We study computationally the dynamics of forced, Brownian particles through a disordered system. As the concentration of mobile particles and/or fixed obstacles increase, we characterize the different regimes of flow and address how clogging develops. We show that clogging is preceded by a wide region of anomalous transport, characterized by a power law decay of intermittent bursts. We analyze the velocity distribution of the moving particles and show that this abnormal flow region is characterized by a coexistence between mobile and arrested particles, and their relative populations change smoothly as clogging is approached. The comparison of the regimes of anomalous transport and clogging with the corresponding scenarios of particles pushed through a single bottleneck show qualitatively the same trends highlighting the generality of the transport regimes leading to clogging.

A quantum thermal device based on three nearest-neighbor coupled spin-1/2 systems controlled by the magnetic field is proposed. We systematically study the steady-state thermal behaviors of the system. When the two terminals of our system are in contact with two thermal reservoirs, respectively, the system behaves as a perfect thermal modulator that can manipulate heat current from zero to specific values by adjusting magnetic-field direction over different parameter ranges, since the longitudinal magnetic field can completely block the heat transport. Significantly, the modulator can also be achieved when a third thermal reservoir perturbs the middle spin. We also find that the transverse field can induce the system to separate into two subspaces in which neither steady-state heat current vanishes, thus providing an extra level of control over the heat current through the manipulation of the initial state. In addition, the performance of this device as a transistor can be enhanced by controlling the magnetic field, achieving versatile amplification behaviors, in particular substantial amplification factors.

Recent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose minimization guarantees the accurate EP estimation. In this study we show that there exists a host of loss functions, namely, those implementing a variational representation of the $\alpha$-divergence, which can be used for the EP estimation. By fixing $\alpha$ to a value between $-1$ and 0, the $\alpha \text{−}\text{NEEP}$ (Neural Estimator for Entropy Production) exhibits a much more robust performance against strong nonequilibrium driving or slow dynamics, which adversely affects the existing method based on the Kullback-Leibler divergence $(\alpha =0)$. In particular, the choice of $\alpha =-0.5$ tends to yield the optimal results. To corroborate our findings, we present an exactly solvable simplification of the EP estimation problem, whose loss function landscape and stochastic properties give deeper intuition into the robustness of the $\alpha \text{−}\text{NEEP}$.

We investigate thermal and quantum phase transitions of the $J_1\text{−}{J}_2\text{−}{J}_3$ transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling ($J_3$) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic $J_3$ gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic $J_3$. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

Suppression of noise and vibration suppression is important in various fields, such as the living environment, industrial development, and national defense and security. The bandgap properties of phononic crystal metamaterials provide an approach for controlling and eliminating harmful vibrations in equipment and noise in the environment. In this study, we used two types of two-dimensional honeycomb gyroscopic metamaterials: free and constrained. The dynamic equations of the two systems were established using angular momentum and Lagrange theorems. The dispersion relations of the two systems were obtained based on the Bloch theorem, and the influence of the gyroscope angular momentum or gyroscope speed on the dispersion relations was analyzed. Numerical simulations were conducted to analyze the wave propagation characteristics and polarization under different excitation conditions in a limited space for both types of metamaterial structures. The constrained-type and free-type metamaterials were compared, and the regularities of the dispersion relations and wave propagation characteristics by the gyroscope effect were summarized. This study provided a comprehensive and in-depth understanding of the bandgap and wave propagation properties of gyroscopic metamaterials and provided ideas for the design of bandgap modulation in metamaterials.

In two-component nonlinear Schrödinger equations, the force exerted by incident monochromatic plane waves on an embedded dark soliton and on dark-bright-type solitons is investigated, both perturbatively and by numerical simulations. When the incoming wave is nonvanishing only in the orthogonal component to that of the embedded dark soliton, its acceleration is in the opposite direction to that of the incoming wave. This somewhat surprising phenomenon can be attributed to the well-known negative effective mass of the dark soliton. When a dark-bright soliton, whose effective mass is also negative, is hit by an incoming wave nonvanishing in the component corresponding to the dark soliton, the direction of its acceleration coincides with that of the incoming wave. This implies that the net force acting on it is in the opposite direction to that of the incoming wave. This rather counterintuitive effect is a yet another manifestation of negative radiation pressure exerted by the incident wave, observed in other systems. When a dark-bright soliton interacts with an incoming wave in the component of the bright soliton, it accelerates in the opposite direction; hence the force is pushing it now. We expect that these remarkable effects, in particular the negative radiation pressure, can be experimentally verified in Bose-Einstein condensates.

Scaled Brownian motions (SBMs) with power-law time-dependent diffusivity have been used to describe various types of anomalous diffusion yet Gaussian observed in granular gases kinetics, turbulent diffusion, and molecules mobility in cells, to name a few. However, some of these systems may exhibit non-Gaussian behavior which can be described by SBM with diffusing diffusivity (DD-SBM). Here, we numerically investigate both free and confined DD-SBM models characterized by fixed or stochastic scaling exponent of time-dependent diffusivity. The effects of distributed scaling exponent, random diffusivity, and confinement are considered. Different regimes of ultraslow diffusion, subdiffusion, normal diffusion, and superdiffusion are observed. In addition, weak ergodic and non-Gaussian behaviors are also detected. These results provide insights into diffusion in time-fluctuating diffusivity landscapes with potential applications to time-dependent temperature systems spreading in heterogeneous environments.

This paper solves in one and two dimensions the steady noninteractive active Fokker-Planck (FP) equation and finds that its velocity distribution admits, under limiting cases, a dual behavior. Briefly, when the inertial relaxation time is smaller than the orientation time, the active FP equation admits a bimodal shape, whereas the inverse condition is seen to admit a Gaussian one. Once the velocity distribution functions are available, they are used to find their effect on the system's transport properties, such as its mean-square speed. In the process, a useful mathematical identity for the first kind Bessel function as a sum of bimodal exponential functions is spotted.

The existence of neutral species carries profound ecological implications that warrant further investigation. In this paper, we study the impact of neutral species on biodiversity in a spatial tritrophic system of cyclic competition, in which the neutral species are identified as the fourth species that may affect the competition process of the other three species under the rock-paper-scissors (RPS) rule. Extensive simulations showed that neutral species can promote coexistence in a high mobility regime within the system. When coexistence occurs, we found that the state can be maintained by two mechanisms: Species can either (i) adhere to traditional RPS rule or (ii) form patches to resist invasion. Our findings might aid in understanding the impact of neutral species on biodiversity in ecosystems.

The macroscopic fundamental diagram (MFD) is a large-scale description of the traffic in an urban area and relates the average car flow to the average car density. This MFD has been observed empirically in several cities but how its properties are related to the structure of the road network has remained unclear so far. The MFD displays in general a maximum flow $q^{*}$ for an optimal car density $k^{*}$ which are crucial quantities for practical applications. Here, using numerical modeling and dimensional arguments, we propose scaling laws for these quantities $q^{*}$ and $k^{*}$ in terms of the road density, the intersection density, the average car size and the maximum velocity. This framework is able to explain the scaling observed empirically for several cities in the world, such as the scaling of $k^{*}$ with the road density, the relation between $q^{*}$ and $k^{*}$ and the impact of buses on the overall capacity $q^{*}$. This work opens the way to a better understanding of the traffic on a road network at a large urban scale.

One of the central problems in epigenetics is how epigenetic modification patterns and chromatin structure are regulated in the cell nucleus. The polymer Potts model, a recently studied model of chromatins, is introduced with an offset in the interaction energy as a parameter, and the equilibrium properties are investigated using the mean-field analysis of the lattice model and molecular dynamics simulations of the off-lattice model. The results show that in common with both models, a phase emerges, which could be called the compact-disordered phase, in which the polymer conformation is compact and the epigenetic modification pattern is disordered, depending on the offset in the interaction energy and the fraction of the modified nucleosomes.

Recently we introduced the active Dyson Brownian motion model (DBM), in which $N$ run-and-tumble particles interact via a logarithmic repulsive potential in the presence of a harmonic well. We found that in a broad range of parameters the density of particles converges at large $N$ to the Wigner semicircle law as in the passive case. In this paper we provide an analytical support for this numerical observation by studying the fluctuations of the positions of the particles in the nonequilibrium stationary state of the active DBM in the regime of weak noise and large persistence time. In this limit we obtain an analytical expression for the covariance between the particle positions for any $N$ from the exact inversion of the Hessian matrix of the system. We show that, when the number of particles is large $N\gg 1$, the covariance matrix takes scaling forms that we compute explicitly both in the bulk and at the edge of the support of the semicircle. In the bulk the covariance scales as $N^{-1}$, while at the edge it scales as $N^{-2/3}$. Remarkably we find that these results can be transposed directly to an equilibrium model, the overdamped Calogero-Moser model in the low-temperature limit, providing an analytical confirmation of the numerical results obtained by Agarwal et al. [J. Stat. Phys. 176, 1463 (2019)]. For this model our method also allows us to obtain the equilibrium two-time correlations and their dynamical scaling forms both in the bulk and at the edge. Our predictions at the edge are reminiscent of a recent result in the mathematics literature in Gorin and Kleptsyn [arXiv:2009.02006 (2023)] on the (passive) DBM. That result can be recovered by the present methods and also, as we show, using the stochastic Airy operator. Finally, our analytical predictions are confirmed by precise numerical simulations in a wide range of parameters.

The mechanical strain can control the frequency of two-level atoms in amorphous material. In this work, we would like to employ two coupled two-level atoms to manipulate the magnitude and direction of heat transport by controlling mechanical strain to realize the function of a thermal switch and valve. It is found that a high-performance heat diode can be realized in the wide piezo voltage range at different temperatures. We also discuss the dependence of the rectification factor on temperatures and couplings of heat reservoirs. We find that the higher temperature differences correspond to the larger rectification effect. The asymmetry system-reservoir coupling strength can enhance the magnitude of heat transfer, and the impact of asymmetric and symmetric coupling strength on the performance of the heat diode is complementary. It may provide an efficient way to modulate and control heat transport's magnitude and flow preference. This work may give insight into designing and tuning quantum heat machines.

The thermodynamic uncertainty relation (TUR) is an inequality showing the tradeoff relationship between the relative fluctuation of current observables and thermodynamic costs. It is one of the most important results of stochastic thermodynamics. There are various applications for TUR, one of which is the recent finding of thermodynamic constraints on the time window in which anomalous diffusion of Brownian particles can occur, including subdiffusion and superdiffusion, which are slower and faster than normal diffusion, respectively. These constraints are quite nontrivial because they are not generally derived from the asymptotic normal-diffusive behavior of the anomalous diffusion itself. In this study, we applied multidimensional TUR to the subdiffusion of Brownian particles obeying multivariate Langevin dynamics with a translationally invariant Hamiltonian in equilibrium. Multidimensional TUR is an improved TUR that includes information on another observable in addition to the one currently being considered. The use of an additional observable yields tighter bounds on the current fluctuation than those obtained using TUR. As an example, we demonstrated our theory using the one-dimensional Rouse model, which is known as a simple and analytically tractable model of polymer chains. We demonstrated that we improved the bounds for the persistence time of subdiffusion of the Rouse model, which became tighter as a more correlated observable with the current was used.

The present work consists of a numerical study of the dynamics of irrational polygonal billiards. Our contribution reinforces the hypothesis that these systems can be strongly mixing, although never demonstrably chaotic, and discusses the role of rotational symmetries on the billiards boundaries. We introduce a biparametric polygonal billiard family with only $C_n$ rotational symmetries. Initially, we calculate through the relative measure $r(\ell ,\theta ;t)$ the phase space filling. This is done for some integer values of $n$ and for a plane of parameters $\ell \times \theta$. From the resulting phase diagram, we can identify the fully ergodic systems. The numerical evidence that symmetrical polygonal billiards can be strongly mixing is obtained by evaluating the position autocorrelation function ${\mathrm{Cor}}_x\left(t\right)$, which follows a power-law-type decay $t^{-\sigma }$. The strongly mixing property is indicated by $\sigma =1$. For odd, small values of $n$, the exponent $\sigma \simeq 1$ is found. On the other hand, $\sigma <1$ (weakly mixing cases) for small, even values of $n$. Intermediate $n$ values present $\sigma \simeq 1$ independently of parity. For larger values of symmetry parameter $n$, the biparametric family tends to be a circular billiard (integrable case). For such values of $n$, we identified even less ergodic behavior at the pace at which $n$ increases and $\sigma$ decreases.

Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak-coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning.

The mechanisms by which isolated condensed matter systems thermalize is a topic of growing interest. Thermalization is known to be linked to the emergence of chaos in the dynamics of a system. We show that a solid state scattering system, containing superconducting elements, can thermalize scattered states without affecting the degree of entanglement of the scattered states. We consider a composite $NSNSNSNSN$ nanowire composed of ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+x}$ superconducting segments ($S$) and normal conducting segments ($N$). We consider parameter regimes where all current flow is due to tunneling currents that are facilitated by quasibound state resonances inside the SNSNSNS structure. At certain energies, scattered pure states approach ergodicity, even though they remain pure.

Utilizing a paradigmatic model for the motion of interacting self-propelled particles, we demonstrate that local accelerations at the level of individual particles can drive transitions between different collective dynamics, leading to a control process. We find that the ability to trigger such transitions is hierarchically distributed among the particles and can form distinctive spatial patterns within the collective. Chaotic dynamics occur during the transitions, which can be attributed to fractal basin boundaries mediating the control process. The particle hierarchies described in this paper offer decentralized capabilities for controlling artificial swarms.

The dynamics of quasi-two-dimensional coalescence of isotropic droplets in nematic liquid crystal environment was studied. Investigations were made in confined geometry of a Hele-Shaw optical cell with different transverse droplet sizes. The existence of three distinct dynamic regimes was found for coalescence, namely, short-, middle-, and long-time regimes. The fast dynamics of bridge transformation was visualized. At short time the dynamics of droplet transformation is similar to the transformation of free (three-dimensional) droplets. At later stages, two regimes of the coalescence at different timescales are determined by Poiseuille flow. Experimental data are discussed on the basis of existing theories.