We consider a system of hardcore particles advected by a fluctuating potential energy landscape, whose dynamics is in turn affected by the particles. Earlier studies have shown that as a result of two-way coupling between the landscape and the particles, the system shows an interesting phase diagram as the coupling parameters are varied. The phase diagram consists of various different kinds of ordered phases and a disordered phase. We introduce a relative timescale $\omega$ between the particle and landscape dynamics, and study its effect on the steady state properties. We find there exists a critical value $\omega ={\omega }_c$ when all configurations of the system are equally likely in the steady state. We prove this result exactly in a discrete lattice system and obtain an exact expression for ${\omega }_c$ in terms of the coupling parameters of the system. We show that ${\omega }_c$ is finite in the disordered phase, diverges at the boundary between the ordered and disordered phase, and is undefined in the ordered phase. We also derive ${\omega }_c$ from a coarse-grained level description of the system using linear hydrodynamics. We start with the assumption that there is a specific value ${\omega }^{*}$ of the relative timescale when correlations in the system vanish, and mean-field theory gives exact expressions for the current Jacobian matrix $A$ and compressibility matrix $K$. Our exact calculations show that Onsager-type current symmetry relation $AK=K{A}^T$ can be satisfied if and only if ${\omega }^{*}={\omega }_c$. Our coarse-grained model calculations can be easily generalized to other coupled systems.

In this paper we analyze the adiabatic crossing of a resonance for Hamiltonian systems when a double-resonance condition is satisfied by the linear frequency at an elliptic fixed point. We discuss in detail the phase-space structure on a class of Hamiltonians and area-preserving maps with an elliptic fixed point in the presence of a time-dependent exciter. Various regimes have been identified and carefully studied. This study extends results obtained recently for the trapping and transport phenomena for periodically perturbed Hamiltonian systems, and it could have relevant applications in the adiabatic beam splitting in accelerator physics.

The random language model [Phys. Rev. Lett. 122, 128301 (2019)] is an ensemble of stochastic context-free grammars, quantifying the syntax of human and computer languages. The model suggests a simple picture of first-language learning as a type of annealing in the vast space of potential languages. In its simplest formulation, it implies a single continuous transition to grammatical syntax, at which the symmetry among potential words and categories is spontaneously broken. Here this picture is scrutinized by considering its robustness against extensions of the original model, and trajectories through parameter space different from those originally considered. It is shown here that (i) the scenario is robust to explicit symmetry breaking, an inevitable component of learning in the real world, and (ii) the transition to grammatical syntax can be encountered by fixing the deep (hidden) structure while varying the surface (observable) properties. It is also argued that the transition becomes a sharp thermodynamic transition in an idealized limit. Moreover, comparison with human data on the clustering coefficient of syntax networks suggests that the observed transition is equivalent to that normally experienced by children at age 24 months. The results are discussed in light of the theory of first-language acquisition in linguistics, and recent successes in machine learning.

We show that the forces generated by active enzyme molecules are strong enough to influence the dynamics of their surroundings under artificial crowded environments. We measured the behavior of polymer microparticles in a quasi-two-dimensional system under aqueous environment, at various area fraction values of particles. In the presence of enzymatic activity, not only was the diffusion of the suspended particles enhanced at shorter time-scales, but the system also showed a transition from subdiffusive to diffusive dynamics at longer time-scale limits. Similar observations were also recorded with enzyme-functionalized microparticles. Brownian dynamics simulations have been performed to support the experimental observations.

When an external field is applied across a liquid-crystal cell, the twist and tilt distributions cannot be calculated analytically and must be extracted numerically. In the standard approach, the Euler-Lagrange equations are derived from the minimization of the free energy of the system and then solved via finite-difference methods, often implemented in commercial software. These tools iterate from initial solutions that are compatible with the boundary conditions, providing limited to no flexibility for customization. Here we present a genetic algorithm that outputs fast and accurate solutions to the integral form of the equations. In our approach, the evolutionary routine is sequentially applied at each position within the bulk of the cell, thus overcoming the necessity of assuming trial solutions. The full range of twist angles from $-{90}^{\circ }$ to ${90}^{\circ }$ is considered. In this way, the predictions of our routine strongly support the experimentally observed polarization transformations of light incident on different spatially varying twisted nematic liquid-crystal cells, patterned with different topologies on the two alignment layers.

The mean-field theory (MFT) of simple structural glasses, which is exact in the limit of infinite spatial dimensions, $d\to \infty$, offers theoretical insight as well as quantitative predictions about certain features of $d=3$ systems. In order to more systematically relate the behavior of physical systems to MFT, however, various finite-$d$ effects need to be accounted for. Although some efforts along this direction have already been undertaken, theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally structured models whose behavior smoothly converges to that described by the MFT as $d$ increases, so as to permit a controlled dimensional extrapolation. Using this approach, we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable, the non-Gaussian parameter ${\alpha }_2$. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.

The evolution of a shock-induced fluid layer is numerically investigated in order to reveal the underlying mechanism of the Richtmyer-Meshkov instability under the effect of a reshock wave. Six different types of fluid layer are initially set up to study the effect of amplitude perturbation, fluid-layer thickness, and phase position on the reshocked fluid-layer evolution. Interface morphology results show that the interface-coupling effect gets strengthened when the fluid-layer thickness is small, which means the development of spikes and bubbles is inhibited to some extent compared to the case with large initial fluid-layer thickness. Two jets emerge on interface ${\mathrm{II}}_1$ under out-of-phase conditions, while bubbles are generated on interface ${\mathrm{II}}_1$ when the initial phase position is in-phase. The mixing width of the fluid layer experiences an early linear growth stage and a late nonlinear stage, between which the growth of the mixing width is considerably inhibited by the passage of the first and the second reshock and mildly weakened during phase reversion. The amplitude growth of interfaces agrees well with the theoretical model prediction, including both the linear and nonlinear stages. In the very late stage, the amplitude perturbation growth tends to differ from the theoretical prediction due to the squeezing effect and stretching effect.

We present a study of the intermittent properties of a shell model of turbulence with statistics of $\sim {10}^7$ eddy turn over time, achieved thanks to an implementation on a large-scale parallel GPU factory. This allows us to quantify the inertial range anomalous scaling properties of the velocity fluctuations up to the 24th-order moment. Through a careful assessment of the statistical and systematic uncertainties, we show that none of the phenomenological and theoretical models previously proposed in the literature to predict the anomalous power-law exponents in the inertial range are in agreement with our high-precision numerical measurements. We find that at asymptotically high-order moments, the anomalous exponents tend toward a linear scaling, suggesting that extreme turbulent events are dominated by one leading singularity. We found that systematic corrections to scaling induced by the infrared and ultraviolet (viscous) cutoffs are the main limitations to precision for low-order moments, while high orders are mainly affected by the finite statistical samples.. The high-fidelity numerical results reported in this work offer an ideal benchmark for the development of future theoretical models of intermittency in dynamical systems for either extreme events (high-order moments) or typical fluctuations (low-order moments). For the latter, we show that we achieve a precision in the determination of the inertial range scaling exponents of the order of one part over ten thousand (fifth significant digit), which may be considered a record for out-of-equilibrium fluid-mechanics systems and models.

The Brain Connectome Project has made significant strides in uncovering the structural connections within the brain on various levels. This has led to the question of how brain structure and function are related. Our research explores this relationship in an adaptive neural network in which synaptic conductance between neurons follows spike-time synaptic plasticity rules. By adjusting the plasticity boundary, the network exhibits diverse collective behaviors, including phase synchronization, phase locking, hierarchical synchronization (phase clusters), and coexisting states. Using graph theory, we found that hierarchical synchronization is related to the community structure, while coexisting states are related to the hierarchical self-organizing and core-periphery structure. The network evolves into several tightly connected modules, with sparsely intermodule connections resulting in the formation of phase clusters. In addition, the hierarchical self-organizing structure facilitates the emergence of coexisting states. The coexistence state promotes the evolution of the core-periphery structure. Our results point towards the equivalence between function and structure, with function emerging from structure, and structure being influenced by function in a complex dynamic process.

In this work, we used a dynamical system derived from an avian vocal production model to generate synthetic songs that mimic the Zonotrichia capensis songs. We confirmed that these synthetic renditions elicited behavioral responses similar to those evoked by real songs in wild songbirds of the same species. Specifically, we observed an increase in the singing rate of individual birds when a playback device was introduced into their territories. The success of our approach instills confidence in the hypotheses underpinning the model and provides a valuable tool for investigating a wide range of biological questions.

We examine the ordering, pinning, and dynamics of two-dimensional pattern-forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range attraction form anisotropic crystal, stripe, and bubble states. When the system is tuned across the stripe transition in the presence of a substrate, we find that there is a peak effect in the critical depinning force when the stripes align and become commensurate with the substrate. Under an applied drive, the anisotropic crystal and stripe states can exhibit soliton depinning and plastic flow. When the stripes depin plastically, they dynamically reorder into a moving stripe state that is perpendicular to the substrate trough direction. We also find that when the substrate spacing is smaller than the widths of the bubbles or stripes, the system forms pinned stripe states that are perpendicular to the substrate trough direction. The system exhibits multiple reentrant pinning effects as a function of increasing attraction, with the anisotropic crystal and large bubble states experiencing weak pinning but the stripe and smaller bubble states showing stronger pinning. We map out the different dynamic phases as a function of filling, the strength of the attractive interaction term, the substrate strength, and the drive, and demonstrate that the different phases produce identifiable features in the transport curves and particle orderings.

We analyze the fine structure of nonlinear modal interactions in inviscid and viscous Burgers flows in 1D, which serve as toy models for the Euler and Navier-Stokes dynamics. This analysis is focused on preferential alignments characterizing the phases of Fourier modes participating in triadic interactions, which are key to determining the nature of energy fluxes between different scales. We develop diagnostic tools designed to probe the level of coherence among triadic interactions and apply them to Burgers flows corresponding to different initial conditions, including unimodal, extreme (in the sense of maximizing the growth of enstrophy in finite time), and generic. We find that in all cases triads involving energy-containing Fourier modes align their phases so as to maximize the energy flux toward small scales, and most of this flux is realized by only a handful of triads revealing a universal statistical distribution. We then identify individual triads making the largest contributions to the flux at different wave numbers and show that they represent a mixture of local and nonlocal interactions, with the latter becoming dominant at later times. These results point to the possibility of constructing a strongly reduced modal representation of Burgers flows that would require a much smaller number of degrees of freedom. Another interesting observation is that removing the spatial coherence from the extreme initial data (by randomizing the phases while retaining the magnitudes of the Fourier coefficients) does not profoundly change the nature of triadic interactions and synchronization as well as the resulting fluxes in these flows.

This work describes a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.

The eigenstate thermalization hypothesis for translation invariant quantum spin systems has been proved recently by using random matrices. In this paper, we study the subsystem version of the eigenstate thermalization hypothesis for translation invariant quantum systems without referring to random matrices. We first find a relation between the quantum variance and the Belavkin-Staszewski relative entropy. Then, by showing the small upper bounds on the quantum variance and the Belavkin-Staszewski relative entropy, we prove the subsystem eigenstate thermalization hypothesis for translation invariant quantum systems with an algebraic speed of convergence in an elementary way. The proof holds for most of the translation invariant quantum lattice models with exponential or algebraic decays of correlations.

Critical wetting is of crucial importance for the phase behavior of a simple fluid or Ising magnet confined between walls that exert opposing surface fields so that one wall favors liquid (spin up), while the other favors gas (spin down). We show that arrays of boxes filled with fluid and linked by channels with appropriately chosen opposing walls can exhibit long-range cooperative effects on a length scale far exceeding the bulk correlation length. We give the theoretical foundations of these long-range couplings by using a lattice gas (Ising model) description of a system.

In a bare bosonic site coupled to two reservoirs, we explore the statistics of boson exchange in the presence of two simultaneous processes: squeezing the two reservoirs and driving the two reservoirs. The squeezing parameters compete with the geometric phaselike effect or geometricity to alter the nature of the steady-state flux and noise. The even (odd) geometric cumulants and the total minimum entropy are found to be symmetric (antisymmetric) with respect to exchanging the left and right squeezing parameters. Upon increasing the strength of the squeezing parameters, loss of geometricity is observed. Under maximum squeezing, one can recover a standard steady-state fluctuation theorem even in the presence of phase-different driving protocol. A recently proposed modified geometric thermodynamic uncertainty principle is found to be robust.

In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.

We study the mixed-type classical dynamics of the three-particle Fermi-Pasta-Ulam-Tsingou (FPUT) model in relationship with its quantum counterpart and present new results on aspects of quantum chaos in this system. First we derive for the general $N$-particle FPUT system the transformation to the normal mode representation. Then we specialize to the three-particle FPUT case and derive analytically the semiclassical energy density of states, and its derivatives in which different singularies are determined, using the Thomas-Fermi rule. The result agrees with the numerical energy density from the Krylov subspace method, as well as with the energy density obtained by the method of quantum typicality. Here, in paper I, we concentrate on the energy level statistics (level spacing and spacing ratios), in all classical dynamical regimes of interest: the almost entirely regular, the entirely chaotic, and the mixed-type regimes. We clearly confirm, correspondingly, the Poissonian statistics, the Gaussian orthogonal ensemble statistics, and the Berry-Robnik-Brody (BRB) statistics in the mixed-type regime. It is found that the BRB level spacing distribution perfectly fits the numerical data. The extracted quantum Berry-Robnik parameter is found to agree with the classical value within better than one percent. We discuss the role of localization of chaotic eigenstates, and its appearances, in relation to the classical phase space structure (Poincaré and smaller alignment index plots), whose details will be presented in paper II, where the structure and the statistical properties of the Husimi functions in the quantum phase space will be studied.

We undertake a thorough investigation into the phenomenology of quantum eigenstates, in the three-particle Fermi-Pasta-Ulam-Tsingou model. Employing different Husimi functions, our study focuses on both the $\alpha$-type, which is canonically equivalent to the celebrated Hénon-Heiles Hamiltonian, a nonintegrable and mixed-type system, and the general case at the saddle energy where the system is fully chaotic. Based on Husimi quantum surface of sections, we find that in the mixed-type system, the fraction of mixed eigenstates in an energy shell $[E-\delta E/2,E+\delta E/2]$ with $\delta E\ll E$ shows a power-law decay with respect to the decreasing Planck constant $\hslash$. Defining the localization measures in terms of the Rényi-Wehrl entropy, in both the mixed-type and fully chaotic systems, we find a better fit with the $\beta$ distribution and a lesser degree of localization, in the distribution of localization measures of chaotic eigenstates, as the controlling ratio ${\alpha }_{\mathcal{L}}=t_H/t_T$ between the Heisenberg time $t_H$ and the classical transport time $t_T$ increases. This transition with respect to ${\alpha }_{\mathcal{L}}$ and the power-law decay of the mixed states, together provide supporting evidence for the principle of uniform semiclassical condensation in the semiclassical limit. Moreover, we find that in the general case which is fully chaotic, the maximally localized state, is influenced by the stable and unstable manifold of the saddles (hyperbolic fixed points), while the maximally extended state notably avoids these points, extending across the remaining space, complementing each other.