A particle jumps between the nodes of a graph interacting with local spins. We show that the entanglement entropy of the particle with the spin network is related to the length of the minimum cycle basis. The structure of the thermal state is reminiscent of the string net of spin liquids.

The Floquet-Magnus expansion is a useful tool to calculate an effective Hamiltonian for periodically driven systems. In this study, we investigate the convergence of the expansion for a one-body nonlinear system in a continuous space, a driven anharmonic oscillator. In this model, all eigenstates of the time-evolution operator are found to be localized in energy space, and the expectation value of the energy is bounded from above. We first propose a general procedure to estimate the radius of convergence of the Floquet-Magnus expansion for periodically driven systems with an unbounded energy spectrum. By applying it to the driven anharmonic oscillator, we numerically show that the expansion diverges for all driving frequencies even if the anharmonicity is arbitrarily small. This conclusion contradicts the widely accepted belief that the divergence of the Floquet-Magnus expansion is a direct consequence of quantum ergodicity, which implies that each eigenstate of the time-evolution operator is a linear combination of all available eigenstates of the unperturbed Hamiltonian and the system heats up to infinite temperature after long intervals.

Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the necessary and sufficient conditions of quantum compatibility for a given collection of $n$ measurements in $d$-dimensional space. From the compatibility criterion for two-qubit measurements, we compute the incompatibility probability of a pair of independent random measurements. For a pair of unbiased random qubit measurements, we derive that the incompatibility probability is exactly $\frac{3}{5}$. Detailed results are also presented in figures for pairs of general qubit measurements.

The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a low-dimensional theory in the thermodynamic limit. In this paper, we extend the formulation used by Watanabe and Strogatz to obtain a low-dimensional description of a system of arbitrary size of identical oscillators coupled all-to-all via their higher-order modes. To demonstrate an application of the formulation, we use a second harmonic globally coupled model, with a mean-field equal to the square of the Kuramoto mean-field. This model is known to exhibit asymmetrical clustering in previous numerical studies. We try to explain the phenomenon of asymmetrical clustering using the analytical theory developed here, as well as discuss certain phenomena not observed at the level of first-order harmonic coupling.

The properties of cardiac muscle are anisotropic, and the degree of anisotropy may be different in the intracellular and extracellular spaces. In the electrical bidomain model, such “unequal anisotropy ratios” of the conductivity lead to unanticipated behavior. In the mechanical bidomain model, unequal anisotropy ratios of the mechanical moduli might also result in unanticipated behavior. In this study, mathematical modeling based on the mechanical bidomain model is used to calculate the distribution of mechanotransduction in cardiac tissue when it is stretched. This analysis demonstrates that unexpected phenomena arise when the mechanical anisotropy ratios are unequal.

Liquid crystalline ordering of anisotropic particles in two dimensions is important in many physical and biological systems and their phase behavior is still a topic of interest. A generalized van der Waals theory is formulated, accounting for repulsive excluded volume and attractive van der Waals and Maier-Saupe interactions, for rectangles confined to two dimensions. The phase ordering transitions and equation of state are analyzed as a function of the model parameters (aspect $\mathrm{ratio}L/B$ and isotropic and anisotropic interaction parameters $\chi$ and $\nu$). Different phase transitions are observed: continuous isotropic-nematic (high $L/B$ and $\nu$), first-order isotropic-nematic (intermediate $L/B$ and small $\nu$), and continuous isotropic-tetratic (small $L/B$ and $\nu$) followed by a continuous tetratic-nematic transition at higher densities. Increasing $L/B$ decreases the pressure, and this effect is more pronounced in the nematic than in the isotropic phase. Increasing both interaction parameters decreases pressure and can lead to phase separation.

With the aid of nondestructive microfocus x-ray computed tomography (CT), we performed three-dimensional (3D) tracer dispersion experiments on randomly unconsolidated packed beds. Plumes of nonreactive sodium iodide solution were point injected into a sodium chloride solvent as a tracer for the evaluation of the dispersion process. The asymptotic dispersion coefficient was obtainable within the experimental scale and was summarized over Péclet numbers from 11.7 to ∼860. Then, the lattice Boltzmann method and moment propagation method were used to elucidate the mechanisms embedded in the dispersion phenomenon. The methods were rigorously verified against the classical Taylor dispersion problem and extended to simulate fluid flow and tracer dispersion in high-resolution 3D digital porous structures from CT. The method of moments, Lagrangian velocity correction function, and dilution index were thoroughly analyzed to evaluate the dispersion behaviors. Numerical simulations revealed ballistic and superdiffusive regimes at the transient times, whereas asymptotic dispersion behaviors appear at longer characteristic times. Besides, the observed transient times unanimously persist over convective length scales of around 12 particles transversely and 16 particles longitudinally. The estimated dispersion coefficients from simulation are in consistence with the experimental result. Furthermore, the simulation also enabled the identification of regimes, including diffusive, power law, and mechanical dispersion. Thus, the proposed experimental and computational schemes are of practical means to study dispersion behaviors by direct pore scale imaging and modeling.

Parabolic equation (PE) methods have long been used to efficiently and accurately model wave phenomena described by hyperbolic partial differential equations. A lesser-known but powerful application of parabolic equation methods is to the target scattering problem. In this paper, we use noncanonically shaped objects to establish the limits of applicability of the traditional approach and introduce wide-angle and multiple-scattering approaches to allow accurate treatment of concave scatterers. The PE calculations are benchmarked against finite-element results, with good agreement obtained for convex scatterers in the traditional approach, and for concave scatterers with our modified approach. We demonstrate that the PE-based method is significantly more computationally efficient than the finite-element method at higher frequencies where objects are several or more wavelengths long.

We describe a general and simple paradigm for discrete time crystals (DTCs), systems with a stable subharmonic response to an external driving field, in a classical thermal setting. We consider, specifically, an Ising model in two dimensions, as a prototypical system with a phase transition into stable phases distinguished by a local order parameter, driven by thermal dynamics and periodically kicked with a noisy protocol. By means of extensive numerical simulations for large sizes—allowed by the classical nature of our model—we show that the system features a true disorder-DTC order phase transition as a function of the noise strength, with a robust DTC phase extending over a wide parameter range. We demonstrate that, when the dynamics is observed stroboscopically, the phase transition to the DTC state appears to be in the equilibrium two-dimensional Ising universality class. However, we explicitly show that the DTC is a genuine nonequilibrium state. More generally, we speculate that systems with thermal phase transitions to multiple competing phases can give rise to DTCs when appropriately driven.

Laser-generated plasma gratings are dynamic optical elements for the manipulation of coherent light at high intensities, beyond the damage threshold of solid-state-based materials. Their formation, evolution, and final collapse require a detailed understanding. In this paper, we present a model to explain the nonlinear dynamics of high-amplitude plasma gratings in the spatially periodic ponderomotive potential generated by two identical counterpropagating lasers. Both fluid and kinetic aspects of the grating dynamics are analyzed. It is shown that the adiabatic electron compression plays a crucial role as the electron pressure may reflect the ions from the grating and induce the grating to break in an X-type manner. A single parameter is found to determine the behavior of the grating and distinguish three fundamentally different regimes for the ion dynamics: completely reflecting, partially reflecting or passing, and crossing. Criteria for saturation and lifetime of the grating as well as the effect of finite ion temperature are presented.

A simple Markovian theory for the prediction of averages and correlations of discrete hydrodynamics near parallel solid walls is presented. The discrete momentum of bins is defined through a finite element basis function. The effect of the walls on the fluid is through irreversible extended friction forces appearing in the very equations of hydrodynamics. The Markovian assumption is critically assessed from the exponential decay of the eigenvalues of the correlation matrix of the discrete transverse momentum. We observe that for bins smaller than molecular dimensions, allowing one to resolve the density layering near the wall, the dynamics near the wall is non-Markovian. Bins larger than the molecular size do behave in a Markovian way. We measure the nonlocal viscosity and frictions kernels that appear in the discrete hydrodynamic equations, which are given in terms of Green-Kubo formulas. They suffer dramatically from the plateau problem. We use a recent procedure for reliably extracting the transport kernels out of the plateau-problematic Green-Kubo formula. With the so-measured transport kernels the nonlocal theory predicts very well the decay of the average of the transverse momentum when the initial velocity profile is a plug flow. The theory allows us to derive the slip boundary condition with microscopic expressions for the slip length and the hydrodynamic position of the wall. The slip boundary condition is not satisfied at the initial stages of the discontinous plug flow, but good agreement is obtained at later stages.

We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space [J. Phys. A: Math. Gen. 16, 3971 (1983); J. Phys. A: Math. Gen. 17, 1049 (1984)], after separating the regular and chaotic eigenstates, in the regime of slightly distorted circle billiard where the classical transport time in the momentum space is still large enough, although the diffusion is not normal. This is a continuation of our recent papers [Phys. Rev. E 88, 052913 (2013); Phys. Rev. E 98, 022220 (2018)]. In quantum systems with discrete energy spectrum the Heisenberg time $t_H=2\pi \hslash /\mathrm{\Delta }E$, where $\mathrm{\Delta }E$ is the mean level spacing (inverse energy level density), is an important timescale. The classical transport timescale $t_T$ (transport time) in relation to the Heisenberg timescale $t_H$ (their ratio is the parameter $\alpha =t_H/t_T$) determines the degree of localization of the chaotic eigenstates, whose measure $A$ is based on the information entropy. We show that $A$ is linearly related to normalized inverse participation ratio. The localization of chaotic eigenstates is reflected also in the fractional power-law repulsion between the nearest energy levels in the sense that the probability density (level spacing distribution) to find successive levels on a distance $S$ goes like $\propto S^{\beta }$ for small $S$, where $0\le \beta \le 1$, and $\beta =1$ corresponds to completely extended states. We show that the level repulsion exponent $\beta$ is empirically a rational function of $\alpha$, and the mean $\langle A\rangle$ (averaged over more than 1000 eigenstates) as a function of $\alpha$ is also well approximated by a rational function. In both cases there is some scattering of the empirical data around the mean curve, which is due to the fact that $A$ actually has a distribution, typically with quite complex structure, but in the limit $\alpha \to \infty$ well described by the beta distribution. The scattering is significantly stronger than (but similar as) in the stadium billiard [Nonlin. Phenom. Complex Syst. (Minsk) 21, 225 (2018)] and the kicked rotator [Phys. Rev. E 91, 042904 (2015)]. Like in other systems, $\beta$ goes from 0 to 1 when $\alpha$ goes from 0 to $\infty$. $\beta$ is a function of $\langle A\rangle$, similar to the quantum kicked rotator and the stadium billiard.

We consider the problem of the propagation of modulated waves in one-dimensional discrete lattices with linear bandpass-type dispersion relation. We are interested specifically in the cases where the gap frequency $f_0$ and the cutoff frequency $f_{\text{max}}$ verify $0<f_0<f_{\text{max}}<2f_0$. Analytical investigations of such models commonly use the rotating wave approximation in which only the fundamental harmonic is taken into consideration. This approach is routinely justified by the physical argument that the zeroth and higher harmonic frequency terms cannot propagate, being out of band. Using a simple model of electrical lattice as a case study, we show analytically that accounting for the generation of those terms is indispensable for the accurate prediction of modulated solitary waves supported by the model. Moreover, a carefully designed numerical investigation of the propagation of an exact and consistent second-order approximation of such waves reveals that the second-order harmonic included is transmitted throughout the network the same as the fundamental harmonic is. Thus, we unveil the pitfall of the rotating wave approximation that is detrimental to its reliability for most of the models to which it has commonly been employed. We also suggest how to avoid this pitfall.

We study a model with excitable neurons modeled as stochastic units with three states, representing quiescence, firing, and refractoriness. The transition rates between quiescence and firing depend exponentially on the number of firing neighbors, whereas all other rates are kept constant. This model class was shown to exhibit collective oscillations (synchronization) if neurons are spiking autonomously, but not if neurons are in the excitable regime. In both cases, neurons were restricted to interact through excitatory coupling. Here we show that a plethora of collective phenomena appear if inhibitory coupling is added. Besides the usual transition between an absorbing and an active phase, the model with excitatory and inhibitory neurons can also undergo reentrant transitions to an oscillatory phase. In the mean-field description, oscillations can emerge through supercritical or subcritical Hopf bifurcations, as well as through infinite period bifurcations. The model has bistability between active and oscillating behavior, as well as collective excitability, a regime where the system can display a peak of global activity when subject to a sufficiently strong perturbation. We employ a variant of the Shinomoto-Kuramoto order parameter to characterize the phase transitions and their system-size dependence.

We investigate the upper bound on angular momentum transport in Taylor-Couette flow theoretically and numerically by a one-dimensional background field method. The flow is bounded between a rotating inner cylinder of radius $R_i$ and a fixed outer cylinder of radius $R_o$. A variational problem is formulated and solved by a pseudo-time-stepping method up to a Taylor number $\text{Ta}={10}^9$. The angular momentum transport, characterized by a Nusselt number Nu, is bounded by $\text{Nu}\le c{\text{Ta}}^{1/2}$, where the prefactor $c$ depends on the radius ratio $\eta =R_i/R_o$. Three typical radius ratios are investigatedi.e., $\eta =0.5,0.714,\text{and}0.909$, and the corresponding prefactors $c=0.0049,0.0075,\text{and}0.0086$ are found to improve (lower) the rigorous upper bounds by Doering and Constantin [C. Doering and P. Constantin, Phys. Rev. Lett. 69, 1648 (1992)] and Constantin [P. Constantin, SIAM Rev. 36, 73 (1994)] by at least one order of magnitude. Furthermore, we show, via an inductive bifurcation analysis, that considering a three-dimensional background velocity field is unable to lower the bound.

Vortex-loop renormalization is used to compute the specific heat of superfluid ${}^4\mathrm{He}$ near the lambda point at various pressures up to 26 bars. The input parameters are the pressure dependence of $T_{\lambda }$ and the superfluid density, which determine the nonuniversal parameters of the vortex core energy and core size. The results for the specific heat are found to be in good agreement with experimental data, matching the expected universal pressure dependence to within about $5\%$. The nonuniversal critical amplitude of the specific heat is found to be in reasonable agreement, a factor of four larger than the experiments. We point out problems with recent Gross-Pitaevskii simulations that claimed the vortex-loop percolation temperature did not match the critical temperature of the superfluid phase transition.

Plastic instabilities in amorphous materials are often studied using idealized models of binary mixtures that do not capture accurately molecular interactions and bonding present in real glasses. Here we study atomic-scale plastic instabilities in a three-dimensional molecular dynamics model of silica glass under quasistatic shear. We identify two distinct types of elementary plastic events, one is a standard quasilocalized atomic rearrangement while the second is a bond-breaking event that is absent in simplified models of fragile glass formers. Our results show that both plastic events can be predicted by a drop of the lowest nonzero eigenvalue of the Hessian matrix that vanishes at a critical strain. Remarkably, we find very high correlation between the associated eigenvectors and the nonaffine displacement fields accompanying the bond-breaking event, predicting the locus of structural failure. Both eigenvectors and nonaffine displacement fields display an Eshelby-like quadrupolar structure for both failure modes, rearrangement, and bond breaking. Our results thus clarify the nature of atomic-scale plastic instabilities in silica glasses, providing useful information for the development of mesoscale models of amorphous plasticity.

We numerically investigate the contribution of the microstreaming to the acoustic radiation force acting on a small elastic spherical particle placed into an ultrasonic standing wave. When an acoustic wave scatters on a particle the acoustic radiation force and the microstreaming appear as nonlinear time-averaged effects. The compressible Navier–Stokes equations are solved up to second order in terms of the small Mach number using a finite element method. We show that when the viscous boundary layer thickness to particle radius ratio is sufficiently large and the particle is sufficiently dense, the acoustic microstreaming dominates the acoustic radiation force. In this case, our theory predicts migration of the particle to the velocity node (pressure antinode).

A relationship between stability and self-optimization is found for weakly dissipative heat devices. The effect of limited control on operation variables around an steady state is such that, after instabilities, the paths toward relaxation are given by trajectories stemming from restitution forces which improve the system thermodynamic performance (power output, efficiency, and entropy generation). Statistics over random trajectories for many cycles shows this behavior as well. Two types of dynamics are analyzed, one where an stability basin appears and another one where the system is globally stable. Under both dynamics there is an induced trend in the control variables space due to stability. In the energetic space this behavior translates into a preference for better thermodynamic states, and thus stability could favor self-optimization under limited control. This is analyzed from the multiobjective optimization perspective. As a result, the statistical behavior of the system is strongly influenced by the Pareto front (the set of points with the best compromise between several objective functions) and the stability basin. Additionally, endoreversible and irreversible behaviors appear as very relevant limits: The first one is an upper bound in energetic performance, connected with the Pareto front, and the second one represents an attractor for the stochastic trajectories.