A nominally two-dimensional spin model wrapped onto a cylinder can profitably be viewed, especially for long cylinders, as a one-dimensional chain. Each site of such a chain is a ring of spins with a complex state space. Traditional correlation functions are inadequate for the study of correlations in such a system and need to be replaced with something like mutual information. Being induced purely by frustration, the disorder of a cylindrical zero-temperature triangular Ising antiferromagnet (TIAFM) and attendant correlations have a chance of evading the consequences of the Perron-Frobenius theorem which describes and constrains correlations in thermally disordered one-dimensional systems. Correlations in such TIAFM systems and the aforementioned evasion are studied here through a fermionic representation. For cylindrical TIAFM models with open boundary conditions, we explain and derive the following characteristics of end-to-end mutual information: period-three oscillation of the decay length, halving of the decay length compared to what Perron-Frobenius predicts on the basis of transfer matrix eigenvalues, and subexponential decay—inverse square in the length—for certain systems.

The canonical ensemble plays a crucial role in statistical mechanics in and out of equilibrium. For example, the standard derivation of the fluctuation theorem relies on the assumption that the initial state of the heat bath is the canonical ensemble. On the other hand, the recent progress in the foundation of statistical mechanics has revealed that a thermal equilibrium state is not necessarily described by the canonical ensemble but can be a quantum pure state or even a single energy eigenstate, as formulated by the eigenstate thermalization hypothesis (ETH). Then a question raised is how these two pictures, the canonical ensemble and a single energy eigenstate as a thermal equilibrium state, are compatible in the fluctuation theorem. In this paper, we theoretically and numerically show that the fluctuation theorem holds in both of the long- and short-time regimes, even when the initial state of the bath is a single energy eigenstate of a many-body system. Our proof of the fluctuation theorem in the long-time regime is based on the ETH, while it was previously shown in the short-time regime on the basis of the Lieb-Robinson bound and the ETH [Phys. Rev. Lett. 119, 100601 (2017)]. The proofs for these time regimes are theoretically independent and complementary, implying the fluctuation theorem in the entire time domain. We also perform a systematic numerical simulation of hard-core bosons by exact diagonalization and verify the fluctuation theorem in both of the time regimes by focusing on the finite-size scaling. Our results contribute to the understanding of the mechanism that the fluctuation theorem emerges from unitary dynamics of quantum many-body systems and can be tested by experiments with, e.g., ultracold atoms.

The appealing theoretical measure of irreversibility in a stochastic process, as the ratio of the probabilities of a trajectory and its time reversal, cannot be accessed directly in experiments since the probability of a single trajectory is zero. We regularize this definition by considering, instead, the limiting ratio of probabilities for trajectories to remain in the tubular neighborhood of a smooth path and its time reversal. The resulting pathwise medium entropy production agrees with the formal expression from stochastic thermodynamics and can be obtained from measurable tube probabilities. Estimating the latter from numerically sampled trajectories for Langevin dynamics yields excellent agreement with theory. By combining our measurement of pathwise entropy production with a Markov chain Monte Carlo algorithm, we infer the entropy-production distribution for a transition path ensemble directly from short recorded trajectories. Our work enables the measurement of irreversibility along individual paths and path ensembles in a model-free manner.

Monte Carlo simulations on the structural change of hard sphere-platelet mixtures were performed to investigate the effect of particle size. We quantitatively analyzed local equilibrium structures of sphere-platelet mixtures with varying size ratios under various sphere and platelet density conditions. Based on the simulation results, we investigated the structural transitions such as isotropic to anisotropic, clustering, and so on. When a small amount of small-sized sphere is added to a large-sized platelet system, the mixture structure transitions from isotropic to nematic ones as the platelet number density increases. On the other hand, the platelet forms clusters with the addition of a large number of spheres. In a small platelet–large sphere system, the spheres form aggregates by increasing platelet density instead. The platelet and spherical particles exhibit different structural transitions depending on the size and density. In the limit of small and large size ratios, the structures of the platelet-sphere mixture obtained from the Monte Carlo simulation are close to those shown by previous theoretical and experimental studies, respectively. Because the primary actor shifts from sphere to platelet as the size ratio changes, the transition boundary shifts continuously. When the size ratio is close to unity, the most complicated behavior is observed, with both the platelet and sphere simultaneously acting the leading part.

An analysis of the IR absorbance for the segmented functional groups of liquid crystal dimers mesogen and linker enabled the orientation order to be determined and information about the dipole interactions in the nematic and twist-bend nematic phases to be obtained. The long axis orientational order increases as the temperature decreases in the nematic phase, although much more slowly than for the classical nematics, and then reverses this trend in the twist-bend nematic phase due to the tilt of the molecules. In the nematic phase, the short axis of the molecule performs an isotropic uniform rotation and has a uniaxial alignment. In the twist-bend nematic phase, however, biaxial ordering occurs and grows significantly in accordance with the helical deformation of the director. Changes in the mean absorbance in the twist-bend nematic phase were observed: a decrease for the longitudinal dipole at the nematic-twist-bend nematic phase transition, thus emphasizing the antiparallel axial interaction of the dipoles, while the absorbance of the transverse dipoles remains unchanged up to 340 K, and then the latter become parallelly correlated.

We report the discovery and elucidation of giant spatiotemporal orientational fluctuations in nematic liquid crystal drops with radial orientation of the nematic anisotropy axis producing a central “hedgehog” defect. We study the spatial and temporal properties of the fluctuations experimentally using polarized optical microscopy, and theoretically, by calculating the eigenspectrum of the Frank elastic free energy of a nematic drop of radius $R_2$, containing a spherical central core of radius $R_1$ and constrained by perpendicular boundary conditions on all surfaces. We find that the hedgehog defect with radial orientation has a complex excitation spectrum with a single critical mode whose energy vanishes at a critical value ${\mu }_c$ of the ratio $\mu =R_2/R_1$. When $\mu <{\mu }_c$, the mode has positive energy, indicating that the radial hedgehog state is stable; when $\mu >{\mu }_c$, it has negative energy indicating that the radial state is unstable to the formation of a lower-energy state. This mode gives rise to the large-amplitude director fluctuations we observe near the core, for $\mu$ near ${\mu }_c$. A collapse of the experimental data corroborates model predictions for $\mu <{\mu }_c$ and provides an estimate of the defect core size.

We present calculations of eigenmode energies and wave functions of both azimuthal and polar distortions of the nematic director relative to a radial hedgehog trapped in a spherical drop with a smaller concentric spherical droplet at its core. All surfaces interior to the drop have perpendicular (homeotropic) boundary conditions. We also calculate director correlation functions and their relaxation times. Of particular interest is a critical mode whose energy, with fixed Frank constants, vanishes as the ratio $\mu =R_2/R_1$ increases toward a critical value ${\mu }_c$, where $R_2$ is the radius of the drop and $R_1$ that of the inner droplet, and then becomes negative for $\mu >{\mu }_c$. Our calculations form a basis for interpreting experimental measurements of director fluctuations relative to a radial hedgehog state in a spherical drop. We compare results with those obtained by previous investigations, which use a calculational approach different from ours, and with our experimental observations.

We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden quasiconservation laws, in which certain higher multipole moments can only decay due to dangerously irrelevant corrections to hydrodynamics. We present two simple examples of this phenomenon. First, an isotropic dipole-conserving fluid in the infinite plane conserves an infinite number of harmonic multipole charges within linear response; we calculate the decay or growth of these charges due to dangerously irrelevant nonlinearities. Second, we consider a model with $xy$ and $x^2-y^2$ quadrupole conservation, in addition to dipole conservation, which is described by isotropic fourth-order subdiffusion, yet has dangerously irrelevant sixth-order corrections necessary to relax the harmonic multipole charges. We confirm our predictions for the anomalously slow decay of the harmonic conserved charges in each setting by using numerical simulations, both of the nonlinear hydrodynamic differential equations, and in quantum automaton circuits on a square lattice.

A series of models for reversible filling of a triangular lattice with equilateral triangles has been developed and investigated. There are eight distinct models that vary in the set of prohibitions. In zeroth approximation, these models allow one to estimate the influence of the particles’ shape and complementarity of their pair configurations on the self-assembly of dense monolayers formed by reversible filling. The most symmetrical models were found to be equivalent to hard-disk models on the hexagonal lattice. When any contact of hard triangles by vertices is prohibited, the dense monolayers are disordered, and their entropy tends to the constant. If only one pair configuration is prohibited, the close-packed layer appears through the continuous phase transition. In other cases, the weak first-order transition resulting in the self-assembly of close-packed layers is observed.

Fractals are ubiquitous in nature and random walks on fractals have attracted lots of scientific attention in the past several years. In this work, we consider discrete random walks on a class of fractal scale-free trees (FST), whose topologies are controlled by two integer parameters (i.e., $u\ge 2$ and $v\ge 1$) and exhibit a wide range of topological properties by suitably varying the parameters $u$ and $v$. The mean trapping time (MTT), referred to as $T_y$, which is the mean time it takes the walker to be absorbed by the trap fixed at site $y$ of the FST, is addressed analytically on the FST, and the effects of the trap location $y$ on the MTT for the FST and for the general trees are also analyzed. First, a method, which is based on the connection between the MTT and the effective resistances, to derive analytically $T_y$ for an arbitrary site $y$ of the FST is presented, and some examples are provided to show the effectiveness of the method. Then, we compare $T_y$ for all the possible site $y$ of the trees, and find the sites where $T_y$ achieves the minimum (or maximum) on the FST. Finally, we analyze the effects of trap location on the MTT in general trees and find that the average path length (APL) from an arbitrary site to the trap is the decisive factor which dominates the difference in the MTTs for different trap locations on general trees. We find, for any tree, the MTT obtains the minimum (or maximum) at sites where the APL achieves the minimum (or maximum).

The susceptible-infected (SI) model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address this problem here using a novel formulation inspired by the mathematical treatment of many-body quantum systems. This allows us to organize the time-dependent expectation values for the state of individual nodes in terms of contributions from subgraphs of the network. We compute these contributions systematically and find a set of symmetry relations among subgraphs of differing topologies. We use our novel approach to compute the spreading of information on three different sample networks. The exact solution, which matches with Monte Carlo simulations, visibly departs from the mean-field results.

In amorphous materials, groups of particles can rearrange locally into a new stable configuration. Such elementary excitations are key as they determine the response to external stresses, as well as to thermal and quantum fluctuations. Yet, understanding what controls their geometry remains a challenge. Here we build a scaling description of the geometry and energy of low-energy excitations in terms of the distance to an instability, as predicted, for instance, at the dynamical transition in mean-field approaches of supercooled liquids. We successfully test our predictions in ultrastable computer glasses, with a gapped spectrum and an ungapped (regular) spectrum. Overall, our approach explains why excitations become less extended, with a higher energy and displacement scale upon cooling.

We study the dynamical rearrangement of gravitationally unstable multilayer fluid inside the narrow vertical gap of a Hele-Shaw cell. Four layers of immiscible fluids are superposed inside the cell, which is subsequently turned over. We vary the fluid properties and the relative thicknesses of the layers. One of the layers is air, the others are immiscible liquids: olive oil, water-glycerin mixture, and perfluorohexane. The concentration of the glycerin-water mixture is used to vary its viscosity. We classify various different dynamics of stirring and breakthrough of adjacent layers. We note a prominent phenomenon, where an air finger breaks through the high-viscosity layer to erupt as a hemisphere into the lower-viscosity perfluorohexane layer above it. These eruptions have a periodic neck pinch-off accompanied with high-speed airflow which breaks up some of the low-viscosity liquid to eject a spray of fine droplets. We use high-speed video to characterize the details of the eruptions and how wetting, contact lines and three-dimensionalities play a key role. We also investigate the center-of-mass trajectories for each layer and notice counterflows, where the center of some layers can temporarily move against buoyancy. The top and bottom layers can interchange by channeling through the intermediate layers, which subsequently overturn on longer timescales. We also point out some unexpected dynamics occurring in the triple- and four-phase interactions. Specifically, droplet motions are as much affected by local viscosity as by the density gradients.

In this work, the explicit formulations of the Grad's distribution function for the 45 moments (G45)-based gas kinetic scheme (GKS) are presented. Similar to the G13 function-based gas kinetic scheme (G13-GKS), G45-GKS simulates flows from the continuum regime to the rarefied regime by solving the macroscopic governing equations based on the conservation laws, which are widely used in conventional Navier-Stokes solver. These macroscopic governing equations are discretized by the finite volume method, where the numerical fluxes are evaluated by the local solution to the Boltzmann equation. The initial distribution function is reconstructed by the G45 distribution function, which is a higher order truncation of the Hermite expansion of distribution function compared with the G13 distribution function. Such high order truncation of Hermite expansion helps the present solver to achieve a better accuracy than G13-GKS. Moreover, the reconstruction of distribution function makes the development of explicit formulations of numerical fluxes feasible, and the evolution of the distribution function, which is the main reason why the discrete velocity method is expensive, is avoided. Several numerical experiments are performed to examine the accuracy of G45-GKS. Results show that the accuracy of the present solver for almost all flow problems is much better than G13-GKS. Moreover, some typical rarefied effects, such as the direction of heat flux without temperature gradients and thermal creep flow, can be well captured by the present solver.

We present a methodology to investigate phase diagrams of quantum models based on the principle of the reduced basis method (RBM). The RBM is built from a few ground-state snapshots, i.e., lowest eigenvectors of the full system Hamiltonian computed at well-chosen points in the parameter space of interest. We put forward a greedy strategy to assemble such a small-dimensional basis, i.e., to select where to spend the numerical effort needed for the snapshots. Once the RBM is assembled, physical observables required for mapping out the phase diagram (e.g., structure factors) can be computed for any parameter value with a modest computational complexity, considerably lower than the one associated to the underlying Hilbert space dimension. We benchmark the method in two test cases, a chain of excited Rydberg atoms and a geometrically frustrated antiferromagnetic two-dimensional lattice model, and illustrate the accuracy of the approach. In particular, we find that the ground-state manifold can be approximated to sufficient accuracy with a moderate number of basis functions, which increases very mildly when the number of microscopic constituents grows—in stark contrast to the exponential growth of the Hilbert space needed to describe each of the few snapshots. A combination of the presented RBM approach with other numerical techniques circumventing even the latter big cost, e.g., tensor network methods, is a tantalizing outlook of this work.

The enormous amount of currently available data demands efforts to extract meaningful information. For this purpose, different measurements are applied, including Shannon's entropy, permutation entropy, and the Lempel-Ziv complexity. These methods have been used in many applications, such as pattern recognition, series classification, and several other areas (e.g., physical, financial, and biomedical). Data in these applications are often presented in binary series with temporal correlations. Herein, we compare the measures of information entropy in binary series conveying short- and long-range temporal correlations characterized by the Hurst exponent $H$. Combining numerical and analytical approaches, we scrutinize different methods that were not efficient in detecting temporal correlations. To surpass this limitation, we propose a measure called the binary permutation index (BPI). We will demonstrate that BPI efficiently discriminates patterns embedded in the series, offering advantages over previous methods. Subsequently, we collect stock market time series and rain precipitation data as well as perform in vivo electrophysiological recordings in the hippocampus of an experimental animal model of temporal lobe epilepsy, in which the BPI application in both public open source and experimental data is demonstrated. An index is proposed to evaluate information entropy, allowing the ability to discriminate randomness and extract meaningful information in binary time series.

The spontaneous formation and subsequent growth, dissolution, merger, and competition of social groups bears similarities to physical phase transitions in metastable finite systems. We examine three different scenarios, percolation, spinodal decomposition, and nucleation, to describe the formation of social groups of varying size and density. In our agent-based model, we use a feedback between the opinions of agents and their ability to establish links. Groups can restrict further link formation, but agents can also leave if costs exceed the group benefits. We identify the critical parameters for costs and benefits and social influence to obtain either one large group or the stable coexistence of several groups with different opinions. Analytic investigations allow us to derive different critical densities that control the formation and coexistence of groups. Our approach sheds light on the early stage of network growth and the emergence of large connected components.

Finding the globally optimal network is an unsolved problem in synchrony optimization. In this paper, an efficient edge-adding optimization method based on global information is proposed. The edge-adding scheme is obtained through the eigenvector corresponding to the maximum eigenvalue of the system's Jacobian matrix. With different frequency distributions, we find that the optimized networks have similar features, concluded as three conditions: (i) The deviations of nodes' frequencies from the mean value are linear with the nodes' degrees, (ii) the oscillators form a bipartite network divided according to the frequencies of the oscillators, and (iii) oscillators are only connected to those with sufficiently large frequency differences. An optimal network can be constructed directly based on these three conditions for a given distribution of natural frequencies. We show that the critical coupling strengths of these constructed networks approach the theoretical lower bound. The constructed networks are or at least close to the globally optimal ones for synchrony.