes through scattering-dependent factors. A finite-difference numerical experiment with uniformly distributed, uncorrelated sources confirms these predictions: crosscorrelation reconstructs both direct and scattered arrivals, whereas deconvolution and crosscoherence produce late, unphysical phases while diminishing scattered-wave energy. These results clarify the kinematic content and limitations of amplitude normalization in interferometric processing and provide guidance for interpreting coda and scattered-wave signals and for designing filters that suppress pseudo arrivals.

In this work, we describe a possible mechanism to set the radial scale of zonal flows, which may be applicable to the $E\times B$ staircase found in the global full-$f$ simulations such as in Dif-Pradalier et al., [Phys. Rev. Lett. 114, 085004 (2015)]. One-dimensional numerical simulation results of the Cahn-Hilliard model—extended to include zonal flow friction—can be understood from a heuristic nonlinear analysis. The staircase step size $\mathrm{\Delta }$ is found to decrease as the dimensionless zonal flow friction $\mu$ increases. It scales like $\mathrm{\Delta }\sim log{\mu }^{\alpha }$, with $\alpha \simeq -0.41$, up to a constant offset.

We consider the dipolar spin ice on a 2D Apamea lattice whose geometry is derived from the square spin ice. We propose ground-state candidate configurations and show that not all vertices are in energetically favorable states. There is no macroscopic degeneracy of the ground-state candidate. By using the numerical Metropolis method, we demonstrate the existence of three phases of magnetic order and explain their origins. A good agreement between the Metropolis and XMCD experiment is demonstrated, and the improved Apamea lattice geometry for the experimental observation of the dynamics in the ordered state is proposed.

The token-based Brownian circuit harnesses the Brownian motion of particles for computation. The conservative join (CJoin) is a circuit element that synchronizes two Brownian particles, and its realization using repelling particles, such as magnetic skyrmions or electrons, is key to building the Brownian circuit. Here, a theoretical implementation of the CJoin using a simple quantum dot circuit is proposed, incorporating an internal state, a double quantum dot that functions as a one-bit memory, storing the direction of two-particle transfer. A periodic reset protocol is introduced, allowing the CJoin to emit particles in a specific direction. The stochastic thermodynamics under periodic resets identifies the thermodynamic cost as the work done for resets minus the entropy reduction due to resets, with its lower bound remaining within a few multiples of $k_{\mathrm{B}}T$ at temperature $T$. Applying the speed limit relation to a subsystem in bipartite dynamics, the number of emitted particles is shown to be relatively tightly bounded from above by an expression involving the subsystem's irreversible entropy production rate and dynamical activity rate.

Synchronization is a fundamental phenomenon in networked dynamical systems with applications ranging from power grids to biological networks. While much progress has been made in understanding synchronization in chaotic and periodic systems through the master stability function (MSF) framework, less attention has been given to systems exhibiting simpler attractors, such as fixed points or quasiperiodic (torus) behaviors. This paper addresses this gap by systematically analyzing the synchronization properties of coupled systems with point and torus attractors using the MSF approach. The results show that systems with point attractors can display an unexpected synchronization scenario in which stable synchrony can emerge in disjoint regions of the coupling parameter space. We propose a generalized classification scheme for synchronization types in such systems, drawing parallels to existing frameworks for chaotic and periodic oscillators. This study contributes to a more comprehensive understanding of synchronization behavior in complex networks.

Given an evolutionary model, such as Wright-Fisher or Moran, the $n\text{−}\mathrm{coalescent}$ problem consists of going backward in time to find, for example, the time to the most recent common ancestor (MRCA) and the topology of the tree. In the literature, this problem is mainly addressed by directly computing the random variable $t$, the time to reach the MRCA. It is shown here that by shifting the focus from the random variable $t$ to the joined variable $(n,t)$, where $n$ is the number of ancestors at time $t$, the problem is greatly simplified. Indeed, $P(n,t)$, the probability of this variable, obeys a simpler master equation that can be solved in a straightforward way for the most general model. This probability can then be used to compute relevant information of the $n\mathrm{coalescent}$ for both random variables $t_n$ (random time to reach a given state $n$) and $n_t$ (random number of ancestors at a given time $t$). The cumulative distribution function for $t_1$, for example, is $P(1,t)$. This article presents a unified framework for coalescent models—whether time continuous or time discrete—along with their explicit analytical solutions, expressed in terms of transition rates between states. The application of this method to the Moran model or the Kingman's coalescent, where the results are known, is provided for comparison.

An experimental investigation was conducted to explore the interplay of turbulence and noninertial effects introduced by off-axis rotation on isotropic-turbulence dynamics using tomographic particle image velocimetry. A cubic box, generating isotropic turbulence with the aid of eight mixers positioned at each corner, rotated with a turntable, was subjected to different rotational speeds. Particular focus was placed on the changes in distinct turbulence quantities, including the Kolmogorov, Taylor, and integral scales, as well as changes in the velocity spectra. An inspection within a central subregion featuring isotropic flow with nearly zero mean flow revealed distinct rotation-induced anisotropic effects. The analysis of the longitudinal and transverse autocorrelation functions indicated rotation-induced changes predominantly at larger scales. The compensated spectral counterparts demonstrated a scale-dependent response to rotation, where energy distribution exhibited minor changes at smaller scales and significant alterations at larger scales, affecting the extent of the inertial subrange. The inverse-turbulent Rossby number $R{o}_{\epsilon }^{-1}=2\mathrm{\Omega }\langle k\rangle /\epsilon$, where $\mathrm{\Omega }$ represents the rotational speed, $\langle k\rangle$ is the turbulence kinetic energy, and $\epsilon$ denotes the energy-dissipation rate, demonstrated a monotonic relationship between rotational speed and various turbulence characteristics. As the $R{o}_{\epsilon }^{-1}$ value increases, there is an increase in turbulence levels and the dissipation rate, while the Kolmogorov microscale, Taylor microscales, and integral scales decrease. Also, changes in the tangential direction were more significant than those in the vertical axis of rotation.